intro to map week 1.pdf

UCL DEPARTMENT OF Civil Environmental and Geomatic Engineering CEGEG034 Mapping Science

Introductions to Maps based on Prof. Ian Dowman 2009

Dietmar Backes

Content of this lecture: Fundamental definitions

Examples and Key-characteristics of maps

Methods of Mapping

Some accuracy measures for Maps

Geometric corrections and registrations of images

DJB2011


2

Terminology

Maps are traditionally paper documents. Now the information which used to be depicted on a paper map is stored

in digital form.

Image maps are now very common e.g. Google Earth. Subsequently we will use the term MAP to cover information stored in

both paper and digital form.

Digital data can be presented in paper form, but also in other ways such as perspective views, but these can still be referred to as maps.

Remark:

This Lectures gives a first glimpse on key issues which will be discussed in detail at later parts of this module.

DJB2011


The role of Maps

A Map is a traditional method of recording and displaying objects and their spatial location and distribution

Maps are an indispensable aid for everyone from a scientist to a traveller

It serves as a means of communicating the spatial relationship and the forms of the objects

Many maps also give accurate location

Basic elements of a map Location and attribute to that location

Location means where in space

Attribute means what is it about or quality of that location

Types of map Based on the theme of the map

Based on the scale of the map

3

DJB2011


Types of Maps

4

DJB2011


Fit for Purpose

5

We need to assess weather maps are suitable for the application in mind

We need to decide the best way to generate maps which satisfy the requirements of the intended application

DJB2011


Examples of different Maps and their key properties

6

An ancient map of a city in

Mesopotamia on a clay tablet A section of first topographic map of Paris (good horizontal accuracy poor vertical accuracy)

DJB2011


7


DJB2011


8

Ordnance Survey 1:25 000 Ordnance Survey 1:50 000


Topographic Maps

DJB2011


Scale of the Map

9

DJB2011


Global Map with 8 Layers

10

DJB2011


Google Earth/Maps

Data from different sources

Example of image maps, produced from aerial photographs and satellite data

11

DJB2011


Google Earth/Maps

Data acquired at different times

Multitemporal data collection

Seamlines in are a specific disadvantage of image maps

12

DJB2011


Representing the 3rd dimension 2.5D elevation

13

The representations introduced so far are 2D. Heights can be represented by:

Contours

Spot heights

Relief shading

Digital Elevation Models (DEMs)

(rasterised) digital elevation models are convenient for use in a computer and can be displayed in many ways.

We call such representations 2.5 D

DJB2011


2.5D DEM of a large area

14

DJB2011


Representing the 3rd dimension 3D point clouds

The Helicopter mounted ATLAS

system collects approximately

30,000 3D data points per

second.

Flying at an altitude of 150m and

60kph this translates to a density

of 30 points per square metre on

the ground. A typical swath width

at this altitude is 60m

15

Example: ATLAS - High resolution Laser Terrain mapping

This area is subject

to rapid technical

advances!

DJB2011


Applications: 3D City Models

16

Rendered LiDAR point clouds

Examples by Infoterra

DJB2011


17

Applications: 3D City Models

Example Microsoft Virtual World (Bing maps)

DJB2011


18

Applications: 3D City Models Example Virtual Berlin

courtesy of Prof. Kolbe

(in Google maps)

Today 3D visualisations are often

called 3D maps; however it is

more complex to represent and

model semantic information in 3D.

DJB2011


Example Deformation maps: DEMs showing differential movement using interferometric SAR (IfSAR)

19

IZMIT Earthquake

Subsidence in urban areas

Examples by fNPA

Fringe vectors superimposed

onto Landsat TM

4m total displacement detected

Such maps providing millimetre precision in heights

based on complex analysis of Satellite imagery

DJB2011


Sources of Data Existing maps

Existing maps are very useful source of data. Currency of the map with respect to the dynamism of the theme of the map and the area has to be checked before utilising the existing maps

Ground survey Ground survey for some selected location or at random locations are required for

most of the surveying and mapping methods. Ground survey for the entire area is also applicable for certain types of maps

Ground survey is often used to fix Ground Control Points GPS (Global Positioning System) very useful

New Platforms and Mobile Mapping Low flying unmanned aerial vehicles (UAVs) and ground based vehicles are

currently developed and tested for rapid mapping. Such systems deploying a range of sensors. Currency of information will be very high.

Aerial photographs Currency of information available is high if the data is newly acquired

Satellite data Currency of information available is high as the data is available on repeated

coverage

20

DJB2011


Methods of Mapping

Conventional ground surveying Using surveying and levelling instruments such as theodolites

and GPS receivers

Airborne and Spaceborne sensing Aerial photographs - Photogrammetry

Satellite data

Lidar data

Radar data (radargrammetry)

Interferometric data

21

DJB2011


Comparison of methods of mapping

Conventional Ground Surveying Useful for highly accurate large scale maps

Highly labour intensive method and hence unsuitable for larger areal coverage and unsuitable for small scale maps

Airborne sensing (e.g. Photogrammetry from aerial photographs) Useful from large scale to small scale maps

Cost of data acquisition is high

High initial investment is required to derive maps

Requirement of specially trained labour

New techniques such as Lidar and Radar extend the scope

Space borne Sensing (e.g. Photogrammetry from satellite data) Cost of data acquisition is comparatively cheaper

Suitable for medium scale to small scale maps

Suitable for updating the existing maps as the repeated coverage is available

22

DJB2011


Accuracy of maps

Absolute accuracy

depends on a grid being present.

Related to the scale of the map. The horizontal accuracy is usually represented as width of line as the smallest feature that can be interpreted from a map, which is 0.3 mm to 0.5 mm on the map.

hence on 1:50,000 map

0.3 mm to 0.5 mm = 15m to 25m

The horizontal accuracy of 1:50,000 map is 15m to 25m.

The vertical accuracy is usually represented with respect to the contour interval, which in turn depends on the scale of the map and the type of the terrain.

The contour interval for 1:50,000 scale map is 20m and the vertical accuracy of that map is 6m to 10m. The contour interval for 1:50000 scale map can be 10m as well, if the terrain is relatively smoothly undulating and then the expected accuracy of that map is 3m to 5m.

Note also Digital Elevation Models

23

DJB2011


Accuracy of maps

Relative accuracy

Accuracy of an object with reference to another object

irrespective of the absolute accuracy of either of the objects or

accuracy of one location with respect to another location in the same map irrespective of absolute accuracy of either of the

locations

24

DJB2011


Factors affecting the accuracy of the map

Scale

Method of compilation

Generalisation/presentation

Some features are omitted in the map

Some are exaggerated and presented

Some are approximated and presented

Generalisation / Presentation depends on the scale of the

map, type and purpose of the map

25

DJB2011


Generalisation - effect of the Scale of the Map

26 IGN 1:25,000 IGN 1:100,000 IGN 1:250,000

DJB2011


Generalisation - Feature selection or elimination

27

1:10,000 1:25,000 1:50,000 1:100,000

Imhof (1968)

The concept of Mapping will be discussed in detail later in the course.

DJB2011


Assessing accuracy The accuracy can be determined by calculating the closeness of measured co-

ordinates (on the map) to the true value. This is measured by root mean square error.

where v is the residual error and n is the number of points.

The precision of a set of observation - the closeness of measurements to each other - is estimated by the standard deviation ():

where is the mean difference

Reliability is a measure of accuracy given by the proportion of points which fall outside a given limit. The rule of thumb usually applied is that 95% of points will have a

precision of 2 and 99% will have a precision of 3 .

28

n

vv

1

( )2

n

vv

nrmse v

)(2

DJB2011


Absolute Accuracy of UK topographic maps from

Ordnance Survey

29

Scale and method of

original survey

Expected absolute accuracy

at differing confidence level

68% 95% 99%

1:1250 0.5m 0.8m 1.0m

1:2500

Resurveyed / reformed 1.1m 1.9m 2.4m

1:2500

overhaul 2.8m 4.8m 6.0m

1:10000 4.1m 7.1m 8.8m

The detail may be less accurate than these values.

DJB2011


Relative Accuracy of UK topographic maps from

Ordnance Survey

30

Scale and method of

original survey

Expected relative accuracy at

differing confidence level

68% 95% 99%

1:1250 0.4m 0.8 1.0m

1:2500

Resurvey/reformed 1.1m 1.8m 2.3m

1:2500

Overhaul 1.2m 2.3m 3.0m

1:10000 3.5m 6.7m 8.8m

The detail may be less accurate than these values.

DJB2011


Geometric correction and registration of earth

observation data for mapping (e.g. Satellite

images)

Motivation:

As seen in previous section, images collected by airborne

and space borne sensors but also from the Ground are an

efficient data source for mapping.

Fundamental Problem:

How can images, captured from a airborne camera, related to

the maps projected to the curved surface of our Earth?

31

Show Example!

DJB2011


A Spherical earth is presented on a two dimensional flat paper map (most of the time), which needs projection

techniques

This projections cause some distortions will be discussed in the Foundation module in detail

32

Geometric correction and registration of images Mapping on the earth surface

DJB2011


Geometric correction and registration of images Principles of image formation

A frame may be formed in three ways:

1.As a single exposure - that is with no significant movement of the sensor whilst

the image is formed as in the case of a frame camera.

2. As a series of lines almost normal to the track of the sensor. In this case a

single line can be considered without a time parameter but time must be

considered in constructing a full frame. The push broom scanners fall into this

category.

3. As a series of points each recorded at a separate time. This is the most

distorted type of image requiring the most complex mathematical model. The

scanner systems and microwave systems fall into this category.

33

DJB2011



Single Exposure

With a central projection the whole image is exposed at once.

This ensures no distortion due to movement.

34

a

bc

d

A

BC

D

S

f

H

n

N N

n

DJB2011


Cross track (whisk broom) and

along track (pushbroom) scanners

35


DJB2011


Geometric correction and registration of images Sources of errors in airborne and satellite imagery

Effects caused by the earth:

earth rotation,

earth curvature,

relief.

Effects caused by movement of the platform:

position,

attitude.

Effects caused by the operation of the sensor:

panoramic effect,

rotation of the mirror,

non-linearity of the mirror movement.

36

DJB2011


37

imaged

recorded

Earth rotation

Earth curvature a a

a a = dr radial displacement

Geometric correction and registration of images Effects due to the Earth

DJB2011


38


a a' n

f

A

h

H

Displacement due to relief

aa/an = h/H dr/r = h/H

dr = r.(h/H)

DJB2011



39

Sensor Altitude (km) Half swath (km) dr for h= 500m Pixels

1. Aerial camera with

f=150mmm

10 4 200 133

2. Metric camera on

Spacelab

f=300mm

250 90 180 5

3. Landsat 705 90 64 2

4. SPOT nadir 830 30 18 2

5. SPOT 27 830 450 271 27

Examples of relief distortion from various sensors

DJB2011


Geometric correction and registration of images GEOMETRIC DISTORTIONS DUE TO EARTH ROTATION AND

MOVEMENT OF THE PLATFORM

40

Earth rotation Altitude variation Spacecraft velocity

Pitch variation Roll variation Yaw variation

DJB2011


Geometric correction and registration of images Correction of distortions

The systematic effects can be corrected by applying a mathematical transformation based on polynomials

Error due to relief cannot be corrected by this method

Also known as rubber sheeting or rubber sheet wrapping

Use of these method requires ground control points (GCPs)

GCPs must be carefully selected and must be evenly distributed over the image

41

DJB2011


Geometric correction and registration of images transforming image to map

42

Similarity transformation

Affine transformation

Polynomial transformation

dbyaxY

cbyaxX

ybxbbY

yaxaaX

210

210

5

2

4

2

3210

5

2

4

2

3210

bybxbybxbbY

ayaxayaxaaX

DJB2011


Geometric correction and registration of images 2D Similarity transformation 4 Parameter

This transformation is to relate any two-dimensional rectangular co-ordinate

system to any other two-dimensional rectangular co-ordinate system. It preserves

the internal geometry of the transformed system. Two control points required

(minimum).

X = ax - by + c

Y = bx + ay + d

A similarity transformation is performed by applying:

- 1 scale factor ( m = (a2 + b2)),

- 1 rotation angle (tan = b/a),

- 2 translations (c and d).

43

DJB2011


Geometric correction and registration of images 2D affine transformation 6 Parameter

An affine transformation enables adjustment to be applied independently in each

direction. Thus for scanner images, it corrects first-order distortions such as

affinity due to non-orthogonality and scale difference between scan along track

directions which may be caused by earth rotation, map projection and other

geometric distortions.

Three ground control points, at least, are required.

X = ao + a1x + a2y

Y = bo + b1x + b2y

A affine transformation is performed by applying:

- 2 scale factor,

- 2 rotation angle,

- 2 translations.

44

DJB2011


Geometric correction and registration of images Second-order Polynomials 12 Parameter

Polynomials in the form:

X = ao + a1x + a2y + a3x2 + a4y2 + a5xy

Y = bo + b1x + b2y + b3x2 + b4y2 + b5xy

If polynomials are used great care must be taken to ensure that a sufficient number of

control points are available and that they are distributed over the whole area to be

transformed. A minimum of six ground control points are necessary .

Additional terms may be added to equations 6 to correct for higher order distortions, the

need for care in use of control points is greater for higher orders.

45

DJB2011


In order to create a new, corrected, image it is necessary to transform each

pixel individually. The transformation will not generate integer values for the new

row and column positions in the corrected image, hence the density value from

the original image must be assigned to the nearest row and column position in

the new image. This is known as resampling.

Resampling is commonly carried out using

one of three methods:

1.NEAREST NEIGHBOUR

straightforward and computationally economic but

may produce shifts in position and poor visual impression.

1.BILINEAR INTERPOLATION

an acceptable compromise.

1.CUBIC CONVOLUTION

smooths the image but computationally intensive.

ALL RESAMPLING DEGRADES THE IMAGE TO SOME EXTENT.

46

Geometric correction and registration of images Resampling

DJB2011


Following Practical's are offered on a voluntary base:

Character and Key parameter of Maps

Image registration and Geo-referencing

Excel Spreadsheet transformation

Geo-referencing a image in ArcGIS

Information can be found on Moodle

47

Geometric correction and registration of images

Exercises:

DJB2011


48

Any Questions ?

intro to map week 1.pdf

Documents