dem generation from satellite data using rpc
TRANSCRIPT
DEM GENERATION FROM SATELLITE DATA USING RPC
A DISSERTATION
Submitted in partial fulfillment of the
requirements for the award of the degree
of
MASTER OF TECHNOLOGY in
CIVIL ENGINEERING (With Specialization in Computer Aided Design)
By
JAVED AIMED SHAFI
DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
ROORKEE-247 667 (INDIA)
JUNE, 2006
amal Jain
stant Professor
Department of Civil Engineering
Indian Institute of Technology Roorkee
CANDIDATE'S DECLARATION
I hereby declare that the work presented in the dissertation entitled "DEM
GENERATION FROM SATELLITE DATA USING RPC" in the partial fulfillment of
the requirement for the award of the degree of Master of Technology in Civil Engineering
with specialization in Computer Aided Design (CAD), submitted in the Department of
Civil Engineering, Indian Institute of Technology Roorkee, Roorke,e, is an authentic record
of my own work carried out for a period of about ten months from September. 2005 to
June 2006 under the. supervision of Dr. Kamal Jain, Assistant Professor, Department of
Civil Engineering, Indian Institute of Technology Roorkee, Roorkee.
The matter embodied in this dissertation has not been submitted by me for the award of
any other degree or diploma.
Roorkee
Date: So - 6- o 6 Javed Ahmed Shafi)
CERTIFICATE
This is to certify that the above statement made by the candidate is correct to the best of
my knowledge and belief.
Roorkee
Date: 30 - 06-0 6
ACKNOWLEDGEMENTS
All deepest thanks are due to Almighty God, the merciful, the compassionate for the
uncountable gifts given to me.
I would like to express my deepest gratitude to Dr. Kamal Jain, Assistant Professor,
Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, for
his guidance and support over this course of study, and for giving me the opportunity to
work under his guidance. He provided an exciting working environment with many
opportunities to develop new ideas and work on promising applications.
It is my pleasure to acknowledge the help given by the Research Scholar and Staff of
Geomatics Engg. Section, Indian Institute of Technology Roorkee, Roorkee.
I am also thankful to all my friends for their support and encouragement, and all those who
helped me directly or indirectly in preparing this dissertation.
My sincere heartfelt gratitude goes to my family whose prayers, support, concern and
encouragement has been a constant source of inspiration to me.
(Javed Ahmed Shafi)
ii
ABSTRACT
A Digital Elevation Model (DEM) is a regularly spaced raster grid of elevation values
representing the surface terrain. A DEM has wide application in surveying, mapping,
urban planning, and engineering. In remote sensing, DEMs are extensively used in
mapping, orthorectification, GIS, and land classification. Conventional methods of DEM
acquisition includes field surveying and digitizing contours maps.
Apart from conventional methods of DEM acquisition, producing DEM from satellite
data has been a vibrant research and development topic for the last thirty years. One way
to acquire DEM data is to generate it from stereo imagery using photogrammetry. The
fundamental task of photogrammetry is to rigorously establish the geometric relationship
between the sensor image spaces and ground object space, which can be achieved by
physical sensor model. Once this relationship is correctly recovered, one can derive
information about the object strictly from its imagery. The primary drawbacks of the
physical sensor model are that its application requires explicit understanding of each of the
physical parameters and a high level of expertise, and also the intentional concealment of
the physical sensor model by the data provider.
A generalized sensor model viz. Rational Polynomial Coefficients (RPC) Model have
recently drawn considerable interest in the remote sensing community, especially in light
of the trend that some commercial high resolution satellite imagery data are supplied with
RPC without disclosing the physical sensor model. RPCs with stereo pairs, provides full
photogrammetric processing including 3-D reconstruction, DEM generation,
orthorectification, block adjustment and feature extraction.
This thesis report presents a complete methodology for DEM generation from stereo
satellite images using Rational Polynomial Coefficients of the imaging geometry.
Different commercial software's accuracy and performance are checked for DEM
generation from stereo images using RPC approach and the results are evaluated through sample captured by IKONOS.
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CONTENTS
CANDIDATE'S DECLARATION ACKNOWLEDGEMENT ii ABSTRACT iii CONTENTS iv LIST OF FIGURES vi LIST OF TABLES viii LIST OF ACRONYMS ix 1. INTRODUCTION
1.1 General 1 1.2 Problem statement 5 1.3 Objective of Thesis 5 1.4 Organization of Dissertation 6
2. DEM AND RPC MODEL
2.1 Digital Elevation Model 7 2.2 DEM Using Photogrammetry 10 2.3 Rational Polynomial Coefficient Model 14
2.3.1 RPC Mathematical Model 16 2.3.2 RPC Estimation 18 2.3.3 RPC Refining 20
2.4 Investigation into the Accuracy of RPCs 21
2.5 RPC Characteristics Summary 26 3. MATHEMATICAL MODEL, HRS IMAGERY AND SOFTWARES
3.1 Mathematical Model for 3D Reconstruction. 27 3.1.1. 3D Reconstruction with Forward RPCs Model. 27 3.1.2. 3D Reconstruction with Inverse RPCs Model. 32 3.1.3. 3D Reconstruction by Adjusting Elevation. 35
3.2 High Resolution Satellite Imagery 36 3.2.1 IKONOS 36
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3.2.2. Orb View-3 37
3.2.3. QuickBird 38
3.2.4. CARTOSAT 39
3.2.5. SPOT-5 40
3.3. A Review of Software Packages 41 3.3.1. RSI ENVI 4.2 41 3.3.2. PCI Geomatica 9.1 42 3.3.3. ERDAS imaging 8.6 42
4. EXPERIMENTAL DATA AND METHODOLOGY 4.1 Experimental Data 44 4.2 3D Reconstruction Method 45
4.2.1 3D Reconstruction Procedure using Forward RPC Model 45
4.2.2 3D Reconstruction Procedure using Inverse RPC Model 47
4.3 Methodology of DEM Generation using ENVI 49 4.3.1 ENVI's DEM Extraction Module 52
4.4 ERDAS Imagine OrhoBase 54 4.5 PCI Geomatica OrthoEngine 56
5. RESULTS AND ANALYSIS 5.1 Raw Data 59 5.2 DEM Results 61 5.3 Density Slice 65 5.4 Ortho-rectification 66 5.5 3D Surface View 68 5.6 3D WireFrame 73 5,7 Software Performance Analysis 75
6. CONCLUSIONS AND FUTURE SCOPE 6.1 Conclusions 77 6.2 Future Scope 78
REFERENCES 79 APPENDICES
LIST OF FIGURES
Fig No. Title Pg. No.
1.1 Typical Photogrammetric Workflow 3
2.1 Basic forms of storage of DEM 9
2.2 Rigorous Camera Model and RPC model for Complete 3D Object Coordinate
to 2D Image Coordinate Mapping 12
2.3 RPC Framework. 15
2.4 Rational Polynomial Coefficients Estimation 19
2.5 Flowchart to determine the RPC Accuracy 23
3.1 3D Feature Extraction using Forward RPCs 29
3.2 Interactive 3D reconstruction using h adjustment 36
4.1 3D ground Coordinates reconstruction using Forward RPC Model 46
4.2 3D ground coordinates reconstruction using Inverse RPC Model 48
4.3 The workflow for generation of DEM data from stereo imagery in ENVI 51
4.4 DEM Extraction Workflow Diagram 53
4.5 Procedure for DEM Extraction using ERDAS IMAGINE OrthoBase pro 55
4.6 Procedure for DEM Extraction using PCI Geomatica OrthoEngine 58
5.1 IKONOS Stereo Pairs 60
5.2 IKONOS Stereo Image with Regions of Interest 60
5.3 Stereo Anaglyph of IKONOS stereo pair 61
5.4 Selected Tie Points (No. 200) 62
5.5 DEM generated using different Softwares
(a) Sample data 63
(b) RSI ENVI
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(c) ERDAS Imagine
(d) PCI Geomatica
5.6 Plot showing the elevations of the DEMs. 65
5.7 Density Slice of the DEM generated using different Softwares
(a) IKONOS Geo-Ortho kit
(b) RSI ENVI 67
(c) ERDAS Imagine
(d) PCI Geomatica
5.8 Ortho Images generated using different Softwares
(a) IKONOS Geo-Ortho kit
(b) RSI ENVI 68
(c) ERDAS Imagine
(d) PCI Geomatica
5.9 3D surface view of region 1 69
5.10 3D surface view of region 2 69
5.11 3D surface view of region 3 70
5.12 3D surface view of region 4 71
5.13 3D surface view of region 5 71
5.14 3D Surface View of Ortho Image and DEM by ENVI 72
5.15 3D Wireframe using points given by ENVI 73
5.16 3D Wireframe using ERDAS tie points 73
5.17 3D Wireframe by Geomatica (500 points) 74
5.18 3D Wireframe by Geomatica (5000 points) 75
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LIST OF TABLES
Table No Title Page No. 2.1 Maximum And RMSE of RPC Approximation. 22 2.2 Checkpoint Discrepancies From Stereo And 3 Ray RPC Spatial 24
Intersection.
2.3 Comparison Of Error Results With 23 Cps And 7 GCPs. 25 2.4 Comparison Of Error Results With 12 Independent Cps. 25 3.1 IKONOS Standard Products 37 3.2 OrbView-3 Basic Imagery Products 38 3.3 QuielcBird Basic Products 39
3.4 Features Of Softwares For Photogrammetric Processing 43 4.1 Detail Of Experimental Data 45
5.1 Mean And Standard Deviation Of The Dem From Different .64
Source.
5.2 RMSE Of The Elevations Given By Different Softwares. 64
5.3 Defined Density Slice Ranges 66
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LISTS OF ACRONYMS
2D Two-dimensional 3D Three-dimensional CE Circular Error DEM Digital Elevation Model
DPW Digital Photogrammetry Workstation
ENVI Environment for visualizing Images GCP Ground Control Point GIS Geographic Information System
GUI Graphic User Interface
HRS High Resolution Satellite Lat/Lon Latitude/Longitude LE Linear Error MSL Mean Sea Level
NIMA National Imagery and Mapping Agency
RFM Rational Function Model RMSE Root Mean Square Error RPC Rational Polynomial Coefficients RSI Research Scientists, Inc. STDEV Standard Deviation TIFF Tagged Image File Format USGS United State Geological Survey UTM Universal Transverse Mercator WGS84 World Geodetic System 1984
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CHAPTER ONE
INTRODUCTION
1.1 GENERAL
A Digital Elevation Model (DEM) is a regularly spaced raster grid of elevation values
representing the surface terrain. A DEM has wide application in surveying, mapping,
urban planning, and engineering. It can be used in the production of contour maps,
orthophoto maps, and perspective maps. It can also be used in route planning during the
construction of highways and railways. In remote sensing, DEMs are extensively used in
mapping, orthorectification, and land classification. Images are often draped over 3D
terrain models generated using DEMs, to provide a uniquely useful view of the area of
interest. Due to these many uses, there is an increasing demand for DEMs. In many parts
of the world, governments create and provide high quality elevation images for virtually
all of their land areas. But for other areas of the Earth's surface, elevation images are
more difficult to find. There are sources of global elevation data, including data from the
Shuttle Radar Topography Mission (SRTM). These data, however, can have data holes
under certain circumstances, and the resolution is not sufficient for some applications. In
these cases, other ways of acquiring DEMs are needed.
There are a number of production strategies to collect digital elevation data in modem
scientific technologies, including ground survey with total station or GPS, manual
profiling from photogrammetric stereo-models, stereo-model digitizing of contours,
digitizing topographic contour maps, converting hypsographic and hydrographic tagged
vector files, and performing autocorrelation via automated photogrammetric systems. Of
these techniques, the derivation of DEM from vector hypsographic data produces one of
the most accurate models (Habib et al., 2004). Moreover, due to the difficulty of
collecting relevant data and the expensive production procedure, usage of these
techniques are limited and discouraged.
Apart from conventional methods of DEM acquisition, producing DEM from satellite
data has been a vibrant research and development topic for the last thirty years, beginning
with the launch of the first civilian remote sensing satellite. One way to acquire DEM
data is to generate it from stereo imagery using photogrammetry. Stereo viewing of
images has been the most common method used by the mapping, photogrammetry, and
remote sensing communities for elevation modeling.
Traditionally, photogrammetry has been defined as the process of deriving (usually)
metric information about an object through measurements made on photographs of the
object. Any measurement taken on a photogrammetrically processed photograph or
image reflects a measurement taken on the ground. Rather than constantly go to the field
to measure distances, elevation, areas, angles, and point positions on the Earth's surface,
photogrammetric tools allow for the accurate collection of information from imagery.
Photogrammetric approaches for collecting geographic information save time and money,
and maintain the highest accuracy (ERDAS, 2002). During the last two decades,
photogrammetry has experienced a significant change caused by advances in optics,
electronics, imaging, and computer technologies, which made possible the logical
development, the digital photogrammetric workstation. The fundamentals of
photogrammetry remain unchanged, but the operational environment has changed
significantly. Figure 1.1 shows the typical photogrammetric workflow, starting from the
orientation of imagery to the orthorectification and mosaicing.
The fundamental task of photogrammetry is to rigorously establish the geometric
relationship between the image space and object space as it existed at the time of
imaging. Once this relationship is correctly recovered, one can derive information about
the object strictly from its imagery. A Rigorous sensor model describes the geometric
relationship between the object space and the image space. It relates 3D object
coordinates to 2D image coordinates and vice-versa. One of the primary barriers to a
wider adaptation and utilization of satellite imagery was the sensor model. Sensor models
are a key component in restituting the functional relationships between the image space
and the object space, and are essential in image ortho-rectification and stereo intersection.
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interior Orientation
Digital imagery
r /
Aerial Triangulation
Relative Orientation DEM Generation
Absolute Orientation
Ortho phot o Generation
Feature Extraction I
Mosaic
Figure 1.1: Typical Photograrnmetric Workflow
Until recently, only physical sensor models were available to users. These models are
rigorous and highly suitable for adjustment by analytical triangulation and normally yield
a high modeling accuracy (a fraction of one pixel). Furthermore, in physical models,
parameters are statistically uncorrelated as each parameter has a physical significance.
Yet, from the user's point of view, the utilization of a physical sensor model poses some
difficulties. One of the primary drawbacks of the physical sensor model is that its
application requires explicit understanding of each of the physical parameters and a high
level of expertise. Moreover, even with complete understanding of the physical sensor
model, users are still faced with the challenging task of recovering the exterior orientation
of the sensor using a set of Ground Control Points (GCPs). When no GCPs are available,
users cannot recover the exterior orientation of the sensor and therefore unable to perform
various mapping and data collection operations.
With the introduction of generalized sensor models such as, this situation has changed
considerably. Generalized sensor models, such as Rational Polynomial Coefficients
(RPC) sensor Model (Grodecki and Dial, 2003; Tao and Hu, 2001a), have alleviated the
requirement to obtain a physical sensor model, and with it, the requirement for a
comprehensive understanding of the physical model parameters. Furthermore, as the RPC
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sensor model implicitly provides the interior and exterior sensor orientation, the
availability of GCPs is no longer a mandatory requirement. The RPCs, instead of the
physical sensor model information, are provided by vendors to end users for
photogrammetric processing such as orthorectification, stereo reconstruction, 3D feature
extraction and DEM generation. Consequently, the use of the RPC for photogrammetric
mapping is becoming a new standard in high resolution satellite imagery that has already
been implemented in various high resolution sensors, such as IKONOS, Cartosat and
QuickBird.
Recently launched high resolution satellites provide an excellent source of stereo images
for the DEM generation. IKONOS panchromatic 0.82 centimeter resolution stereo image
is used in this dissertation work for DEM generation. Coupled with highly accurate on-
board position and attitude sensors, IKONOS imagery provides the source material for
generation of medium-scale maps without any requirement for Ground Control Points.
Global satellite mapping opens vast areas of the world to exploration and development.
IKONOS has thus ushered in an era of global transparency while at the same time
contributing to utilitarian exploration, mapping, and monitoring applications. QuickBird,
another commercial satellite launched October 2000, even has higher resolution with 0.62
meter panchromatic and 2.44 meter multi-band images, and the same applications with
IKONOS imagery. Recently launched Indian remote sensing satellite Cartosat-1 (IRS-P5)
aims to provide data with higher resolution for cartographic purpose and incorporated
RPC with their imagery product to the end users.
Based on these technologies development, many companies are attracted to develop
photogrammetric software to exploit high resolution imagery. Many commercial digital
photogrammetric software packages has incorporated RPC to process the satellite image,
such as RSI ENVI, ERDAS IMAGINE, PCI Geomatica and ImageStation (Z/I Imaging).
Inspired by the advantages of the RPC and its capability to provide an open approach to
photogrammetric exploitation of the commercial high resolution satellite images, the
purpose of this dissertation work is to explore how the RPC are utilized for extraction of
DEM and 3D models. In particular, we are interested in the user's point of view and in
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showing how RPC Model, together with auxiliary data, could provide an efficient, fast
and economical DEM extraction solution.
1.2 PROBLEM STATEMENT
As explained in earlier section, it is observed that DEM has a wider application and there
is a great need for fast, economical, accurate and high resolution DEM for defense as
well as civilian use. As the conventional method of DEM generation is time consuming
and requires more investment and manpower, one can go for DEM from stereo pairs
using photogrammetric mapping techniques. The RPC technology can improve the
efficiency and productivity of the mapping process, but DEM generation using RPC and
its comparison between various photogrammetric softwares is not carried out by anyone
so far. This dissertation work is just to bridge this gap and made the accuracy assessment
of different softwares.
The photogrammetric software includes:
• RSI ENVI DEM Extraction Module.
• ERDAS IMAGINE OrthoBase and
• PCI Geomatica OrthoEngine pro.
Secondly, the mathematical model and procedure for mapping 2D image coordinates to
3D ground coordinates are studied, in a view to outline the procedure and algorithm for
3D ground coordinates reconstruction and to use it for DEM generation.
Lastly, the recent announcement of Indian Space Research Organization (ISRO) to
provide RPC with their image product to the end users prompted to know and study about
the RPC in detail.
1.3 OBJECTIVES
The major objective of this dissertation is to investigate the accuracy of Rational
Polynomial Coefficients based DEM generation through different photogrammetry
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mapping softwares, and to compare the DEM output results between these commercial
software packages.
Described below are the four specific objectives for this dissertation:
• To study the accuracy of Rational Polynomial Coefficients sensor model as a
replacement for Rigorous sensor model.
• To model the procedure and algorithms for the 3D ground coordinates
reconstruction from 2D image coordinates using RPC approach.
• Accuracy analysis and comparison for DEM generated using different softwares.
• User Friendliness and limitation of different Softwares for DEM generation using
RPC Model.
1.4 ORGANIZATION OF THESIS
This dissertation work is composed of six chapters. General introduction and objectives
are included in Chapter 1.
In Chapter 2, literature review for the DEM generation is provided with an emphasis on
the Rational Polynomial Coefficient model.
In Chapter 3, different mathematical model for 3D ground reconstruction from 2D image
coordinates is presented. Brief introduction to High Resolution satellite Imagery and
different software packages are also placed in this Chapter.
In Chapter 4, Data used and Methodology for the 3D ground coordinates reconstruction
are discussed. Procedures for DEM generation using different softwares are also included
in this chapter.
Chapter 5 is dedicated to Results and Analysis. Capabilities and limitation of the software
packages are also discussed in this Chapter.
Chapter 6 summarizes the whole dissertation work with conclusion and future scope.
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CHAPTER TWO
DEM AND RPC MODEL
This chapter is divided into five sections. The first section deals with the Digital
Elevation Model (DEM), its application, types and acquisition method. The second
section of the chapter will give a brief overview on DEM using photogrammetry
techniques. Rational Polynomial Coefficients Model is discussed in third section. Fourth
section carries the research studies for the investigation of RPC accuracy. Last section
summarizes the characteristics of RPC.
2.1 DIGITAL ELEVATION MODEL
Modern photogrammetry has entered a digital era. Modem photogrammetry covers a
considerably wider domain. Imagery of all types, both passive, such as photography, and
active (i.e., providing its own energy source), such as radar imaging, is used. The
advanced technology of data collection, processing, storage and production is serving for
multidisciplinary fields. Land surface study has been developed by utilizing digital
topographic data, which is characterized by elevation of points (spot height) and contour
lines. Today, the relative surface products such as digital elevation model (DEM),
triangular irregular networks (TIN), or digital terrain model (DTM) can be derived even
without ground-truth data, for example, utilizing ephemeris data that include sensor
geometry information when an image was captured. Afterwards, contour maps, slope
maps and other related information can be obtained on the basis of above-mentioned
products. These topographic data is used to study the nature of the terrain to aid decision
making.
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DEM has a wide application domain. DEM is important for land surface processes,
hydrologic and hydraulic modeling, assessment of land resources, management of
watersheds and ecosystems, calculation of rock volumes. They are particularly useful for:
• Site selection and monitoring.
• Impact studies.
• Mobile telecommunication network engineering.
• Structural geological studies.
• Mission planning.
• Defense simulation.
• Geographic Information Systems.
DEMs form the basis of many GIS applications including watershed analysis, line of
sight (LOS) analysis, road and highway design, and geological bedform discrimination.
DEMs are also vital for the creation of Orthorectified images (ERDAS, 2002).
The methods used to capture and store digital elevation data can be grouped into four
basic approaches (Jensen, 1998): grid, contours, profiles, and triangulated irregular
networks (TIN), illustrated in Fig. 2.1. The most prevalent DEM data structure is the grid
for which the z value at each pixel location in the regular raster in the absolute elevation
(Fig. 2.1.a). Contour lines from existing hard-copy maps may be digitized, resulting in
sample points along a contour that may be connected by vectors to re-display the contour
lines in a vector-based system (Fig. 2.1.b). The individual points sampled along the
contour line may be used to interpolate to a grid to create a DEM. A topographic surface
may be represented by profiles showing the elevation of points along a series of parallel
lines. Ideally, elevation values are recorded at all breaks in slope and at scattered points
in level terrain (Fig. 2.1.c). The TIN data structure uses the positions of the three nearest
points of elevation to form the vertices of triangular facets to calculate terrain slope and
aspect (Fig. 2.1.d). TIN data structures generally require fewer points to be stored than a
raster DEM, capture the critical points that define discontinuities like ridge crests, and
can be topologically encoded so that adjacency analyses are more easily performed.
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(a) Grid-Planar Format
(b) Contours
(c) Profiles (d) TIN
(Jensen, 1998)
Figure 2.1: Basic forms of storage of DEM
There are a number of production strategies to collect digital elevation data in modem
scientific technologies. Acquisition of DEM can be carried out by the means of (1) field
surveying, (2) digitizing from hard-copy contour maps, or (3) derive through
photogrammetric analysis of stereo aerial photographs or satellite stereo images (Petrie
and Kennie, 1990). Field survey sources of elevation data involve actual measurement of
elevation in the field using electronic tacheo-meters (also known as total stations). The
equipment allows highly accurate planimetric and altitudinal measurements. However,
ground surveying is time consuming, restricting its application to small areas. DEMs
generated from ground surveys are typically applied to site-specific projects, particularly
in. civil engineering, or used to supplement photogrammetric data. The hazards and
inaccessibility of mountain environment preclude the use of ground surveys for DEM
generation (Stocks and Heywood, 1994). GPS equipment has been considered as
potentially more practical for ground survey in mountain environments. However, a
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number of limitations do not currently make GPS a viable alternative for collecting a
complete data set for creating a DEM.
The acquisition of DEM over large areas is normally carried out by digitizing the height
information contained in existing topographic maps. Since these maps contain very few
spot heights or elevations, essentially one is dealing with the measurement of contour
lines so that they are represented by suitably structured strings of digital coordinate data.
Subsequently the actual DEM spot height or elevation data is derived by interpolation
from the digitized contour lines. It must be recognized from the outset that such a
procedure will never produce the same metric accuracy as the direct measurement of spot
heights carried out by field Survey or photogrammetric means.
Digital softcopy photogrammetry is revolutionizing the creation and availability of
special purpose DEMs (Petrie and Kennie, 1990). Stereoscopic and digital image
correlation techniques applied to aerial photography provide the most widely available
sources of digital elevation data (Stocks and Heywood, 1994). An analyst obtains two
overlapping views of the terrain using an aerial camera or satellite remote sensing system.
The software operating on a PC or WorkStation environment is used to scale and level
the stereoscopic model and extract a raster of digital elevation information. This DEM
may be edited interactively and used to produce an orthophotograph from one of the input
remotely sensed images. Thus, scientists can now produce their own DEMs using simple
workstation software in their own laboratories for site-specific applications. The z
accuracy of the DEM is only limited by the quality and base-to-height ratios of the aerial
photography or satellite imagery and the x, y, z ground control available. Thus, very high
z resolution DEMs can be created for site-specific remote sensing and GIS applications.
2.2 DEM USING PHOTOGRAMMETRY
Aerial photography and satellite imagery can be used to derive digital elevation data
using photogrammetry. At present, the resolution of suitable imagery and the
sophistication of processing mean that elevation data derived from satellite imagery is
usually only suited to small scale applications covering large areas, such as national,
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continental or global studies (Lillesand and Kiefer, 2000). Stereoscopic and digital image
correlation techniques applied to aerial photography provide the most widely available
'sources of digital elevation data (Stocks and Heywood, 1994). DEM generation using
photogrammetry from remotely sensed imagery is crucial for a variety of mapping
applications such as ortho-photo generation, city modeling and creation of perspective
views. High resolution imaging satellites (e.g., SPOT-5, ASTER, IKONOS,
QUICICBIRD and °REVIEW) constitute an excellent source for efficient, economic, and
accurate generation of DEM data for extended areas of the Earth's surface. In general, the
procedure for DEM generation from stereo-pairs views can be summarized as:
• Feature extraction in one of the scenes of a stereo-pair: Selected features should
correspond to an interesting phenomenon in the scene and/or the object space.
• Identification of the conjugate features in the other scene: This problem is known
as the matching/correspondence problem within the photogrammetric and
computer vision communities.
• Intersection procedure: Matched features in the stereo-scenes undergo an
intersection procedure to produce the ground coordinates of corresponding object
features. The intersection process involves the mathematical model relating the
scene and ground coordinates.
• Point densification: High density elevation data are generated within the area
under consideration through an interpolation in-between the derived object space
features.
The matching problem and the mathematical model relating the scene and ground
coordinates of corresponding points are the most difficult problems associated with DEM
generation from high resolution imaging satellites (Habib et al, 2004). DEM generation
from stereoscopic imagery is contingent on establishing the mathematical model relating
the scene coordinates of conjugate points to the ground coordinates of the corresponding
object point.
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2-D IMA GE SPACE
Interior Orientation — Optics
— Mechanical alignments
— Relates field angles to image detectors
oIrncs
Exterior Orientation — Posifon (Ephemeris) — Attitude (Angles)
— Relates 3—D ground positions to field
angles
3-D GROUND SPA CE
The mathematical relationship between the scene and object coordinates of conjugate
points with perspective geometry of the imaging system can be established using either:
i. Physical or Rigorous Sensor Model or
ii. Generalized or Approximate Sensor Model.
Rigorous sensor model includes physical parameters about the camera/sensor, such as
focal length, principal point location, pixel size, and lens distortions which are known as
Interior Orientation Parameters (IOP), and parameters of the image such as position and
attitude of the perspective center and are known as Exterior Orientation Parameters
(EOP). Figure 2.2 shows a camera viewing an 3D ground space (X, Y, Z) with rays to an
(x, y) image space. Known as rigorous sensor model, it includes physical parameters
about the camera (I0P), and orientation parameters of the image (EOP).The rigorous
sensor model along with all information are then used for orthorectification, stereo
feature extraction, DEM extraction and block adjustment.
(Grodecki and Dial, 2004)
Figure 2.2: Rigorous Camera Model and RPC model for Complete 3D Object
Coordinate to 2D Image Coordinate Mapping.
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Rigorous sensor modeling requires a comprehensive understating of the imaging
geometry (i.e. IOP and EOP). In this type of modeling, the IOP as well as the EOP of the
imaging system are explicitly involved in the mathematical relationship between
corresponding scenes and object coordinates (Habib and Beshah, 1998). Deriving such
characteristics requires the availability of control information, which might be in the form
of a calibration test field, ground control points, and/or onboard navigation units
(GPS/1NS). However, deriving such parameters might be hindered by: lack of sufficient
control, weak imaging geometry and intentional concealment by the data provider (e.g.,
Space Imaging does not provide the IOP and the EOP for their commercially available
IKONOS imagery). Also the block adjustment and ortho-rectification processing model
of physical sensor model is extremely complex making them enormously difficult to
implement. For example the IKONOS System Geometric and Mathematical Model
document consists of 183 pages while the accompanying interface control document for
the thousands of data items used in the IKONOS camera model is 225 pages.
There is increasing interest within the photogrammetric community to adopt generalized
models since they require neither a comprehensive understanding of the imaging
geometry nor the internal and external characteristics of the imaging sensor. Generalized
models include Direct Linear Transformation (DLT), self-calibrating DLT (SDLT),
parallel projection and Rational Polynomials Coefficient (RPC) Model ( Fraser, 2000;
OGC, 1999; Ono et al., 1999; Wang, 1999 and Novak, 1996). Among these models,
Rational Polynomial Coefficient Model ( also known as Rational Function Model i.e.
RFM) gaining popularity for its simplicity and accuracy.
RPC Model have recently drawn considerable interest in the civilian remote sensing
community, especially in light of the trend that some commercial high-resolution satellite
imaging data are supplied with RPC (Cheng and Toutin, 2000), instead of rigorous sensor
models. An RPC model is generally the ratio of two polynomials derived from the
rigorous sensor model and the corresponding terrain information, which does not reveal
the sensor parameters and without disclosing the sensor model. RPC is descrided in detail
in next section.
13
2.3 RATIONAL POLYNOMIAL COEFFICIENT MODEL
Over the past few years, RPC Model has gained considerable popularity. RPC model
provide a generic representation of the camera object-image geometry and yet are simple,
efficient, and accurate. It has been demonstrated by (Grodecki, 2001; Grodecki and Dial,
2003; Tao and Hu, 2001 and 2002; Fraser and Hanley, 2003) that RPCs provide the end
user of the high resolution satellite imagery with the ability to perform full
photogrammetric processing including block adjustment, 3D feature extraction, DEM
generation and orthorectification. The beauty of using RPCs is that it is sensor
independent, which means that the user does not need to know all of the specific internal
and external camera information. Basically it's a lot less complicated. The name Rational
Polynomial derives from the fact that the model is expressed as the ratio of two cubic
polynomial expressions. It is a simple empirical mathematical models relating image
space (line and column position) to latitude, longitude, and surface elevation of the
ground, and provides a functional relationship between the object space (4) , X, 1/)
coordinates and the image space (L, S) coordinates Eq. (2.1).
L = Ns (4) X h ) Ds (4) , X , h )
(2.1)
S — N L (4) , X , h )
DL (4) , X , h )
Where $ is geodetic latitude, A. is geodetic longitude, h is height above the ellipsoid, S
and L are the image sample and line respectively. Actually, a single image involves two
such rational polynomials, one for computing line position and one for the sample
position. The coefficients of these two rational polynomials are computed by the satellite
company from the satellite's orbital position and orientation and the rigorous physical
sensor model. For the better understanding, the photogrammetric mapping workflow
based on RPC is shown in Fig. 2.3 (Hu et al, 2004).
14
Imaging Sensors
Physical Sensor Model
Available?
Terrain Independent Approach
d Terrain Dependent Approach
RPC Solution —DO Parameters Selection I Imagery Vendors+
End Users and Service Providers
RPC Parameters
RPC Refinement
Refined RPCs
Mapping Applications, Ortho -R ec tificat ion, 3 -D Feature Extraction, DEM Generation, Multi-Sensor Integration
(Hu et al, 2004)
Figure 2.3: RPC Framework.
15
2.3.1 RPC Mathematical Model
The Rational Polynomial Coefficient Model has been adopted by Space Imaging
(IKONOS), Indian Remote Sensing Agency (CARTOSAT), ORBIMAGE (OrbView-3),
CNES (SPOT-5) and DigitalGlobe (QuickBird) in their commercial high resolution
satellite imagery products. This sensor model, comprising 78 rational polynomial
coefficients (RPCs) (Appendix A), alongside 10 offset and scale
factors {00 Xo, ho, So, Lo s ,Xs , hs , Ss , Ls} , provided by the image vendors to the end
user, is an alternative sensor model that allows users to perform full photogrammetric
processing in absence of the rigorous physical sensor model. The 78 coefficients
{c1.....c20 ,d2 d10 , e) e20, f2 f2o} are generated in the ground station by fitting the
RPCs to the physical camera model. Separate rational functions are provided for mapping
the object space coordinates to line and sample coordinates, respectively. In order to
minimize the introduction of error during the computation and to improve numerical
precision, image and object space coordinates are normalized between -1 to ±1 range by
applying the offsets and the scale factors (NIMA, 2000) as shown below:
— X() itv _ h — h 0 s h s
(2.2)
= S — S° andY = L — L 0 X S s L s
where is geodetic latitude, A. is geodetic longitude, h is height above the ellipsoid, L
and S are the image line and sample coordinates, and 4)o,an,ho,So,Lo,4)s, Ads ,hs,Ss,Ls
are the latitude, longitude, height, sample and line offsets and scale factors.
Also U, V. W, X and Y are normalized geodetic latitude, geodetic longitude, height above
the ellipsoid, image sample and line coordinates respectively.
s
16
The normalized line and sample RPC equation can be written as (Grodecki and Dial,
2003):
N L (U V W ) C D L , V ,W d T u
and (2.3)
N (U V W ) X = S " — e D s (U,V,W) f r u
Where NL (U,V ,W)= c1 +c2V + c3U + c4W +c5VU +c6VW +c,UW +c8V 2 +c9U 2
+c10W2 +c11UVW+c12 V3 +e13V(12+c14 VW2+cuV2U+ci6U3+cuUW2 (2.4)
+c18V 2W+c19U 2W + c20W 3 = cT u
DL (U,V,W)=1+d2V+d3U-i-d4W+d,VU+d6VW+d7UW +d,V 2 -Ed9U 2
+d12W 2 +d11UVW + di2V 3 + d13VU 2 +d14VI/V 3 + di ,V 3U + d16U 3 +d17UW 3
(2.5)
+d18V 2W + dioU 2W +d20W 3 = d ru
Ns (U,V,W)= el + e2V + e3U +e, +e,VU +e6VW +e,UW +e9V 2 +e9U 2
±eloW2 ±eilUVW+euV3 +e13VU2 ei414172 +el5V 2U+e16 U3 +e17 UW2 (2.6) +e18V 2W + e19U2W +e20W 3 =eTu
Ds (U,V,W)=1+ f2V + f3U + f4W + + f6VW + f2UW + f8V 2 + f9U 2 +f,0W 2 + fuLTVW + fi2V 3 + A3VU 2 14VPV 2 f 5V 2U A6U 3 f t7UW 2 (2.7)
+.48V2W + A9U2W + f20W3 = I Tu
with
u=1/ V U W VU UW 112 U 2 W 2 UVW 113 YU2 VW 2 V 2 U U3 UW 2 V 2 W U 2 W W31T
(2.8)
17
and
c=EcIc2 C 20
d = [1 d 2 d29 f
(2.9)
e= [ele2 e20
f = f2 f20r 2.3.2 RPC Estimation
The RPCs can be estimated with or without the physical sensor model. The RPCs can be
solved by terrain-independent scenario using known physical sensor models or by terrain-
dependent scenario without using physical sensor models. In the first case, the RPCs are
estimated using a direct least-squares solution with an input of the object grid points
(4) , A, , It) and the conjugate image grid points (L, S) with the help of physical sensor
model. In the second case, the RPC tries to approximate the complicated imaging
geometry across the image scene using its plentiful polynomial terms, and the solution is
highly dependent on the actual terrain relief, the number and the distribution of GCPs
across the scene. Both the approaches are discussed in detailed below.
i. Terrain-independent Approach
If the rigorous sensor model is available, the RPC can be solved using a 3-D
object grid (Fig. 2.4) with its grid point coordinates determined using a rigorous
sensor model. This solution is in fact independent of real terrain since no terrain
information is required. This method involves the following steps:
• Determination on grid of sufficient image points. The grid contains
m x n points. These points are evenly distributed across the full extent of the
image. The number of rows m and columns n are often around 10.
• Set up of a 3-D grid of points in ground space. The rigorous sensor model is
used to compute the corresponding object positions of the grid points on the
image. So, the dimension of this 3-D grid is based on the full extent of the
18
image and the range of the estimated terrain relief, i.e., the dimension of the
grid covers the range of the 3-D terrain surface. The grid contains several
elevation layers, and the points on one layer have the same elevation value. To
avoid an ill-conditioned design matrix, the number of layers should be greater
than three.
• RPC fitting. The RPC Model is used to fit the 3-D object grid and the
unknowns are solved using the corresponding image and object grid points.
• Accuracy checking. Another 3-D object grid can be generated in a similar
manner but with double density in each dimension. The corresponding image
positions of these checkpoints are calculated using the rigorous sensor model.
The obtained RPC is then used to calculate the image positions of the object
grid points.
IMAGE SPACE
Line
0)
r Latitude
(Grodecki, 2003)
Figure 2.4: Rational Polynomial Coefficients Estimation.
OBJECT SPACE
19
The RPC determined this way is proved to be able to achieve a very high approximating
accuracy to original physical sensor models. It is reported that the RPC model yields a
worst-case error below 0.04 pixels for IKONOS imagery compared with its rigorous
sensor model under all possible acquisition conditions (Grodecki and Dial, 2001).
Therefore, when the RPC is used for imagery exploitation, the achievable accuracy is
virtually equivalent to the accuracy of the original physical sensor model. This terrain
independent computational scenario makes the RPC a perfect and safe replacement to the
physical sensor models, and has been widely used to determine the RPCs.
ii. Terrain dependent Approach
With no rigorous sensor models at hand, the corresponding image points of
ground points of a 3-D grid cannot be computed. In order to solve for the
unknowns, one has to measure control points and check points from both the
image and the actual DEM or maps. In this case, the solution is heavily dependent
on the actual terrain relief, the number of control points, and the distribution of
control points. This method is essentially terrain-dependent. This method has been
widely used in the remote sensing application where the rigorous sensor model is
far complicated to develop or the accuracy requirement is not, stringent (Toutin
and Cheng, 2000; Tao and Hu, 2001a, b).
2.3.3 RPCs Refining
As proved by its high approximating accuracy for many physical sensor models, the
RPCs has high capability of geometric interpolation. However, the RPCs provided by
imagery vendors may not always approximate the real imaging process well. The
requirements for control information may be not met satisfactorily sometimes, or no
ground control information is used when determining the physical sensor model itself for
different marketing strategies from imagery vendors. High precision products are sold at
a significantly higher price, and even require that users provide GCPs and a DTM. This
presents a problem for many users who are prohibited to release topographic data this
20
way. Recent studies have found that RPCs can be refined in the domain of the image
space or of the ground space, when additional control information becomes available. For
example, the IKONOS Geo products and Standard stereo products will be improved to
sub-meter absolute positioning accuracy using one or more high quality GCPs (Grodecki
and Dial, 2003; Tao and Hu, 2004) or be close to the accuracy of the GCPs whose quality
is low (Hu and Tao, 2002; Tao et al., 2003). So the RPC refining methods will definitely
promote the use of low pricing products for many applications. The RPCs may be refined
directly or indirectly. The direct refming methods update the original RPCs themselves.
So the updated RPCs can be transferred without the need for changing the existing image
transfer format. While the indirect refining introduces complementary or concatenated
transformations in image or object space, and they do not change the original RPCs
directly.
2.4 INVESTIGATIONS INTO THE ACCURACY OF RPCs
There have been a number of tests carried out to determine the accuracy of the RPC.
These break down into those using sensors for which the model is known, such as aerial
frame cameras or SPOT, and those using IKONOS data for which the sensor model is not
known, and for which the tests must compare only results from the RPC, with ground
control points (GCPs).The former are better indicators of the accuracy of the model,
although the latter are of more interest.
Tao and his co-workers have carried out extensive tests on different formulations of the
RPC, mainly on SPOT and aerial photography, Hu and Tao (2001), Tao and Hu (2001a,
2001b, 200k). They conclude that the RPC can give very high accuracy for aerial
photography and SPOT data in the terrain-independent case. The RPC with unequal
denominator often gives a better result. The high order RPC is favorable sometimes, for
example, for SPOT data. The normal equations are usually well conditioned. In the
terrain dependent case the solution is very sensitive to the GCP distribution, and its
design matrix is almost rank deficient. Tao and Hu, (2001a) propose computational
methods to improve the numerical stability of the solution.
21
Yang (2000) also reports on using the rational function model with aerial photography
and SPOT and achieved negligible errors 'when proper polynomial order is used' (under
the terrain-independent case) which means the rational functions derived after block
adjustment can be used to replace the original rigorous models without any significant
accuracy loss. Table 2.1 is the results of stereo pair intersection using rational functions
for both SPOT and camera data. Only the second and the third order functions are used
here because the first order does not have good fitting according to the previous
discussions. While data and software vendors are using the third order rational functions,
it is adequate to use lower order functions in many scenarios, especially when camera
data are involved. This means the derivation process of rational functions should be smart
enough to pick a right order based on the maximum or RMS error threshold, because
lower order always means speed. In the case reported, it is recommended that, since the
rational function approximation is very accurate, the data providers can supply the math
model to end user without revealing the secret numbers of their sensors and for data
users, it is safe to use the rational functions instead of more complicated rigorous model.
Table 2.1: Maximum and RMS (in parenthesis) errors of RPC approximation.
Image
Pair
Polynomial
Order
Use Map Space (m) Use Topocentric Space (m)
Map X Map Y Map Z Map X Map Y Map Z
Spot 2 0.6243
(0.2226)
0.5486
(0.2242)
2.7674
(0.8949)
0.9965
(0.4371)
0.5703
(0.2224)
3.6525
(1.3924)
3 0.4613
(0.1538)
0.5549
(0.2266)
1.3605
(0.5233)
0.4102
(0.1627)
0.6142
(0.2380)
1.6455
(0.5753)
(Yang, 2000)
The RPCs provided with IKONOS imagery allow the object-to-image transformation to
be performed. This gives accuracy in the 3D object space which is consistent with the
specifications for the different IKONOS products such as GEO or Precision. The RPCs
for the GEO product, which are expected to produce a RMS positioning accuracy of
about 25m, are derived solely from satellite ephemeris and attitude data, whereas those
22
for Precision products are computed with the additional aid of ground control. Grodecki
and Dial (2001) report that tests with 140 ground control points gave horizontal accuracy
`of the order of lm while vertical accuracy was of the order of 2m' from a controlled
stereo pair over San Diego. Accuracy of the RPC model is determined using the approach
shown in Fig 2.5.
/ Image coordinates of check points
Imaging Scenario Physical Camera Model
• Grid of Image (L, S) and
ground coordinates
FIT RP C MODEL_ (Equation
1=Numl(U, V, W)/Den 1 (U, V, W) S=Num2(U, V, W)/Den2(U, V, W)
Add/ Remove N RPC coefficients
Collinearity Diagnostics: Pass?
Physical Camera Mode l
Yes
OUTPUT 0 Estimated Coefficients
o RMS errors o Worst case residual errors
• Final RPC camera model
L, S Lrpc Srpc / Image co ordinates of check points
AL Lrpc - L AS = Srpc - S
OUTPUT o max AL, A S o RMS AL, A S
END
(Grodecki and Dial, 2001)
Figure 2.5: Flowchart to determine the RPC Accuracy.
23
Hanley and Fraser (2001) tested IKONOS Geo product by first projecting the control
points onto 'planes of control', to minimize the effect of terrain, and then transform the
image to these points using Similarity, affine and projective transformations. The results
show that 0.3-0.5m geo-positioning accuracy is achievable from the Geo product without
using the Rational Polynomial Coefficients.
Fraser et al (2002a) have extended this work in two dimensions into three, using similar
techniques. Table 2.2 shows the results, first from a stereo solution using only the RPCs
provided with the Geo images. This only shows that the results are within specification.
The true relative accuracy is shown when the same stereo pair is transformed by a
translation, in the first case using 1 single ground control point (repeated with 4 single
GCPs), and in the second case using 4 ground control points (repeated with four sets of 4
GCPs). As with the planimetric test, this does not give a true test of the accuracy of the
RPCs because they were computed only using the camera model and sensor position and
attitude recorded by on-board GPS receivers and star trackers. It does however clearly
indicate that the RPCs can give good results with IKONOS data. Similar test results were
shown in Baltsavias et al (2001).
Table 2.2: Checkpoint discrepancies from stereo and 3 ray RPC spatial intersection.
Image configuration No. of GCPs No. of check Points
RMS discrepancies X Y Z
Standard Stereo solution
0 40 8.2 31.5 1.7
Stereo solution with bias removal by translation
1 39 0.58-0.75 0.41-0.83 0.87-0.98
Stereo solution with bias removal by translation
4 36 0.59-0.69 0.43-0.50 0.83-0.96
(Fraser et al, 2002a)
Interestingly enough, Dial and Grodecki (2002),Fraser et al. (2002b) and Tao et al (2002)
all reported at the 2002 ASPRS conference that the image based transformation (bias
correction) to improve the RPC accuracy using GCPs is more effective. Dial and
24
Grodecki (2002) has further extended the RPC model for block adjustment. Their work
shows that the block adjustment of IKONOS images with the RPCs is also viable.
Toutin (Toutin and Cheng, 2000) has developed a physical IKONOS model using basic
information from the metadata and image files. (For example, approximate sensor
viewing angles can be computed using the nominal collection elevation and the nominal
ground resolution in the across and along scan directions.) The model has ported into PCI
OrthoEngine. Toutin compared three methods of handling IKONOS data and his results
are shown in Table 2.3. It is worth noting that these RPC tests were based on the terrain
dependant case.
More recently Toutin and Cheng (2002) have also reported on tests carried out with
QuickBird data using similar methodology the work done with IKONOS data.
Comparison of error results with 12 independent check points using simple ln order
rational polynomial and Toutin's Rigorous model are shown in Table 2.4, and are almost
identical for the rigorous model, and worse using the 1st order rational polynomial
model. This cannot be compared directly with Table 2.3, where higher order polynomials
were used.
Table 2.3: Comparison of error results with 23 independent check points and 7 GCPs. Correction Method RMS discrepancies (m) Maximum Errors (m)
X Y X Y Simple Polynomial 1.7 4.1 4.1 7.5
Rational Polynomial 2.2 5.2 5.1 10.4 Rigorous Model 1.3 1.3 3.0 3.0
(Toutin and Cheng, 2000)
Table 2.4: Comparison of error results with 12 independent check points. Correction Method RMS discrepancies (m) Maximum Errors (m)
X Y X Y
Rational 1st order Polynomial
4.0 2.1 9.5 4.3
Rigorous Model 1.4 1.3 2.5 2.8
(Toutin and Cheng, 2002)
25
2.5 RPC CHARACTERISTICS SUMMARY
After a brief review of literature, characteristics of the RPC can be summarized as below:
• The RPC model is simple to design and implement, and often execute faster than
physical sensor models.
• RPC is a generic form of polynomial model. The collinearity equation model, the
parallel projection model, and the direct linear transformation model are
essentially the first-order form of the RPC
• It is independent of the sensor geometry and platform.
• It is applicable when the relief displacement does not influence the result
significantly.
• Polynomial expressions are characterized by a great capability for absorption of
accidental distortions. Corrections used in physical sensor models; such as for
earth curvature, atmosphere refraction, and lens distortion, can be accommodated
by the second-order polynomials (Grodecki et al, 2004).
• Many distortions of the image (due to sensor geometry, earth curvature, etc.) are
corrected simultaneously, although the model does not adequately correct relief
displacements, nor does it consider the special geometry of the imaging system
(Novak, 1992).
• It supports any object-space coordinate system, such as geocentric, geographic, or
any map projection coordinate system (Paderes et al, 1989).
• Compared to those physical sensor models, RPC is not suitable for direct
adjustment by analytical triangulation (OGC, 1999).
• The over-parameterization may cause instability and indetermination in the least-
squares solutions (Madani, 1999).
• It is a complex lilting model. It can reach a high fitting accuracy but it may fail
when its denominator reaches zero.
• It is hard to detect and remove blunders embedded in the control information
(Toutin and Cheng, 2000).
26
CHAPTER THREE
MATHEMATICAL MODEL, HRS IMAGERY AND SOFTWARES
The chapter is divided into three sections. The first section deals with the Mathematical
Model for 3D ground coordinates reconstruction. High resolution satellite data products
which support RPCs will be introduced in the second section. The third part in this
chapter will provide a review on the photogrammetric software packages.
3.1 MATHEMATICAL MODEL FOR 3D RECONSTRUCTION
There are several mathematical model and algorithms given in literature for 3D
reconstruction of ground coordinates based on RPC which includes Forward RPC model,
Inverse RPC model, 3D reconstruction with Error Propagation, 3D reconstruction using
Straight Line algorithm and 3D reconstruction by Adjusting Elevation h. A detailed
mathematical model for Inverse and Forward reconstruction and a general idea about
reconstruction by adjusting Elevation is discussed in this section.
3.1.1 3D Reconstruction with Forward RPCs model
The Rational Polynomial Camera model given in equation (3.1) is often referred to as the
"Forward RPC model" (Tao and Hu, 2002). The Forward RPC model provides a
mapping from object space 0 , , h) coordinates and the image space (L, S)
coordinates.
Y Ar t (U ,V ,W ) cr u and X — AT s (U,V,W) eru D L (U ,V ,W) d r u Ds(1,V,W) f ru
All the parameters are already discussed in section 22.1.
Denormalizing RPCs of equation (3.1) one gets:
Le= p(c,k,h) and S = r ,X,h)
(3.1)
(3.2)
27
Where
(4) , X , h) are the geodetic latitude, longitude, and ellipsoidal height,
L, S are the image line and sample coordinates, and
p, r are denormalized RPC models of equation(3.2).
(LT, V, W) _ s + _0 Ns (,,) _s _o 1)(4)' X' h)=. DL(UVW)L i,
and r(4),X,h)— Ds (u, v,w)s s
Applying Taylor's Series expansion one gets the linearized RPC equation at +o, , /20
as follows:
L = P 0o, Ado, k)+[ 581:7.1 z_ zo ]dz, S=r00,2b,ho)+[1...zo ick (3.4)
Where
ap _ ap au ay and ar ar au ay aZ T our ay T az T azT = our ay T az T
with
u=[/ Y U W VU VW UW V2 U2 W2 uvw v3 vu2 vw2 v2 u u3 uw2 v2 w u2w w3]r
y= EU V W r and z=RXh j r
The partial derivatives are calculated as
op ((f l u )cT — u PT Ls (3.5) BUT — (drily
with
au 0740 0 1 0 V 0 W 0 2U 0 VW 0 2VU 0 V2 3W W2 0 2UW 0iT
au = [0 1 0 0 U W 0 2V 0 0 UW 3V2 U2 W2 2VU 0 0 2VW 0 0
y av
aw au ,[ociolovuoo 2W UV 0 0 2VW 0 0 2UW V 2 U2 3W 2
and
ay = [ay ay ay] azr ap ax ahi
(3.3)
28
with
ay [ 1 nn = --uu
Ow Ts T ' r Oh J r
1 OA, 19 3) =[0
A.. 01 a Y = [0 0
hi 1
, '
(Grodecki et al, 2003)
Figure 3.1: 3D Feature Extraction using Forward RPCs
To estimate object space coordinates of a point one needs to measure its image space coordinates in at least two different images. These images might be part of a same-pass
stereo pair or triplet or they might be multiple mono-scopic images from different orbital
passes. For the case with two images, shown conceptually in Fig. 3.1, the observation
equations read:
L i = /91 0 , X , 10-÷ E Li
S1 = r, 0 , X , h) + e si
L 2 = p 2 0,X,O+ 6 1,2
S2 = r2 0 , X , h ) + e s,
The linearized observation equations follow with:
29
Op, azT 2=20
ar i
aZT 11=10
(3P 2 I aZT z=za are
a-z7.6=10
' dz =[dco dX dh], and w =
L,
L2
S2_
(00,x0,k)- ri(00,k,k)
P240,4;h0) _r200,A-0,k)1:
A =
Adz +s =w with Cw (3.6)
where A is the first order design matrix, clz is the vector of corrections to approximate
values of object space coordinates, w is the vector of misclosures, and Cw is a priori
covariance matrix.
The unknown object space coordinates are solved for iteratively. At each iteration step,
application of the least-squares principle results in the following estimated corrections to
the approximate object space coordinates:
A
d z = (AT C,,-1 AY' AT C,Vw. (3.7)
At the subsequent iteration step the vector of approximate model parameters zo is
A A A replaced by z , where z = zo +d z , and the math model is linearized again. The least-
squares estimation is repeated until convergence is reached. The covariance matrix of the
estimated model parameters follows with:
C = (AT .
Calculation of Approximate Ground Coordinates
3D reconstruction with the Forward RPC model requires knowledge of the approximate
object space coordinates. Tao and Hu (2002) proposed to use the truncated RPCs, i.e.
30
•
RPCs with only the first-order terms, to this end. In order for the truncated RPCs to
provide a reasonably accurate solution, the higher order RPC terms have to be negligibly
small. Unfortunately this is often not the case with the IKONOS RPCs; oftentimes
_ neglecting higher order terms results in hundreds of meters of error. Accuracy of the
truncated RPCs can be easily checked by comparing the line and sample coordinates
calculated with the truncated RPCs against the line and sample coordinates calculated
with the original RPCs over the entire RPC range, i.e., ckc, -±(1)3., Xo ±Xs and 170 ± hs . If the truncated RPCs are determined not to be accurate enough, DLTs fitted to the original
RPC model can be used to determine the approximate ground coordinates of the object
point. The DLT fitting process is in principle identical to the RPC fitting process,
description of which can be found in (Tao and Hu, 2001). An algorithm for determining
the object space coordinates with the truncated RPCs is given in (Tao and Hu, 2002).
Since the DLT functional model is essentially identical to the truncated RPC model, the
same algorithm can be applied to the DLT case. In either case the functional model would
read:
L (a° +aU +a 2V + a 3W )
(1 + b 1U + b 2V + b 3W )
S = ( c ° + c U + c 2 V + c 3W ) (1 + d 1 U + d 2V + d 3W )
L(1+ b3W) — ao — a3W = (al — Lbi )U + (a2 — Lb2 )V
S(1+ d3W) — co — c3W = (c1 — Sdi )U + (c2 — Sd 2 )V
y Av
y— (1 + d3W) — — c3W r
S
[(a1 —Lb1) (a2 — Lb2)1 A= L(c, —Sdi ) (c2 — Sd2)
v =[U of
(3.8)
(3.9)
i+b3w) —a0 —a3W
31
The solution for v follows with v= ,41-'y (3.10)
Where
r(c2_sd2) (—a2 -f- Lb2)1 with I A I= (a, —Lb1 )(c2 — 5d2) — (c, — Scil)(a2 — Lb2). I Ai + sd,) (a, -Lk)
3.1.2 3D Reconstruction with Inverse RPCs Model
The "Inverse" RPC model (Tao and Hu, 2002) provides a mapping from image space (L,
S) coordinates at a given height It, to object space (4) , X) coordinates. Inverse RPC
model can be generated from the Forward RPC model. This can done by fitting Inverse
RPCs to a 3D grid of points generated with the Forward RPC model, using e.g. an
algorithm described in (Tao and Hu, 2001). An algorithm for 3D reconstruction with the
Inverse RPC model is given in (Tao and Hu, 2002).
The Forward RPC model provides a mapping from object space (4) , X , h) coordinates
and the image space (L, S) coordinates. For mapping image space (L, S) coordinates to
object space (4) , X , h) coordinates, an "Inverse RPC Model" can be used(Yang, 2000;
Tao, V., Hu, Y., 2002). Inverse RPC Model is shown in equation 3.11 below.
4) N s (L,S,h) cT k D 4, ( L,S,h d
-
T k and (3.11)
N L "S h) e T k A= D 1 (L,S,h) f r k
The notations have their usual meaning. The equation (3.11) expresses the planar object
space coordinates as rational functions of the image space coordinates and the vertical object coordinates.
Where in equation (3.11),
32
(L,S,h),- ci + c2S + c3L + c4h + c5LS + coSh+ c7 Lh+ c5S 2 + c9L2 + c10h2
+cil LSh+ c12S3 + c13SL2 + c14Sh2 + c15S2L + c16 L3 + c 7 Lh2 + c1852h + c19 L2h (3.12)
+c20h3 = crk
Dy s, + (12s+ cut + d4h cys+ d6 sh + dAh + d8S2 + d9L2 + dioh2
+d11LSh + dig + d13SL2 + d14 Sh2 + d15S2L+ d15 L3 + d17 Lh2 + d15S2h+ di9 L2h +d20h3 = (Irk
N x (L,S,h)= e1 + e2S + e3L + e4h + e5LS + e6 Sh + e7 Lh + e8S 2 + e9L2 e10h2 +e11 LSh + e12S3 + e13SL2 e14Sh2 + e15S 2 L + e16L3 + e17 Lh2 + e15S 2h + e19 L2h
= eT k
Dx (L,S,h)= f + f2S + f3L + f4h+ f5LS+ f6Sh+ f7 Lh+ f5S2 + f9L2 + floh2
+filLSh+ fi2S3 + fi3SL2 + fi4Sh2 + fi5S2L+ f or + fi7Lh2 + fi5S2h+ f 9L2h +fait? =f rk
(3.13)
(3.14)
(3.15)
and
S L h I.S Sh 1h SZ L2 h2 Esti sa SGZ LW SZL E Lh2 S2 h Leh (3.16)
Applying Taylor series expansion of 'F and A. towards the input variable h in equation,
one gets the first-order approximations as:
4) =4)0 +—ah -Ah
+ Th
•Ah
(3.17)
Where
33
ah (dr ak )2
ah
(3.18)
DX ( fr ak) ir Jr.
Oh e e Oh
Oh (fr
Ok2 ( ah
(3.19)
ak _ [10 0 0 1 0 L 0 0 2h LS 0 0 2Sh 0 0 2Lh S2 L2 3h2 ]T
Oh
The parameters 4)0 and X0 are estimated by substituting some approximate values of L, S
and h into equation (3.11).
Given a pair of conjugate image points (Lj, Sd and (L2, S2) from a stereo pair and a value
of h, one has
I 4)i , =4)0, + ah —Ah
a(1)2 $2 = S02 –ah •Ah
= 01 + • Ali ah
a X.2 = X02 + —21/2 •Ah ah
Where (L1, Si) and (L2, 82) are line and sample values of left and right image respectively.
Eliminating $ and X from above equation, one has the error equations as:
-194)2 8+1 ah ah ax2 ax, ah ah _
1=
iM1–[S01
A01 X02 (3.20)
34
kin 7 A02)
la2
ah ah ) = 001 -4°02
(( a12 (3.22)
[vi, 1
Where is error matrix. y)4.
Then the Least Square solution to Ni will be
Ah= ( ao 2 I3X
)2 2
'■
alp 2 vv. ah) ah ah
(3.21) (001-002)-w, aS2 akI) ah ah ) (X01 A02) WA.
al ))
ah ah ))
Where 144 and wx are weights for 4) and X .
Yang (2000) proposed an alternative correction with the above form as:
3.1.3 3D Reconstruction by Adjusting Elevation.
In addition to the reconstruction approach that was described earlier, a different
reconstruction approach could be derived by using a user driven approach (Hu, 2004). In
this approach, similarly to the previous approach, the reconstruction is initiated by
identifying a conjugate point pair in the stereo pair. The user will then retrieve the left
image coordinates of the selected point. Using an initial h value, the estimated ground
coordinates of the point can be computed using Equation (3.11). The derived ground
coordinates are then projected to the right image using Equation (3.2) and the user can
then review the projected location against the conjugate point location in the image. By
adjusting the h value of the point, the user can then control the location of the projected
point in the right image, and move it until it overlaps with the conjugate point location.
The iterations are therefore conducted interactively by repetitive re-projections (Fig 3.2).
35
(Hu, 2004) Figure 3.2: Interactive 3D reconstruction using h adjustment.
3.2 HIGH RESOLUTION SATELLITE IMAGERY
Needless to say, owing to the robust nature many High Resolution Imageries are provided
with RPCs. This section gives a general overview on the High Resolution Satellite Data
which provides RPC with their imagery product.
3.2.1 IKONOS
The IKONOS satellite, launched September 24th, 1999 by Space Imaging, has provided
the world with the first source of commercially available, high resolution satellite
imagery. The panchromatic sensor with 82-centimeter imagery provides intelligence
quality imagery both for military applications, as well as for civilian applications. The
3.28-meter multi-spectral sensor provides spectral-radiometric measurements for the
scientific community with promising applications in land-use classification,
environmental monitoring and resource development. Stereo imagery enables terrain and
3-D feature extraction and DEM extraction for planning, communications, and aircraft
safety.
36
Instead of delivering the interior and exterior orientation geometry and other physical
properties associated with physical IKONOS sensor, Space Imaging uses the rational
polynomial camera (RPC) model, to communicate the imaging geometry and image
vendors release image to users with only RPC coefficient. Some IKONOS imagery
products are shown in Table 3.1.
Table 3.1: IKONOS Standard Products.
Product Positional Accuracy Map Scale ' Stereo Option Price
US $ /km2 90 % CE RMS
1. Geo 15 m N/A N/A No 7 2. Geo ortho kit 15 m N/A N/A Yes (RPC*) 12
3. Standard ortho 50 m 25.0 m 1:100,000 No 20 4. Reference 25 m 11.8 m 1:50,000 Yes (RPC*) 29
5. Pro 10.2 m 4.8 m 1:12,000 No 29 6. Precision 4.1 m 1.9 m 1:4,800 Yes (RPC*) 55 7. Precision Plus 2 m 0.9 m 1:2,400 No 255
*Provides RPC with imagery, Refer to I m PAN image
Space Imaging delivers the stereo imagery pairs (Reference and Precision) with a rational
polynomial coefficient (RPC) camera model file. The RPC file provides camera data to
popular software packages for photogrammetric extraction of 3D feature coordinates,
DEM and orthophoto. Geo Ortho Kit also includes the RPC Camera Model.
3.2.2 OrbView-3
Built for Orbital Imaging Corporation (ORBIMAGE), OrbView-3 is supplying high
resolution optical imagery of the Earth The satellite carries a camera that takes one-meter
resolution panchromatic (black-and-white) and four-meter resolution multi-spectral
images of the entire planet and revisits locations in less than three days. Imagery from the
OrbView-3 satellite complements existing geographic information system (GIS) data for
commercial, environmental and national security customers. One-meter panchromatic
imagery clearly depicts houses, automobiles and aircraft and makes it possible to create
37
precise digital maps and three-dimensional fly-through scenarios. Four-meter multi-
spectral imagery provides color and infrared information that is particularly useful in
studying vegetation, making it ideal for use in environmental monitoring, forestry; and
agriculture, as well as to characterize cities, rural areas and undeveloped land. Some of
the OrbView-3 basic imagery is listed below in Table 3.2.
Table 3.2: OrbView-3 Basic Imagery Products.
Product Name Positional Accuracy Stereo Option Price
US $ /km2 90% CE RMS
1. Basic Express 60 m 60 m Yes (RPC*) 34.0
2. Basic Enhanced 25 m 44 m Yes (RPC*) 34.0
3. Basic
1:50,000 25 m 8 m Yes (RPC*) 43.0
1:24,000 12 m 5 m Yes (RPC*) 48.0
*Provides RPC with imagery, Refer to 1.0 m Stereo PAN Image
OrbView Basic Imagery Products are typically used by customers with the ability to
perform their own advanced image processing. OrbView Basic Imagery Products allow
the customer to orthorectify the Basic imagery product and perform three dimensional
feature extractions in addition to more routine image enhancements and processing.
3.2.3 QuickBird
Since the successful launch of DigitalGlobe's QuickBird satellite and the availability of
the data, QuickBird Imagery has quickly become a popular choice for large-scale
mapping using high resolution satellites. First, the satellite has panchromatic and multi-
spectral sensors with resolutions of 61-72 cm and 2.44-2.88m. QuickBird Products offer
customers a variety of options for accurate and timely imagery. DigitalGlobe offers
QuicicBird Imagery Products at three processing levels (Table 3.3) i.e.:
i. Basic Imagery with the least amount of processing (geometrically raw), designed
for customers desiring to process imagery into a useable form themselves,
38
ii. Standard Imagery with radiometric and geometric correction, and delivered in a
map projection, and
iii. Orthorectified Imagery with radiometric, geometric, and topographic correction,
and delivered in a map projection.
Table 3.3: QuickBird Basic Products.
Product Positional Accuracy Stereo Option Price
US $ ilun2 90% CE RMS
I. Basic Imagery 23 m 14 m Yes (RPC*) 22.5
2. Standard Imagery 23 m 14 m No 25.0
3. Ortho Ready Standard 23 in 14 m No (RPC*) 22.5
4. Orthorectified
1:25,000 12.7 in 7.7 m No 90.0
1:12,000 10.2 m 6.2 in No 50.0 (US only)
Custom Variable Variable No 40.0
*Provides RPC with imagery, Refer to 0.6 m PAN image
Basic imagery Products are the least processed of the QuickBird Imagery products. This
product, with the supplied attitude, ephemeris, and camera model information, is suitable
for advanced photogrammetric processing. Basic Stereo Pair Imagery products are
suitable for customers with a high level of image expertise and software, which is capable
of ingesting, processing and/or displaying stereo imagery.
Ortho Ready Standard imagery has no topographic correction, making it suitable for
orthorectification. It is projected to a constant base elevation, which is calculated as the
average terrain elevation. Standard Imagery has a coarse DEM applied to it, which is not
considered orthorectified.
3.2.4 CARTOSAT
CARTOSAT-1 is a state-of-the-art remote sensing satellite built by ISRO, which is
mainly intended for cartographic applications. It is the eleventh satellite to be built in the
39
Indian Remote Sensing (IRS) satellite series. CARTOSAT-1 carries two state-of-the-art
Panchromatic (PAN) cameras that take black and white stereoscopic pictures of the earth
in the visible region of the electromagnetic spectrum. The swath covered by these high
resolution PAN cameras is 30 Ian and their spatial resolution is 2.5 meters. The cameras
are mounted on the satellite in such a way that near simultaneous imaging of the same
area from two different angles is possible. This facilitates the generation of accurate
three-dimensional maps. The images taken by CARTOSAT-1 cameras are compressed,
encrypted, formatted and transmitted to the ground stations. The images are reconstructed
from the data received at the ground stations. Also CARTOSAT-2 and follow-up series
of satellites will acquire images in nadir and stereo modes using paintbrush technique.
The stereo pair of images can be used to derive 3-dimensional information about ground
objects. This essentially means that height/elevation information can be derived using
stereo images that is otherwise not possible using a single image. The sensor geometry
communicated to the end user using several mathematical models, and RPCs are one of
that.
3.2.5 SPOT-5
The SPOT satellite earth observation system was designed by the Centre National
d'Etudes Spatiales (CNES) in France, and consists of 3 currently operational satellites,
SPOT-2, SPOT-4 and SPOT-5. SPOT-5 is their newest and highest resolution satellite.
This satellite was launched in May 2002 and captures 5m panchromatic and 10m multi-
spectral imagery. The High Resolution Stereoscopic (HRS) instrument has two telescopes
and acquires stereo pairs at a 90-second interval, of 120-km swath, along the track of the
satellite, with a B/H ratio of about 0.8. This imagery can be post-processed to produce
2.5m panchromatic imagery, which can then be merged to create 2.5m color imagery.
The SPOT-5 satellite captures scenes of 60km x 60km in size (3600 sq. km), and thus can
cover large areas with pixels as small as .5m. The SPOT-5 sensor is also able to look off-
nadir allowing the satellite to capture imagery over the same area several times a week.
Like IKONOS and QuickBird, the SPOT-5 satellite is not switched on all of the time but
extensive archives over Australia currently exist. The imagery is captured in four bands,
40
however the blue band has been omitted in favour of a mid-infrared band, allowing for
greater vegetation discrimination to occur. Unlike the IKONOS and QuickBird satellite,
the imagery is captured in 8bit format.
3.3 A REVIEW OF SOFTWARE PACKAGES
High demand of high resolution satellite imagery in the civilian remote sensing
community and trend that some commercial high resolution satellite imaging data are
supplied with RPCs, prompted the photogrammetry software makers to incorporate the
RPCs based photogrammetric processing in their product. Many commercial digital
photogrammetric software packages have incorporated the Rational Polynomial
Coefficients for the photogrammetric processing like Orthorectification, 3D Feature
extraction, block adjustment, DEM extraction etc. Some of the softwares are briefly
discussed in this section.
3.3.1 RSI ENVI 4.2
RSI's ENVI is a revolutionary image processing system. From its inception, ENVI was
designed to address the numerous and specific needs of those who regularly use satellite
and aircraft remote sensing data. ENVI provides comprehensive data visualization and
analysis for images of any size and any type-all from within an innovative and user-
friendly environment.
The main module used for this work is DEM Extraction Module. The DEM Extraction
Module is newly introduced in ENVI version 4.2, enables to extract elevation data from
pushbroom stereo images, such as those coming from the ASTER, IKONOS, OrbView-3,
QuickBird, and SPOT satellites. It handles major photogrammetric processing based on a
set of rational polynomial Coefficients (RPCs) that are transparent to users i.e.:
• Orthorectification and Mosaicking
• 3D feature extraction and editing
• Digital elevation model extraction
41
• Support Satellite Model like ASTER, AVHRR, LANDSAT, SPOT and
RADARSAT.
• High Resolution Rigorous Models like IKONOS, QuickBird, SPOT-5,
Generic and RPC Model.
3.3.2 PCI Geomatica 9.1
PCI Geomatica (version 9.1) has very powerful capability to manage geo-
processing steps and achieve geospatial-processing goal. It integrates the latest in remote
sensing, photogrammetry, spatial analysis, and cartographic processing technology. It
supports many sensors photogrammetric processing including imagery containing RPCs.
The main module used for this work is OrthoEngine. It has the following functions:
• Triangulation
• Orthorectification and Mosaicking
• 3D feature extraction, Digital elevation model extraction and editing.
• Support many sensor models: Aerial photography
• Satellite Model like ASTER, AVHRR, LANDSAT, SPOT, RADARSAT,
IKONOS and QuickBird.
3.3.3 ERDAS Imaging 8.6
It provides its customers with an internationally unique program of modem systems for
high accurate 3D data capturing, visualization and modeling of space-related data. From
June 2001, ERDAS and LH Systems, one of the market leaders in remote sensing,
photogrammetry and GIS, belong to Leica Geosystems. ERDAS is a comprehensive
digital photogrammetry package for fast and accurate triangulation, orthorectification, 3D
feature extraction of images collected from various types of cameras and satellite sensors.
For this study, the main module is OrthoBase pro version 8.6, which supports various
camera/sensor models to extract a DEM and generate ortho-rectified images. Other
modules include Virtual GIS, Stereo Analyst, Data Prep, Viewer and Import, for helping
creating, modifying and presenting the DEM extracted. It also has these functions:
42
• Triangulation.
• Orthorectification and Mosaicking.
• 3D feature extraction and editing.
• Digital elevation model extraction.
• Support many sensor and satellite model like SPOT, IKONOS, QuickBird,
SPOT-5 and RPC model.
The features of these software packages for photogrammetric processing of high
resolution satellite data are tabulated below (Table 3.4).
Table 3.4: Features of Softwares for Photogrammetric Processing.
Company Software
Packages
3D-Feature
Extraction
Ortho-
Rectification
Block
Adjustment
DEM
Extraction
RSI ENVI N Y N Y
Leica
Geosystems
Erdas
Imagine
Y Y (1) Y
PCI
Geomatics
Geomatica Y Y (1) Y
(1) Single image resection with GCP but not multi-image block adjustment.
43
CHAPTER FOUR
EXPERIMENTAL DATA AND METHODOLOGY
This chapter deal with the methodology for 3D reconstruction using mathematical models
described in chapter three and procedure for DEM generation using different softwares.
Details about the IKONOS data used for the experimental is discussed in first section.
Method and algorithm used for 3D ground coordinates reconstruction using inverse and
forward RPC model is discussed in second section. Third section gives the methodology
and procedure for the DEM generation using ENVI. Next sections will deal with the
DEM generation using ERDAS Imagine OrthoBase and PCI Geomatica OrthoEngine.
4.1 EXPERIMENTAL DATA
IKONOS Geo-Ortho kit is used for this study. Geo-Ortho kit consists of panchromatic
ortho image, DEM and stereo pair of the area. The two IKONOS stereo images of 0.82
meter spatial resolution are provided in Geotiff format along with RPC and metadata file
in text format. The RPC file contains the 78 coefficients (Appendix A) and the metadata
(Appendix B) contains the GCPs for both the left and right image. Stereo pairs are
acquired on March 19, 2001, which covers an area of 4.76 Km2 and perimeter of 9045
meters. The image covers the area along the San Diego of California in United States of
America. The detail of both images is provided in table 4.1. The study area consist of
variety of ground profile ranging from undulating mountainous beach to plane ground
surface, high rise buildings to leveled parks and stadium. The IKONOS stereo images are
taken on the same orbital pass, one in a forward and the other in a backward direction.
This results both in a superior image quality because of a short time span between the two
images resulting in same lighting conditions and scene content.
44
Table 4.1: Detail of experimental data
Left Image
(po_120093_pan_0010000000.60
Right Image
po_120093_pan_0000010000.tif
Image Size 2364 x 2364 2364 x 2364
Projection RPC Geographic Lat/Lon RPC Geographic Lat/Lon
Pixel Size 0.000039 x 0.000004 Degrees 0.000023 x 0.000006 Degrees
Datum WGS-84 WGS-84
Upper Left Geo 117° 09' 53.47" W, 32° 43' 56.93" N 117° 09' 53.43" W, 32° 43' 56.98" N
Lower Right Geo
117° 08' 06.06" W, 32° 42' 26.64" N 117° 08' 06.02" W, 32° 42' 26.69" N
RPC file po_120093_pan 0010000000_rpc.txt po_120093_pan_0000010000_rpe.txt
4.2 3D RECONSTRUCTION METHOD
The mathematical model discussed in previous chapter three is outlined here as
algorithms and procedure for RPC based 3D ground coordinates reconstruction from the
2D image coordinates.
4.2.1 3D Reconstruction Procedure using Forward RPC Model.
Procedure for computing the object point coordinates (4) , h) from a pair of conjugate
points (Li, Si) and (1.2, 52) in the stereo image using "Forward RPC Model" is
summarized below and shown in figure 4.1.
Step (1). Determine the initial approximate value of the object space coordinates
00 , X0 , 170 ) by solving equation 3.10, by specifying the median values
of the three object coordinates ranges or by the reconstruction results from
the "Inverse RPCs", depending on the type of imagery.
Step (2). Given a pair of conjugate image points (Iq, Sl) and (L2, 5z) from a stereo
pair and the approximated value of 00 , A,„ ha ) , calculate the parameters
A, dz and w of equation 3.6.
45
A
Step (3). Calculate the correction d z =[dy d2 di?) by computing equation
3.7, and then add them to (4 , X0 , h0 .
Step (4). Repeat Step 2 until the specified maximum number of iterations has been
reached or 0 , X.0 , h0 ) all converge.
Start
/ Input ground coordinate offset and scale factors and ( LI, SI) and (L2,S2) conjugate points
Calculate approx. ground coordinates ( v) using equation (3 .10) with mean values of offset and scale factors and conjugate points
from left and right Image
Calculate the values using equation (3.1) with input ( br, V, 111) obtained from previous step.
Calculate A, dz and w using equation (3.6)
Calculate the value dz using correction equation (3.7)
Update the value of i by adding the value dz.
No
Value of dz less than threshold
/ De-normalizing the obtained values (using equation 2.2), one get the result (4), 2i,, h) corresponding to mean values (L, S) i.e.,
L=(Ll+L2)/2 and S—(S1+S2)/2
( End )
Figure 4.1: 3D ground coordinates reconstruction using Forward RPC Model.
TYes
46
Vincent Tao and Yong Hu (2002) show experimentally that the above procedure always
converged when appropriate initial values were given. When the initial approximate
values of 00 , X 0 , ho ) are obtained by solving equation 3.10 or set to be median values
of the ground coordinates ranges, eight iterations are usually enough to converge. When
the initial approximate values are obtained from the result of "Inverse RPC
Reconstruction", two iterations are usually enough.
4.2.2 3D Reconstruction Procedure using Inverse RPC Model
Now one can sketch the procedure for computing the object point coordinates from a pair
of conjugate points (Li, S3) and (L2, S2) in the stereo image. Workflow for the same is
shown in figure 4.2.
Step (1). Find an initial approximate value of elevation h. This can often be
specified as the median value of the elevation range (e.g., 0 for the
normalized elevation range [-1, +1]), median value of height offset and
scale or any value of h derived previously.
Step (2). Using equations (3.11 — 3.19) , compute the following values:
Op 7y , cr lc, elk, 1k, Pk)
Derivatives dT —ak CT -Dk , fr ak er ak 80 — and —, with known ah A Oh' ah Oh ah
image coordinates (L, S) for the both left and right image.
Step (3). Calculate the correction Ah using equation 3.21 or equation 3.22, and
then add Ah to h.
Step (4). Repeat Step (3) and update h every time with Ah , until the specified
maximum number of iterations has been reached, or h converges (e.g., the
absolute value of Ah is smaller than a specified threshold, set up based on
the elevation error).
47
Calculate all the parameters from equation (3.11 to 3.19) with inputs (L1, S1), (L2, S2) and h.
Calculate the elevation correction Abusing equation (3.21) or equation (3.22). Add Ah to h
Value of Ah less than threshold?
Step (5). Substitute the final h value into equation 3.11 together with image point
coordinates (L3, Si) and (L2, 82), then calculate the mean object point
coordinates from 0)015 A) and ($02, 2L02), = (4)0i +4°0/2 ,
A = (A-Di ± X02)/2 •
Start
Set an initial elevation value h (e.g. normalized between -1 to +1) or mean of offset and scale factors. Get ( L, S) conjugate points from both left and right image.
Yes
Final value of h
Calculate (4), A) with known values of h, (LI, Si) and (L2, S2)
End
Figure 4.2: 3D ground coordinates reconstruction using Inverse RPC Model.
48
The above procedure was described in Yang (2000) with the correction equation 3.22
being used in Step 3. Vincent Tao and Yong Hu (2002) show experimentally that the
result with an improved accuracy can be obtained by using the correction equation 3.21
rather than equation 3.22.
4,3 METHODOLOGY OF DEM GENERATION USING ENVI.
The process of creating DEMs from stereo imagery is somewhat complicated, but can be
automated. The ENVI DEM Extraction Module introduced in version 4.2, provides user
with fast and user-friendly environment for epipolar images building, stereo 3D
measurement and DEM generation. ENVI takes stereo imagery from pushbroom sensors
and creates DEMs with or without ground control points, requiring only minimal
guidance from the user. The DEM Extraction Module supports the data coming from
pushbroom stereo images, such as those coming from the ASTER, IKONOS, OrbView-3,
QuickBird and SPOT satellites. It is important that the imagery have associated rational
polynomial coefficients (RPCs) which contain necessary information about the sensor
model. In addition, RPCs are used in tie point generation and to calculate the stereo
image pair relationship.
The DEM extraction process requires a stereo pair of images containing RPC positioning
from either an along track or an across track satellite acquisition. Along track stereo
images are acquired on the same orbital pass by a satellite which usually has more than
one sensor looking at the Earth from different angles. Across track stereo images are
those taken by the same sensor on multiple orbits. Extraction of DEMs from stereo
images typically involves the following steps: sensor camera modeling, auto tie-point
collection, creation of epipolar images, image matching, DEM Geocoding, and DEM
editing (Fig. 4.3).
Sensor Camera Modeling. In the sensor camera modeling step, the goal is to
construct the geometrical relationship between 2D image space and 3D ground
space. In ENVI the relationship between image space and ground space is
modeled through RPCs. This means that ENVI uses the Rational Polynomial
49
Coefficients (RPC) provided with the stereo images, or computed by ENVI based
on the rigorous sensor camera model (ASTER and SPOT). In ENVI's DEM
Extraction Module, RPCs are required for IKONOS, ORBVIEW-3 and QuickBird
data, and can be computed on the fly for SPOT and ASTER data.
ii. Auto Tie Point Collection and Validation. ENVI implements a relatively robust
algorithm to collect tie points automatically. It first extracts a number of evenly
distributed distinct feature points from the left image, and then applies an area-
based matching technique to find their conjugate points in the right image, while
at the same time taking any geometric distortions between the two images into
account. ENVI also provides automatic prediction capability, which allows for
automatic determination of the conjugate point in the other image provided that
the user gives an image point in one image.
Creation of Epipolar Images. Epipolar geometry represents the fact that a
ground point and the two optical centers of the stereo images (or in the case of
Pushbroom sensors, the optical centers of the particular scan lines containing the
pixels representing that point) lie on the same plane. This means that a given point
in one image and its conjugate point in the second image must lie on a known line
in the second image. This knowledge can be used for creating epipolar images in
order to reduce the search space for finding corresponding image points during
automatic image matching. Epipolar images are stereo pairs in which the left and
right images are oriented so that ground features have the same y-coordinates on
both images. Using epipolar images converts the two-dimensional image
correlation problem to one dimension, thus greatly increasing the speed of image
matching as well as the reliability of matching results.
iv. Image Matching. Image matching enables the software to find conjugate points
on both left and right image that correspond to the same ground feature. The
output of an image matching procedure is typically called a parallax image, which
stores the x-coordinate difference (along epipolar lines) between the left and right
images. It is the parallax image that is used to build a DEM. Thus, the quality of
image matching largely determines the quality of the output DEM.
Compute RPCs Based on Sensor Model
Auto Tie Point Collection and Validation )iDEM Geocoding and
Edi ing DEM )
Stereo Image Pair
GCPs
v. DEM Geocoding. Typically the DEM generated at this stage is not in the
projection system and output pixel spacing that is eventually desired. Therefore
the output DEM from the epipolar projection is re-projected into the desired
output map projection and resolution. If GCPs are provided, the absolute
orientation of the computed terrain model can also be established in this step.
vi. DEM Editing. Upon the completion of automated DEM extraction, the results
often benefit from manual review and editing to remove errors. ENVI provides a
number of editing methods including replace with constant value; replace with
mean value, smooth filter, median filter, noise removal, triangulate, and thin plate
spline smooth.
-‘\
(Shippert and Yang, 2006)
Figure 4.3: The workflow for generation of DEM data from stereo imagery in ENVI.
Fundamental for DEM generation as described by the ENVI in the previous section is
almost same for most of the software, but the procedure is somewhat different from each
other. In the next section, procedure for the DEM generation is discussed in detail with
the working flowchart.
Create Epipolar Images _2
Image Matching
51
4.3.1 ENVI's Dem Extraction Module.
The DEM Extraction Module walks through nine steps to extract a DEM. The module
allows to step forward, backwards, and to save the workflow at any step so that one can
continue at a later time. The functionality provided in the nine steps is also available to
run separately from the module using the Topographic menu on the ENVI main menu
bar. The module workflow is illustrated in Figure 4.4, and the steps are outlined here.
Step (1). Selecting the Stereo Image Pair: Select the left and right images. When the
Stereo Image pair has been selected, the RPCs are computed and the Scene
Elevation in Meters values are filled in with the data or user can supply the
minimum and maximum elevation of the region.
Step (2). Selecting Ground Control Points: This step is optional. User can select the
source for the Ground Control Point data (if it is available) for better accuracy
or can skip this to go to 4th step.
Step (3). Viewing, Adding, Editing GCPs: Edit, add, and view GCPs. User can
choose to read in a GCP file and edit it, or manually enter the GCPs in Step 2.
Step (4). Collecting Tie Points: Select the source of the tie points required for DEM
extraction. User can have them automatically generated by the module, load
an existing tie points file, or choose to enter the tie points manually. For this
dissertation work, it is set to automatic generation and different number of tie
points are generated to check the accuracy.
Step (5). Viewing, Adding, Editing GCPs: Edit, add, and view tie points to minimize
the y parallax.
Step (6). Generating Epipolar Images: Create and save the left and right epipolar
images.
Step (7). Setting Output DEM Projection: Set the projection system, the output DEM
pixel size, and the number of rows and columns in the output. ENVI
automatically extract projection information from the RPCs and set default
value for output.
52
Step (8). Selecting DEM Extraction Parameters: Define minimum correlation,
moving window size and terrain detail, and specify where to save the DEM
result.
Step (9). Examining the DEM Result: Display the DEM result. User may use the
DEM Editing Tool to edit the displayed the result.
Step 1 Input Stereo Image Pair /
\ Select G CP P air
Step 2 Edit GCPs?
0
r. 'Yes 1
Step 3
r
Edit GCPs
• 4:4 Select Tie P oint Options
Step 4 Edit Tie Points?
No
Yes Step 5
Step 6
I Step 7
r Step 8
\ Edit Tie Po ints
\ Select Epipolar P arameters
\ Select DEM Projection Parameters
\ Select DEM Extraction Parameters
r Examine DEM Results
Step 9
Edit DEM?
'Yes
Edit DEM
C Done
Figure 4.4: DEM Extraction Workflow Diagram
53
4.4 ERDAS IMAGINE ORTHOBASE
In this section of the methodology, steps to extract DEM using ERDAS Imagine
OrthoBase pro (version 8.6) are presented. The workflow of DEM generation is shown in
figure 4.5.
Step (1). Model Setup: Create a new OrthoBase project and create a new block file
with the IKONOS data. The Model setup dialog begins the next series of steps
wherein specify the sensor model to apply to the block file. In this work,
IKONOS Geometric model is selected from the list which has a unique model.
The next step of Block Property Setup dialog opens and displays the
Reference System information. For IKONOS data, the projection is always
initially set to Geographic (Lat/Lon). Likewise, the datum is always set to
WGS 84. The projection can be changed by the Set Projection option. The
next in Block Property Setup is Reference Units Section in which horizontal
and verticals units are to be defined. For IKONOS data, the reference units are
default i.e. horizontal in degrees and vertical units in meter.
Step (2). Input Data: Next series of step opens the OrthoBase Dialog. From the Add
Frame option, select the IKONOS stereo images by using the TIFF format
from the drop-down menu. The associated RPC file must be in the same
folder. ERDAS automatically search and read the RPC file if it is within the
folder. If the RPC file is not there in same folder, ERDAS will prompt the
user to give the path of associated RPC file.
Step (3). Edit Properties: Open the Frame Properties dialog box and check the Left
and Right file and the associated RPC file. Change the files if there is any
discrepancy. Minimum and maximum elevations are derived defaults from the
metadata files that accompany IKONOS images.
Step (4). Tie Points Collection: Open the Point Measurement Tool. It is designed to
collect GCPs and tie points that are common to two images so that the images
can be correlated. Collect some (5-10) tie points manually and then run
automatic tie points generation. Automatic tie point generation will not run
54
without some initial tie points. Specify the number of tie points to be
generated and the size of search window and the threshold. Step (5). Triangulation; Now select the Triangulation properties and click the
checkbox of refinement with Polynomials and specify the polynomial order.
Perform the triangulation on clicking on Run Triangulation. This will give the elevation at the tie Points with RMS errors.
Step (6). DEM Extraction: Now select the DTM Extraction dialog from Process and
open its Property dialog box. Select output DTM type as DEM and specify the
output DEM file. Select the output pixel size or select the default values. Click on the button 'RUN' to run the DEM extraction process.
Create New Project
Define the output file projection and Units. Select Sensor Mo del
\ Select input data i.e. left and right stereo pairs in Tiff format and the RP Cs file in text format
Collect tie points manually Define automatic tie points properties
Run automatic tie points generation
ir
\
Define Triangulation Properties
/ Perform Triangulation.
\ Run the automatic DEM generation from stereo pairs
Define DEM Properties
.11 ( END
/
Figure 4.5: Procedure for DEM Extraction using ERDAS IMAGINE OrthoBase pro..
55
4.5 PCI GEOMATICA ORTHOENGINE
PCI Geomatica OrthoEngine's automatic DEM Extraction module allows creating Digital
Elevation Models (DEMs) from stereo air-photos and stereo images. Image correlation is
used to extract matching pixels in two overlapping images and then use the sensor
geometry from a computed math model to calculate x, y, and z positions. Automatic
DEM extraction allows you to batch epipolar generation, batch the DEM extraction
process, geocode DEMs, and create absolute or relative DEMs. The process of DEM
generation is very straightforward and can be carried out by very little knowledge
background. The procedure is shown in figure 4.6 and it consists of the following steps:
Step (1). Project Setup: Create a new project with RPC Math Model using the
Standard Rational Functions model and active the option of input GCPs/ Tie
Points from the IKONOS file. In the dialog box 'Set Projection' OrthoEngine
prompts you to set up the projection information for the output files, the
output pixel spacing, and the projection of your GCPs. Enter the appropriate
projection information for your project. For the data used in this dissertation,
the output projection is defined as per projection defined for the Orthorectified
image provided by the data provider.
Step (2). Data Inputs: Now select the Data Input option from the drop-down menu of
the OrthoEngine. Select the left and right stereo pairs from the option 'New
Image'. It should be noted that the image pairs and the RPC text file should be
in same folder.
Step (3). Collect GCPs and Tie Points: Now go to 'Collect GCPs and Tie Points'
option and from that select automatic tie points option to perform automated
tie points generation based on image matching. It will perform tie points
generation and gives a residual report as output. For the data used here, no of
tie points generated are 100.
Step (4). Create Epipolar Images: On the OrthoEngine window in the Processing Step
list, select DEM from Stereo and click the Create Epipolar Image icon. Under
56
Epipolar Selection choose Maximum Overlapping Pairs and set the Minimum
Percentage Overlap to an appropriate value for your project. This will allow
OrthoEngine to automatically select the right and left images for the epipolar
pair. Set the Working Cache, the Down Sample Factor and The Down Sample
Filter as desired. In this step images are transformed so that parallax effect
exists only in x direction.
Step (5). Automatic DEM generation: On the OrthoEngine window in the Processing
Step list, select DEM From Stereo and click the Extract DEM automatically
icon. Select the Epipolar pair from the Stereo Pair Selection table. Enter a
Minimum and Maximum Elevation noting that if you are working with a
Specific Model project. Choose the DEM detail desired from the drop-down
list. Set the Pixel Sampling Interval based on the desired resolution of the
output DEM.
Step (6). Edit the DEM: Click the manually edit generated DEM icon from the DEM
from Stereo Processing Step selection. Load the Epipolar DEM and edit the
failed pixels in the DEM.
Step (7). DEM Geocoding: Once the DEM has been edited, return to the Automatic
DEM Extraction window and select Create Geocoded DEM. Browse to the
folder where the DEM will be saved and type a filename for the Geocoded
DEM.
57
Create New Project Select Math Model
Define the output file projection.
11
Select input data i.e. left and right stereo pairs in Geotiff format and the RP Cs file in text format
lir
Collect tie points automatically Give the no of tie points to be generated
III
Create Epipolar image from stereo pairs Specify the Left and Right images.
III
Run the automatic DEM generation from stereo pairs Provide the approx. min and max. elevation (It can be height
offset and scale value)
III
DEM Editing and Geo coding
/
END
Figure 4.6: Procedure for DEM Extraction using PCI Geomatica OrthoEngine.
58
CHAPTER FIVE
RESULT AND DISCUSSION
5.1 RAW DATA
The unrectified stereo image pairs, along with RPC are used as input for the DEM
extraction. Both the stereo pairs are shown in Fig 5.1 and their RPCs are provided in the
appendix A.
For the better result discussion, the raw stereo image is categories into five regions as
Area of Interest as shown in Fig. 5.2. The first region covers the left upper part of the
image. This part covers the Downtown area of San Diego with high rise buildings. The
density of high rise buildings is more in this part.
The second region covers the right upper of the image. This part covers with an area of
high ground level with a flyover crossing over the road. San Diego Aerospace Museum is
also situated in this part. This part is at high elevation.
The third region consists of right lower part of the image. This area is rocky with
undulating ground. Beyond of this part is Imperial Beach (not seen in image) of Pacific
Ocean. San Diego Convention Centre is also in this area opposite the beach.
The fourth region covers the left lower part of image. This region consists of low rise
buildings with several road networks and flyovers. This area is at low elevation.
The fifth and last region covers the central part of the image. The San Diego. QUalcomm
Football Stadium and the multilayer flyover is the area of interest in this region.
59
(a): Left Image (b): Right Image Figure 5.1: IKONOS Stereo Pair
Figure 5.2: IKONOS Stereo Image with Regions of Interest.
60
An anaglyph visualization made from the IKONOS stereo pair is shown in Fig. 5.3 for
the region 1. The x parallax can be observed clearly in the image. Selection of tie points
in this region must be done very carefully to minimize the y parallax. Higher density of
tie points in this region can add to the accuracy of DEM. IKONOS stereo images are
taken on the same orbital pass, one in a forward and the other in a backward direction.
This results both in a superior image quality because of a short time span between the two
images resulting in same lighting conditions and scene content. The stereo anaglyph (Fig.
5.3) clearly justifies this statement.
Figure 53: Stereo Anaglyph of IKONOS stereo pair.
5.2 DEM RESULTS
Evenly distributed tie points are taken for the DEM generation in all the softwares.
Automatically generation of tie points were carried and then it is edited to minimize the
parallax. Number of tie points generation in ERDAS and Geomatica is limited, but ENVI
61
can generate as many as one wants (Depends on Computer configuration). Fig: 5.4 show
the tie points generated in ENVI. The number of tie point is 200.
Figure 5.4: Selected Tie Points.
There are 200 tie points are generated in ERDAS and 100 in Geomatica. Geomatica and
ENVI provide full image matching support and thus can generate tie points
automatically, but in ERDAS this capability is absent. First some tie points has to be
selected manually, then automatic tie points generation can be perform. Different sets of
tie points are generated in ENVI starting from 100 to 1500 to check the accuracy. But the
results shown by the different sets are almost same, except some areas in region 1, which
show vertically exaggerated profile. This is due to high parallax and density of high rise
buildings. DEM generated using different softwares are shown below (Fig. 5.5). On
visual analysis DEM generated using ERDAS and DEM provided with IKONOS data is
same in the sense of clipping area. DEM generated by Geomatica (Fig. 5.5 d) shows
some failed pixel values in the first region, this is because of high rise buildings in the
proximity which cause high parallax.
62
L
(a): Sample Data (b): RSI LA VI
(c): ERDAS Imagine (d): PCI Geomatica
Figure 5.5: DEM generated using different Softwares
The basic statistics of the DEM generated using different softwares are listed in table 5.1.
The minimum and maximum elevations in the DEM with their mean and standard
deviation are compared in the table. The result given by ERDAS is almost similar to that
of the sample DEM provided with Geo-Ortho kit. There is slight difference in the results
given by ENVI and Geomatica, this is because during the DEM generation process, the initial values of minimum and maximum elevation is provided to Geomatica as input.
63
The minimum and maximum elevation values shown in table 5.1 corresponding to Geomatica is provided by user. Taking these initial elevation values, Geomatica proceed
further for DEM generation. In case of ENVI, it takes the height offset and scale factors
from the RPC file and calculate the minimum and maximum scene elevation.
Table 5.1: Mean and Standard Deviation of DEM.
S. No DEM Source Elevation Range Mean Std deviation
Minimum Maximum
I. Sample Data -29.807718 66.452492 3.227595 24.55971
2. ENVI -50.0 77.0 -0.380813 25.583584
3. ERDAS -28.767096 64.477707 4.193706 24.658877
4. Geomatica -30.0 80.0 -6.985711 26.041936
The RMS errors are calculated for the DEM results given by different softwares with the
sample DEM data provided with Geo-Ortho kit. Evenly distributed fifty points are
selected from the sample DEM and corresponding line, sample and elevations values are
recorded manually (Appendix C). Corresponding to the selected line and sample values,
elevation values are picked manually from the DEM generated using ERDAS, ENVI and
Geomatica. RMS errors are calculated from the sample data elevations and the observed
elevations from the DEM given by softwares. Errors are also calculated between the
results given by softwares. Table 5.2 shows the RMS errors between the different results.
The variations in elevation obtained from the different sources are plotted in Figure 5.6.
Table 5.2: RMSE of the elevations given by different softwares.
Sample Data ENVI ERDAS Geomatica
Sample Data - 6.835854 6.589727 8.303025
ENVI 6.835854 - 5.504751 8.081811
ERDAS 6.589727 5.504751 - 7.996158
Geomatica 8.303025 8.081811 7.996158 -
64
Figure 5.6: Plot showing the elevations of the DEMs.
53 DENSITY SLICE
After the DEM generation, Density slicing for all the DEMs is carried out for the better understanding of the result and to draw conclusion from them. Fig. 5.7 shows the density slice for the DEM generated using ENVI, ERDAS and Geomatica. Density slice of sample DEM is also carried out to compare the results as obtained from the softwares. The elevation values are distributed into eight slices and each slice is represented by different color. The density slice color ranges are shown in table 5.3. Same elevation range and color slice is used for all the DEMs. Visual interpretation of the density slice reveals that the result obtained from ERDAS and IKONOS data is same in the sense of clipping area, resolution and elevations. On closely examine, DEM generated using ENVI shows the better results. In the case of ERDAS, density slice is some blurred but in ENVI's case (Fig. 5.7 b), even the Roads, streets and houses can easily be distinguished. Density slice of DEM from Geomatica is somewhat similar to ENVI, but shows some failed pixels value as shown in DEM (white areas in the left lower region Fig. 5.7 d).
65
Here it is to be noted that the maximum elevation in the image is 66.4525 meters and the minimum elevations is -29.8077 meters. These elevations are ellipsoidal height and to
convert it in to orthometric heights one needs to add geoid height of the image area.
Table 5.3: Defined Density Slice Ranges.
Serial No.
elevation Range Color Slice
(-29.8077 — 66.4525)
From To Name Color
1. -29.8077 -17.7752 ecT---
I r17.7752 1
-5.7427 Green
3. 1 I
1-5.7427 1
6.2899 Blue
k. I r
6.2899 18.3224 Yellow
S. 183224 303549 , I
i 130.3549 I42.3874
I Cyan
1 6. a---;e7ita
7. (12.3874 1154.4200 Maroon
8. 54.4200 66.4525 Sea Green
5.4 ORTHORECTIFICATION
After the completion of DEM, the image is orthorectified using the same softwares based on RPC. The RPC and the tie points generated for the DEM extraction is used here for
the orthorectification of the raw stereo image. All the three softwares provide full support for the RPC based orthoreetification.
66
For the 3D surface view of the image using DEM, it needs to be orthorectified. Ortho
image produced by ERDAS and ENVI are almost similar to that of the ortho image provided with the IKONOS Geo-Ortho kit (Fig. 5.8). Ortho image given by Geomatica is somewhat different in resolution and orientation but gives the same result when 3D surface view is generated.
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67
(b): RSI ENVI (a): Sample Data
(d): PCI Geomatica (c): ERDAS Imagine
Figure 5.8: Ortho Image generated using different Softwares
5.5 3D SURFACE VIEW.
For further analysis, 3D surface view is generated using the DEM and the ortho image.
The 3D surface view is generated in ENVI and the result from all the sources is almost
same. In the first region of the image (Fig 5.9), the profile is undulating with high rise
68
buildings in more numbers. This area of San Diego is known as Downtown, where most
of the business and commercial setup is located.
Figure 5.9: 3D surface view of region 1.
Figure 5.10: 3D surface view of region 2.
In the second region of interest (Fig 5.10), San Diego aerospace museum is located. It is cylindrical in built which can be easily seen in this area. One road crossing is their, from which a flyover is crossing over it.
69
The third region of the image is rocky, and it is highly undulating as seen in the Fig. 5.11
and ahead of this is Imperial Beach. The picture of Imperial Beach in the Appendix E
clearly shows the undulating nature of this area.
Figure 5.11: 3D surface view of region 3.
There is not so much area of interest in region four (Fig 5.12), but several network of
roads and passing of flyovers over it can be clearly depicted in the image. Well defined
streets and roads can be clearly seen in 3D.
In the fifth region of the image (Fig 5.13), San Diego Qualcomm Football stadium can be
seen. This stadium looks like a 'bowl' with flat base and vertical corners. This stadium is
in horse-shoe shaped, it is often refer as 'Bowl Stadium'. The picture of the Qualcomm
stadium in Appendix D clearly justifies this analysis.
70
Figure 5.12: 3D surface view of region 4.
Figure 5.13: 3D surface view of region 5.
Fig 5.14 shows the full 3D surface view of the image generated by DEM draped over the ortho-image given by ENVI.
71
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72
5.6 3D VVIREFRANIE
Next analyses of the results are carried out by plotting the ground coordinates obtained
from the different Softwares using a contour and DEM plotting software 'Surfer'.
Elevation corresponding to 200 tie points is picked manually from the ENVI DEM results
and then it is plotted against the line and sample values. The profile of the 3D Wireframe
(Fig. 5.15) obtained from the plotting is similar to the profile as obtain from the 3D
surface view of the image and DEM.
Figure 5.15: 3D Wireframe using ENVI points.
Figure 5.16: 3D Wireframe using ERDAS tie points.
73
The next Wireframe is generated using the triangulation report given by ERDAS
OrthoBase. It gives the ground coordinates (i.e. Lat/Lon and elevation) after performing
the triangulation. The facility for this report is not available in ENVI. Result obtained by
plotting 3D Wireframe (Fig. 5.16) is similar to that obtained from ENVI and from 3D
surface view of image and DEM.
Next 3D Wireframe is genereated using results obtained from Geomatica OrthoEngine.
Two sets of tie points are taken from the OrthoEngine and elevations are plotted against
the corresponding latitude and longitude. Fig. 5.17 shows the 3D generated using 500
points, and Fig. 5.18 shows the 3D generated using 5000 points from the result given by
OrthoEngine. 3D Wireframe obtained from 500 points is some similar to that of the
ENVI and ERDAS. 3D plotted with 5000 points is more accurate than those obtained
earlier. The high rise buildings in the region 1 can be easily depicted in that region. Many
conical projections are shown in that region which represents elevation of the high rise
buildings in that area. The 'Y' shaped road in the third region is clearly distinguished
with undulating grounds. Results of region 2 and 4 also make sense as compared with the
sample image.
Figure 5.17: 3D Wireframe by Geomatica tie points (500 points).
74
It can be said that the 3D Wireframe plotted by 5000 points using the results obtained by
the OrthoEngine is more descriptive.
Figure 5.18: 3D Wireframe by Geomatica (5000 points)
5.7 SOFTWARES PERFORMANCE ANALYSIS
Performances of all the three softwares are checked for their speed, accuracy and user
friendly. DEM generation and orthorectification process is carried out on the same PC to
check the time taken for different process.
Data Input: In term of data input, ENVI provides fast and easy selection of data, there is
no need to specify the sensor types, projection system. Data input is similar for all types
of sensor model (RPC). At the other hand, in ERDAS and Geomatica sensor type and
output file projection has to be specified.
Tie Points Selection: For the step of tie points selection, ENVI generated it
automatically by image matching techniques and it is the same case with Geomatica. But
this facility is absent in ERDAS. First few initial tie points has to be selected then
automatic tie points generation can be performed. Number of tie points selection is
limited in Geomatica and ERDAS, but it is not the case with ENVI. Although all the
75
three softwares provides tie points editing tool; but ENVI tie points editing tool is more
versatile. ENVI gives the error rank of each and every tie points in increasing order, thus
anyone can edit the tie points with higher rank.
Epipolar Image Generation: Epipolar image generation capability is available in ENVI
and Geomatica. First these softwares build epipolar images and then perform parallax
image generation to extract elevation from the parallax image. In case of ERDAS, it
performs triangulation using the stereo pair and selected tie points and gives the ground
coordinates as output.
DEM Extraction: Using the triangulation results, ERDAS proceeds forward for the
DEM generation. In this task ERDAS takes very few seconds of time and gives the DEM
as output. ENVI and Geomatica at the other hands, first build the epipolar and then
proceed forward for the DEM generation. At this stage, Geomatica prompt the user to
give scene minimum and maximum elevation as input to proceed further which may be
matter of confusion for non- technical and inexperienced users.
DEM Editing: All the three softwares provide support for DEM result and editing, but
on using the tools one can observe that the Dem editing tool of ENVI is more versatile. It
provides a number of region selection tools and interpolation techniques.
As the accuracy of result is concerned, ERDAS provides better results as compared to
that of ENVI and Geomatica as shown in Fig. 5.5 and Fig. 5.7. the mean and the standard
deviation of the DEM generated using ERDAS is close to the mean and standard
deviation of the sample data DEM (table 5.1). The RMS error is minimum for the
elevations from the DEM generated by ERDAS (table 5.2).
76
CHAPTER SIX
CONCLUSION AND FUTURE SCOPE
6.1 CONCLUSION
The RPC framework provides a comprehensive photogrammetric solution in a variety of
applications. It offers greater flexibility and enables non-technical users to exploit the full
potential of high-resolution imagery. Using this framework, users are able to overcome
two traditional barriers in photogrammetric processing, namely the requirement for a
physical sensor model and the requirement of providing GCPs in order to derive the
sensor orientation. This dissertation report reviewed several DEM extraction techniques
from stereo pairs based on RPC model. Several photogrammetric software pacicages are
used for the DEM generation and their performances are examined. It is observed from
above work that extracting a DEM automatically from IKONOS data is a relatively
straightforward procedure. Stereo pair of images is still the main source for DEM
extraction with the highest accuracy of elevation.
The major objective of this dissertation to investigate the accuracy of Rational
Polynomial Coefficients based DEM generation through different photogrammetry
mapping softwares, and to compare the DEM output results between these commercial
software packages are achieved.
The four specific objectives for this dissertation are concluded as:
• The Rational Polynomial Coefficients sensor model provides full accuracy as a
replacement for Rigorous Sensor model.
• The modeling of procedure and algorithms for the 3D ground coordinates
reconstruction from 2D image coordinates using RPC approach have been
elaborated.
77
• Results of the DEM generated using different softwares are shown with basic
statistics. The RMS error between the sample data and the DEM generated using
softwares are found to be in between 6.589727 to 8.303025.
• Versatility and limitation of different Softwares for DEM generation using RPC
Model have been studied and discussed.
Currently, the implementation of the RPC model scheme and its adaptation in practice
heavily depends on data vendors. As users cannot generate their own RPCs, their ability
to adopt and utilize the RPC model framework depends on the availability of RPCs that
are supplied with the raw imagery data. It should also be noted currently there is no
single standard in RPC representation and exchange (for example, file format).
6.2 FUTURE SCOPE
The current work here serves as a motivation and explanation for the ongoing work on
the RPC based photogrammetric exploration for block adjustment, 3D feature extraction,
DEM generation and orthorectification. RPC model has a big domain of application from
modeling of aerial camera to satellite sensors. Aerial camera modeling using RPC can be
explored and may be applied to carry different photogrammetric tasks.
RPC has a very good scope and big domain and the study conducted here is only a part of
it. The study conducted here was purely for DEM generation, and it can be extended for
other photogrammetric tasks like 3D feature extraction which is field of interests these
days. Height calculation of targets from single image can also be tried using RPC
approach.
The 3D ground coordinates reconstruction algorithm modeled in chapter four can be used
for the development of software. This approach will help to save the money spent to buy
sophisticated and costly photogrammetric softwares. Better GUI can be created for the
interactively selection of tie points or image matching techniques can be incorporated
into it for the same.
78
REFERENCES
1. Baltsavias, E., Pateraki, M, and Zhang, L. 2001. "Radiometric and geometric evaluation of IKONOS GEO images and their use for 3-D building modeling", Proceedings of ISPRS Joint Workshop "High Resolution Mapping from Space", 19-21 September, Hanover, Germany.
2. Cheng, P., and Toutin, T. 2000. "Orthorectification of IKONOS Data Using Rational Function", Abstract, Proceeding of ASPRS Annual Convention
(CD-ROM), 22-26 May, Washington D.C., American Society for Photogrammetry and Remote Sensing, Bethesda, Maryland, unpaginated.
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82
APPENDICES
APPENDIX A
Rational Polynomial Coefficients for Left and Right Images Provided with IKONOS Geo-Ortho kit.
RPC FOR LEFT IMAGE LINE OFF: -W02641.00 Pixels SAMP_OFF: +001653.00 pixels LAT OFF: +32.72160000 degrees LONG OFF: -117.13360000 degrees HEIGHT OFF: +0036.000 meters LINE_SCALE: 4-007001.00 pixels SAMP_SCALE: 4-003510.00 pixels LAT_SCALE: +00.01990000 degrees LONG_SCALE: +000.07560000 degrees HEIGHT SCALE: +0223.000 meters LINE NUM_COEFF _1: -4.827884622965599E-04 LINTE_NUM_COEFF_2: +9.919778825814262E-01 LINE NUM_COEFF 3: -6.310213031846629E-02 LINE NUMCOEFF4: -1.289366538044707E-02 LINE_NUM_COEFF_5: +1.363129980154946E-03 LINE NUMCOEFF6: +1.941449974041343E-03 LINE NUM_COEFF_7: -1.438292800314764E-04 LINE NUM_COEFF_8: -6.522834153278603E-04 LINE NUMCOEFF9: -7.539867391479586E-05 LINE NUM_COEFF_10: -2.461780690878912E-05 LINE_NUM_COEFF _11: +2.266029046929076E-07 LINE_NUM_COEFF12: +3.029355459252911E-05 LINE_NUM_COEFF_13: -8.208733313727461E-06 LINE_NUM_COEFF_14: -3.455639558340569E-06 LINE_NUMCOEFF_15: +9.845372797691749E-06 LINE NUM_COEFF_16: +4.866811586205718E-07 LINE NUM_COEFF_17: +2.201510121977653E-07 LINE NUM_COEFF_I8: -7.198975948135676E-06 LINE NLTMCOEFF19: +1.037253059300070E-07
RPC FOR RIGHT IMAGE LINE_OFF: +002727.00 pixels SAMP OFF: +001360.00 pixels LAT_OFF: +32.71870000 degrees LONG_OFF: -117.13340000 degrees HEIGHT OFF: +0036.000 meters LINE_SCALE: +006831.00 pixels SAMP_SCALE: +001959.00 pixels LAT_SCALE: +00.01820000 degrees LONG_SCALE: +000.07090000 degrees HEIGHT SCALE: +0223.000 meters LINE_NUM_COEFFJ: -9.690675098855092E-04 LINE_NUM_COEFF_2: +9.534894322005902E-01 LINE_NUM_COEFF_3: -5.915772236938047E-02 LINE NUM_COEFF_4: -1.320699359990742E-02 LINE NUM_COEFF_5: +4.119772912892072E-03 LINE NUM_COEFF_6: +2.445291808505743E-03 LINE_NUM_COEFF_7: -2.123340844353039E-04 LINE NUM_COEFF_8: +1.236617346054952E-03 LINE NUNI_COEFF_9: -2.528930479105435E-04 LINE NUM_COEFF_10: -3.356901234830760E-05 LINE NUM_COEFF_11: -8.499037700126357E-07 LINE NUM_COEFF_12: +8.491119607250386E-05 LINE NUM_COEFF_13: -3.586568223053857E-05 LINE_NUM_COEFF_14: -9.385852637774035E-06 LINE_NUM_COEFF_15: -7.741978400333158E-06 LINE_NUM_COEFF 16: +2.265462728737396E-06 L1NE_NUM_COEFF_17: +6.177916724573950E-07 LINE_NUM_COEFF 18: -1.584595049046643E-05 LINE NUM_COEFF 19: +6.149336595876931E-07
LINE NUM COEFF 20: -1-4.701193538111520E-08 LINE_DEN_COEFF_1: +1.000000000000000E+00 LINE_DEN_COEFF2: -8.114204844995470E-04 LINE_DEN_COEFF_3: +1.544559529507819E-03 LINE_DEN_COEFF 4: +1.580448743945071E-03 LINE_DEN_COEFF5: +1.149114667920926E-05 LINE_DEN_COEFF_6: -6.849663459700063E-06 LINE_DEN_COEFF_7: -2.593350212636785E-07 LINE_DEN_COEFF_8: +3.679645621115528E-05 LINE_DEN_COEFF_9: -6.553681868971766E-06 LINE_DEN_COEFF_10: -4.274883166358692E-06 LINE_DEN_COEFF_I 1 : -5.072946137815120E-09 LINE_DEN_COEFF_12: -9.636332372378258E-09 LINE_DEN_COEFF_13: +2.417687039685177E-09 LINE_DEN_COEFF_14: +2.691238294127357E-09 LINE DEN COEFF15: +1.398791477161003E-08 LINE_DEN_COEFF_16: -7.287014964848045E-10 LINE_DEN_COEFF_17: -1.583911262397542E-09 LINE_DEN_COEFF_18: +1.619484974125586E-09 LINE_DEN_COEFF_19: -14.046114393681560E-09 LINE_DEN_COEFF_20: +1.211445977052259E-09 SAMP NUM_COEFF_I : -5.569473080291414E-04 SAMP NUM_COEFF 2: +4,043859144227192E-01 SAMP_NUM_COEFF 3: +6.160191108418653E-01 SAMP_NUM_COEFF_4: -2.136547287798444E-02 SAMP_NUM_COEFF_5: +3.537003550506667E-05 SAMP NUM_COEFF_6: +8.864142566383684E-04 SAMP_NUM_COEFF_7: +9.016891323668910E-04 SAMP_NUM_COEFF_8: +7.529294858343602E-04 SAMP NUM_COEFF_9: +9.892024338054651E-04 SAMP_NUM_COEFF_10: -3.539412854485401E-05 SAMP_NUM_COEFF_11: -4.132282007597161E-06 SAMP NUM_COEFF_12: +1.006258026565186E-05 SAMP_NUM_COEFF_13: +3.863944882363721E-06 SAMP_NUM_COEFF_I4: -1.214549933413815E-06 SAMP_NUM_COEFF_15: +2.988144068441174E-05 SAMP_NUM_COEFF_16: -3.887041088528994E-06 SAMP NUM_COEFF_17: -2.700408715382785E-06 SAMP_NUM_COEFF_18: +1.779576468217210E-07 SAMP_NUM_COEFF_19: +2.502801973289984E-08 SAM? NUM_COEFF_20: +8.833762852784522E-08
LINE_NUM_COEFF_20: +1.341156159850574E-07 LINE DEN COEFF 1: +1.000000000000000E+00 LINE DENCOEFF_2: +1.152887077590108E-03 LINE_DEN_COEFF_3: +4,595152985785583E-03 LINE DEN_COEFF 4: +2.214940431015355E-03 LINE_DEN_COEFF_5: -2.973413392486126E-06 LINE_DEN_COEFF_6: -1.615660464402396E-05 LINE_DEN_COEFF_7: -3.031842682802664E-06 LINE DEN_COEFF_8: +9.427215605067836E-05 LINE_DEN_COEFF_9: -3.636431369774082E-05 LINE_DEN COEFF_10: -1.099197498259613E-05 LINE_DEN_COEFF_I 1: +1.816822989293131E-09 LINEDEN_COEFF_12: -4.187534182216805E-09 LINE_ DEN_ COEFF 13: -7.825849423946783E-10 LINE_DEN_COEFF_14: +3.269043567262280E-09 LINE_DENCOEFF _15: +3.616111333467883E-08 LINE_DEN_COEFF_16: -6.282704121257443E-09 LINE DEN_COEFF_17: -2.472572706316985E-09 LINE DEN_COEFF_18: -1.462867854718749E-08 LINE_DEN_COEFF_19: +1.338626718324586E-08 LINE_DEN_COEFF_20: +2.399469504650304E-09 SAMP NUM_COEFF_1: +6.505062055338800E-04 SAMP NUM_COEFF 21+6.790087806599008E-01 SAMP_NUM_COEFF_3: +1.009450768206952E+00 SAMP_NUM_COEFF_4: +2.810193108355631E-02 SAMP_NUM_COEFF_5: +4.146726179209319E-03 SAMP_NUM_COEFF_6: +1.645055919284453E-03 SAMP_NUM_COEFF_7: +2.303183375243168E-03 SAMP_NUM_COEFF_8: +1.458645944119422E-03 SAMP NUM_COEFF_9: +4.599594567953199E-03 SAMP NUM_COEFF_10: +5.777756929020079E-05 SAMP NUM_COEFF_11: -1.842299958744447E-05 SAMP N1JM_COEFF_12: +6.327163927273207E-05 SAMP NUM_COEFF_13: -2.852521824517798E-05 SAMP_NUM_COEFF_14: -7.734188661300733E-06 SAMP_NUM_COEFF_15: +9.746250009443844E-05 SAMP_NUM_COEFF_16: -3.676380112453109E-05 SAMP NUM_COEFF_I 7: -1.133492145356726E-05 SAMP NUM_COEFF_18: -2.664624190384635E-06 SAMP_NUM_COEFF_19: -4.440204717478913E-06 SAMP NUM_COEFF_20: -3.186587700658798E-07
SAMP DEN COEFF 1: +1.000000000000000E+00 SAMP DENCOEFF2: -8.114204844995470E-04 SAMP DEN COEFF 3: +1.544559529507819E-03 SAMP DEN_COEFF_4: +1.580448743945071E-03 SAMP DEN COEFF 5: +1,149114667920926E-05 SAMP_DENCOEFF 6: -6.849663459700063E-06 SAMP DEN COEFF 7: -2.593350212636785E-07 SAMP_DEN_COEFF8: 4-3.679645621115528E-05 SAMP DEN COEFF 9: -6.553681868971766E-06 SAMP_DENCOEFF_10: -4.274883166358692E-06 SAMP DEN COEFF 11: -5.072946137815120E-09 SAMP DEN COEFF 12: -9,636332372378258E-09 SAMP DEN COEFF 13: +2.417687039685177E-09 SAMP DEN COEFF I4: +2.691238294127357E-09 SAMP_DEN_COEFF_15: +1.398791477161003E-08 SAMP DEN COEFF 16: -7.287014964848045E-10 SAMP_DEN_COEFF_17: -1,583911262397542E-09 SAMP_DENCOEFF_18: +1.619484974125586E-09 SAMP_DEN_COEFF19: +4.046114393681560E-09 SAMP_DEN_COEFF_20: +1,211445977052259E-09
SAMPDENCOEFF I: +1.000000000000000E+00 SAMP_DENCOEFF2: +1.152887077590108E-03 SAMP DEN COEFF 3: +4.595152985785583E-03 SAMPDENCOEFF4: +2.214940431015355E-03 SAMP DEN COEFF S: -2.973413392486126E-06 SAMPDENCOEFF6: -1.615660464402396E-05 SAMP DEN COEFF 7: -3.031842682802664E-06 SAMP DEN COEFF 8: +9.427215605067836E-05 SAMP DEN COEFF 9: -3.636431369774082E-05 SAMP DEN COEFF 10: -1,099197498259613E-05 SAMP DEN COEFF 11: +1.816822989293131E-09 SAMP_DEN COEFF 12: -4.187534182216805E-09 SAMP DEN COEFF 13: -7,825849423946783E-10 SAMPDENCOEFF 14: +3.269043567262280E-09 SAMP DEN COEFF 15: +3.616111333467883E-08 SAMP_DEN COEFF16: -6282704121257443E-09 SAMP DEN COEFF 17: -2,472572706316985E-09 SAMP_DEN_COEFF1 8: -1 A62867854718749E-08 SAMP_DEN_COEFF_19: +1.338626718324586E-08 SAMP DEN COEFF 20: +2.399469504650304E-09 _
APPENDIX B
Contents of Metadata
Component ID Product Image ID
Component File Name Geographic Corner
Coordinates
File Provided With Raw Stereo Right Image 0000010000
000001 po_120093_pan_0000010000.tif
Number of Coordinates: 4 Coordinate: 1
Latitude: 32.7116877483 degrees Longitude: -117.1648715879 degrees
Coordinate: 2 Latitude: 32.7325652146 degrees
Longitude: -117.1598325026 degrees Coordinate: 3
Latitude: 32.7283026760 degrees Longitude: -117.1351330719 degrees
Coordinate: 4 Latitude: 32.7074261885 degrees
Longitude: -117.1401776715 degrees
Images. Left Image
0010000000 001000
:po 120093_pan_0010000000.tif Number of Coordinates: 4
Coordinate: 1 Latitude: 32.7116877483 degrees
Longitude: -117.1648715879 degrees Coordinate: 2
Latitude: 32.7325652146 degrees Longitude: -117.1598325026 degrees
Coordinate: 3 Latitude: 32.7283026760 degrees
Longitude: -117.1351330719 degrees Coordinate: 4
Latitude: 32.7074261885 degrees Longitude: -117.1401776715 degrees
APPENDIX C
Elevations values (in meters) corresponding to line and sample values picked from the
DEM obtained from the different source. S. No Sample Line Sample .Data ERDAS ENVI GeomOca '-
1 466 34 37.768 36.508 28.600 36.600 2 708 200 43.617 43.200 44.687 41.500 3 942 62 -29.808 -21.600 -21.600 -19.730 4 1208 109 51.237 38.200 41.500 58.400 5 1450 179 7.208 -3.100 -3.100 -2.730 6 1653 265 23.598 25.000 25.000 23.900
7 1623 328 34.678 30.900 29.210 34.600
8 295 148 39.672 34.300 35.261 35.100
9 647 250 41.079 44.400 42.950 39.428
10 905 507 29.953 36.135 36.639, 38.250
11 1123 554 35.147 51.795 66.792 52.360
12 1475 640 -0.202 -4.900 2.873 21.900
13 1412 859 16.807 5.600 9.647 9.543
14 826 914 6.043 13.100 14.654 12.638
15 537 492 22.354 12.000 20.900 15.968
16 686 570 32.364 27.753 29.011 25.963
17 436 429 32.384 34.562 33.164 35.430
18 717 679 21.493 40.900 19.867 22.530
19 1162 718 38.550 38.748 43.194 19.658
20 1428 781 13.816 17.059 16.298 19.254
21 1772 1648 17.796 19.431 22.164 19.470
22 1186 1593 -4.050 -10.260 -7.287 9.300
23 826 1562 -10.673 -9.513 -7.267 -7.796
24 757 1516 -11.219 -6.300 -9.163 0.500
25 506 1477 -5.540 -5.697 -3.591 -6.718
26 147 1133 0.496 -4.264 1.900 -0.670
27 561 883 5.959 6.400 6.457 9.953
28 1031 1008 16.193 16.638 17.598 14.638
29 350 1141 -0.342 -1.717 -0.987 -0.285
30 710 1313 -6.091 -4.636 -3.364 -1.456
31 374 829 21.582 31.200 32.987 29.100
32 1085 727 27.532 28.303 27.684 26.458
33 1585 977 29.893 28.987 19.100 24.400
IV
34 1116 1274 -7.185 -3.878 -1.587 -1.254 35 686 1227 -0.638 -1.870 0.563 4.222 36 1170 1350 -13.145 -16.134 -12.511 -6.135 37 303 1235 -3.040 1.192 -2.186 0.025 38, 491 1750 -13.171 -17.500 -9.864 -15.360 39 920 610 32.774 33.506 32.547 30,258 40 1170 766 34.437 40.700 41.932 25.300 41 1516 485 6.147 2.622 5.017 0.259 42 139 1094 -2.381 -1.797 -0.987 -0.564 43 678 1274 -2.482 -1.406 0.099 5.100 44 381 715 8.706 10.546 11.956 8.259
45 990 535 35.579 36.769 35.987 34.562
46 1592 457 25.215 24.850 19.118 22.568
47 1795 621 9.500 19.100 11.527 33.300
48 . 1850 1519 -29.801 -28.767 -19.648 -26.782
49 1710 1635 18.232 21.366 23.591 22.553
50 991 1261 -0.567 -5.911 -2.671 -18,100
APPENDIX D
Photograph of San Diego Qualcomm football stadium (region 5 in sample data).
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APPENDIX E
Photograph of Imperial Beach San Diego (region 3 in sample data) showing rocky and
undulating ground surface.