1 hyperspectral remote sensing keck center, national academies, washington, dc 10 december 2013...
TRANSCRIPT
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HyperspectralRemote Sensing
Keck Center, National Academies, Washington, DC
10 December 2013
Workshop Instructor:
Dr. Ronald G. [email protected] and [email protected]
ASPRS/Potomac Region’sGeoTech 2013
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Dr. Ronald G. ResminiThe MITRE Corporation and
George Mason University
Please call me Ron
v: 703-470-3022
[email protected] and [email protected]
http://mason.gmu.edu/~rresmini/
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What sort of remote sensing system acquired this image?Is it a panchromatic visible? multispectral? hyperspectral? panchromatic infrared?
polarimetric? SAR? How can you tell?
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Introduction toHyperspectral Imagery (HSI)
Remote Sensing
and to ENVI®
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writ large...the phenomenology of spectra;remote material detection, identification, characterization
and quantification
Introduction to Hyperspectral Imagery (HSI)
Remote Sensing
HSI is, fundamentally:
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HSI Remote Sensing:Frame of Reference...•Remote sensing of the earth
airbornespaceborneground (portables)
• But bear in mind other apps:medicalindustrialmany, many others
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Applications of HSI RSApplications of HSI RS
• Geology• Forestry• Agriculture• Mapping/land use, land cover analysis• Atmospheric analysis• Environmental monitoring• Littoral zone RS• Many, many others
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• Where/how do we do HSI remote sensing?
• What is the nature of what is measured?
• What is there to measure?
• How is it done?
• Are there distinguishing observables?
• etc...
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Electromagnetic EnergyElectromagnetic Spectrum
Electromagnetic EnergyElectromagnetic Spectrum
Electromagnetic Spectrum
Wavelength
(nm)
Cosmic Rays
Gamma Rays
X Rays
Microwaves (Radar)
Radio & Television WavesUV
105 106 107 108 109 1010 1011 10121011010-110-210-310-410-5
Shorter WavelengthsHigh Energy
Shorter WavelengthsHigh Energy
Longer WavelengthsLow Energy
Longer WavelengthsLow Energy
V / NIR / SWIR / MWIR / LWIR
Optical Region
400 14000
400
0.4
400
0.4
14000
14.0
14000
14.01500
1.5
1500
1.53000
3.0
3000
3.0
5000
5.0
5000
5.0 700
0.7
700
0.7
NIR MWIRSWIRRG LWIR B LWIRWavelength
(nm)(m)
Wavelength (nm)(m)
Emitted Energy
Reflected Energy
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HSI Sensors Measure Radiance
)microflick(f1msrm
W0.100
msrcm
W22
Check-out the fancylingo used in the field
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Reflected vs. Emitted EnergyReflected vs. Emitted Energy
1
104
1000
100
10
0.1 1 1053 7
Irra
dia
nc
e (W
-m-2-u
m-1)
Wavelength (µm)
Earth Emission
(100%)
EarthReflectance
(100%)
radian
t exitance (W
-m-2-u
m-1)
MWIR
Assumes no atmosphere
.4 .7
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NIR SWIR MWIR LWIRRB G
0.4 mm 1.5 3.0 5.0 14.0 mm0.7
Panchromatic or single b&w imagePanchromatic or single b&w image
0.4 mm 1.5 3.0 5.0 14.0 mm0.7
A normal color-composite imageA normal color-composite image
0.4 mm 1.5 3.0 5.0 14.0 mm0.7
Hyperspectral: hundreds of narrow bands – hundreds of imagesHyperspectral: hundreds of narrow bands – hundreds of images
0.4 mm 1.5 3.0 5.0 14.0 mm0.7
Multispectral: tens of broad bands – tens of imagesMultispectral: tens of broad bands – tens of images
0.4 mm 1.5 3.0 5.0 14.0 mm0.7
Sa
mp
ling
Fu
nct
ion
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So...what sort of remote sensing system acquired this image?
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BTW, This is Dispersion:
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Interaction of energy and objectsInteraction of energy and objects
Transmitted Energy
Absorbed Energy
Reflected EnergyV-MWIR
Emitted EnergyMW-LWIR
Energy Balance Equation: EI () = ER() + EA() + ET() Energy Balance Equation: EI () = ER() + EA() + ET()
Incident Energy
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NASA AVIRIS Cuprite, NV, HSI Data, (1995)
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An AVIRIS (NASA) HSI Image Cube
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The Spectrum is the Fundamental Datum of HSI RS
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Levels of Spectral Information Levels of Spectral Information
Quantification: Determines the abundance of materials.
Characterization: Determines variability of identified material (e.g. wet/dry sand, soil particle
size effects).
Identification: Determines the unique identity of the foregoing generic categories (i.e. material
identification).
Discrimination: Determines generic categories of the foregoing classes.
Classification: Separates materials into spectrally similar groups.
Detection: Determines the presence of materials, objects, activities, or events.
Quantification: Determines the abundance of materials.
Characterization: Determines variability of identified material (e.g. wet/dry sand, soil particle
size effects).
Identification: Determines the unique identity of the foregoing generic categories (i.e. material
identification).
Discrimination: Determines generic categories of the foregoing classes.
Classification: Separates materials into spectrally similar groups.
Detection: Determines the presence of materials, objects, activities, or events. Panchromatic Panchromatic
Low Spectral ResolutionLow Spectral Resolution
High Spectral ResolutionHigh Spectral Resolution
Hyperspectral
(100’s of bands)
Hyperspectral
(100’s of bands)
Multispectral
(10’s of bands)
Multispectral
(10’s of bands)
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Image from the NASA Langley Research Center, Atmospheric Sciences Division.http://asd-www.larc.nasa.gov/erbe/ASDerbe.html
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Electromagnetic EnergyAtmospheric Absorption
Electromagnetic EnergyAtmospheric Absorption
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Reflectance: Is the ratio of reflected energy to incident energy. Varies with wavelength Function of the molecular properties of the material.
Reflectance Signature: A plot of the reflectance of a material as a function of wavelength.
Reflectance: Is the ratio of reflected energy to incident energy. Varies with wavelength Function of the molecular properties of the material.
Reflectance Signature: A plot of the reflectance of a material as a function of wavelength.
Reflected EnergyReflected Energy
Red brick KaoliniteSandy loamConcreteGrass
All solids and liquids have reflectance signatures that
potentially can be used to identify
them.
All solids and liquids have reflectance signatures that
potentially can be used to identify
them.
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Emissive EnergyBasic Concepts
Emissive EnergyBasic Concepts
• Blackbody – A theoretical material that absorbs and radiates 100% of the energy incident upon it. BB curve is a function of temperature and wavelength.
• Planck’s Law – gives shape of blackbody curve at a specific temperature.• Wien’s Displacement Law – determines wavelength of peak emittance.
• Blackbody – A theoretical material that absorbs and radiates 100% of the energy incident upon it. BB curve is a function of temperature and wavelength.
• Planck’s Law – gives shape of blackbody curve at a specific temperature.• Wien’s Displacement Law – determines wavelength of peak emittance.
Wavelength (µm) 0.2 0.4 0.7 1 2 3 5 8 10 30
Sp
ectr
al R
adia
nt
Em
itta
nce
PeakEmittance
300KAmbient
250K
500K
800K
373KBoilingWater
6000KSun
3000KLight Bulb
1500KHot Coals
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1
52 12
kT
hc
BB ehcM
The Planck or Blackbody Radiation Equation:
mm
W2Units:
TM
TM
BB
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Emissive EnergyEmissive Energy• Emissivity - is a measure of how efficiently an object radiates
energy compared to a blackbody at the same temperature. Varies with wavelength Function of the molecular properties of the material.
• Emissivity Signature - A plot of emissivity as a function of wavelength. All materials have emissivity signatures that potentially can be used to identify them.
• Emissivity - is a measure of how efficiently an object radiates energy compared to a blackbody at the same temperature. Varies with wavelength Function of the molecular properties of the material.
• Emissivity Signature - A plot of emissivity as a function of wavelength. All materials have emissivity signatures that potentially can be used to identify them.
Blackbody
Graybody
Selective emitter(emissivity signature)
Selective emitter(emissivity signature)
Em
issi
vity
0
0.5
1.0
Wavelength
Red brick KaoliniteGrass Water
Black paint Concrete
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Spectral Signature LibrariesSpectral Signature Libraries
• Spectral signatures of thousands of materials (solid, liquid, gas) have been measured in the laboratory and gathered into “libraries”.
• Library signatures are used as the basis for identification of materials in HSI data.
• Spectral signatures of thousands of materials (solid, liquid, gas) have been measured in the laboratory and gathered into “libraries”.
• Library signatures are used as the basis for identification of materials in HSI data.
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Understanding Spectral Data: Signature Variability Factors
Understanding Spectral Data: Signature Variability Factors
Brightness BRDF Target morphology • shape• orientation
Particle size Moisture Spectral mixing
Brightness BRDF Target morphology • shape• orientation
Particle size Moisture Spectral mixing
Composition • original • change over time
Surface quality • roughness• weathering
Shade & Shadow Temperature
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Reflected EnergyReflected Energy• The manner in which a material reflects energy is primarily a
function of the optical properties and surface roughness of the feature.
• Most objects are diffuse reflectors
• The manner in which a material reflects energy is primarily a function of the optical properties and surface roughness of the feature.
• Most objects are diffuse reflectors
Specular Reflectance
Specular Reflectance
Diffuse Reflectance
Diffuse Reflectance
Angle of Incidence = Angle of Reflectance
Smooth Surface
Rough Surface
(Microscopic)
Energy Scattered in
All Directions
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Emissive EnergyIdentification of GasesEmissive EnergyIdentification of Gases
DetectedSignature
Plume
Wavelength
Emission
Background (Cool)
Gas (Warm)
Gases appear in either emission or absorption depending on the temperature contrast between the gas and the background.
Same Temperature
Same Temperature
Wavelength
No Detection
Background
Gas
Wavelength
Absorption
Background (Warm)
Gas (Cool)
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• Spatial Resolution
• Radiometric Resolution
• Temporal Resolution
• Spatial Resolution
• Radiometric Resolution
• Temporal Resolution
ResolutionsResolutions
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HSI Fundamentals SummaryHSI Fundamentals Summary
• Hyperspectral remote sensing involves measuring energy in the Visible – LWIR portions of the electromagnetic spectrum.
• Some of the measured energy is reflected from objects while some energy is emitted from objects.
• Every material has a unique spectral signature.
• Spectral image data are collected such that signatures can be extracted for material detection, classification, identification, characterization, and quantification.
• Spectral, spatial, radiometric, and temporal resolution determine the capabilities of the remote sensing sensor/system.
• Hyperspectral remote sensing involves measuring energy in the Visible – LWIR portions of the electromagnetic spectrum.
• Some of the measured energy is reflected from objects while some energy is emitted from objects.
• Every material has a unique spectral signature.
• Spectral image data are collected such that signatures can be extracted for material detection, classification, identification, characterization, and quantification.
• Spectral, spatial, radiometric, and temporal resolution determine the capabilities of the remote sensing sensor/system.
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Properties of the Data Cube
• # of samples, lines, bands• Headers, preline, postline, footers, etc.• Data type• Interleaving (BIP, BIL, BSQ)• Byte order• Wavelengths, FWHM• Bad bands list• Band names (very optional)• The logical and physical data cube• The ENVI “.hdr” file• History file (it doesn’t exist) – keep notes!
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An AVIRIS (NASA) HSI Image Cube
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• What you need to know about your data; a check-list:
• Date, time, location, ground elevation, platform elevation,
heading, GSD, be able to calculate where the sun is;
i.e., all RS angles (geometry)
• On-going sensor characterization; know what it is; ask for it!
• Spatial sampling; spatial resolution
• Spectral sampling; SRF; spectral resolution
• NESR, NEDr, NED , NEDT
• Issues: smile, keystone, FPA misregistration, vibration,
parallax, scattered light, self-emission, platform
motion/imaging distortions, etc.
There’s More to Know...
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Reconstituted Reflectance High SNR spectra
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
400.0 700.0 1000.0 1300.0 1600.0 1900.0 2200.0 2500.0
Wavelength (nm)
Ref
lect
ance
Conifer Grass
Broad Leaf Sage_Brush
NPV
A couple of slides on SNR, NESR
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0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
400.0 700.0 1000.0 1300.0 1600.0 1900.0 2200.0 2500.0
Wavelength (nm)
Ref
lect
ance
Conifer Grass
Broad Leaf Sage_Brush
NPV
Reconstituted Reflectance Low SNR spectra
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Information Content and Extraction
• HSI RS is based on the measurement of a physical quantity
as a function of wavelength: its spectroscopy
• HSI is based on discerning/measuring the interaction of
light (photons, waves) with matter
• The sun is the source; or active systems; or very hot objects
• Earth RS scenarios involve the atmosphere
• There are complex interactions in the atmosphere
• There are complex interactions between light and targets
of interest in a scene
• There are complex interactions between light, targets of
interest, and the atmosphere
• There’s a lot (lots!) of information in the spectra
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The
Gen
eral
Dat
a A
naly
sis/
Exp
loita
tion
Flo
w
DN
Calibration
Fixes/Corrections
Data Ingest
Look At/Inspect the Data!!
Atmospheric Compensation
Algorithms for Information Extraction
Information Fusion
Geometric/Geospatial
Product/Report Generation
Distribution
Archive/Dissemination
Planning for Additional Collections
Spectral Library Access
Iteration
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HSI Remote Sensing:Frame of Reference...
• A Scientist’s Approach to the Data: look at the data(!)observables have a physical,
chemical, biological, etc. basismust understand nature of observablesbumps and wiggles have real,
physical (spectroscopic) significanceapplication of tools comes last!
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NASA Hyperion:http://edcsns17.cr.usgs.gov/eo1/sensors/hyperion
NASA AVIRIS:http://aviris.jpl.nasa.gov/
NASA AIRS:http://www-airs.jpl.nasa.gov/
ProSpecTIR and SEBASS:http://www.spectir.com/airbornesurveys.html
Probe-1:http://www.earthsearch.com/index.php?sp=10
AHI:http://www.higp.hawaii.edu/~lucey/hyperspectralpaul.html
AISA:http://www.channelsystems.ca/SpectralImaging-AISA.cfm
NRL HICO:http://www.nrl.navy.mil/pao/pressRelease.php?Y=2009&R=90-09r
Some HSI SystemsSome HSI Systems
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Defining HSI Dimensionality• Hundreds of bands of data in an HSI data cube• An HSI pixel (a spectrum) is an n-D vector
n = number of bandsa spectrum is a point in an n-D space
• “Redundancy” of information• Embedding or spanning dimension• Intrinsic dimension/virtual dimension• A distinction
large volume of datadimensionality
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HSI or MSI• 100’s of bands vs. 10’s of bands• Maybe all you need is 6 bands but...
you need six; and you need six; and so on• Atmospheric compensation...• HSI is spectroscopy writ large
its about resolving spectral informationfine spectral featuresbroad spectral features
• Today’s FPAs make HSI a breeze anyway...
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Multispectral - Hyperspectral Signature Comparison
Multispectral - Hyperspectral Signature Comparison
Multispectral Hyperspectral
Resampled to Landsat TM7 Bands
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400
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400
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1500
1.50
1500
1.50
3000
3.00
3000
3.00
700
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700
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NIR SWIRRGB
Wavelength (nm)
(m)
Wavelength (nm)
(m)
Minerals/Geology
SoilsBathymetry
Vegetation
FuelsAerosols
Atmos. Comp.
Plastics
Fabrics
Paints
O2 CO2
Chlorophyll
DOM/CDOM Cirrus
Iron oxides
Similar figures may be constructed for M/LWIR regions.
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Thinking About Spectra;Thinking about HSI
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• Spectral parameterization
• Albedo/brightness
• Band depth
• Band width
• Band shape/superimposed features
• Spectral slope
• Spectral indices
• Derivative spectroscopy
• Wavelet transform
• Combinations
• Pre-processing transforms; e.g., SSA
• All must have a physical basis!
• Tie all observations to physical reality!!
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HSI Algorithms:An Introduction
(Don’t Panic!!)
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•Algorithm types, classes, categories:
an overview•Angular Metrics•SAM
•Distance Metrics•w/, w/o statistics
•Data transformations•PCA, MNF, ICA
•SMA/OSP/CEM/SMF/ACE•Derivative Spectroscopy/
other Parameterization Methods
~P
ropo
rtio
nal t
o In
crea
sing
Deg
ree
of C
ompl
exity
Overview
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An Algorithm Progression
SAM, MD (whole pixel matchers)
SMA (subpixel mixtures)
Orthogonal Subspace
Projection
Spectral Matched Filter
Variations of the
Spectral Matched Filter
JM Distance
B Distance
Traditional MSI
Classification Methods
Spectral
Parameterizations
Spectral
ParameterizationsSpectral
Parameterizations
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The n-D Space — Where Many Algorithms Operate
Each HSI spectrum (or pixel) is an n-D vector that
can be represented as a single point in n-D space.
n-D space is actually where many of our algorithms
operate.
Tn7654321 ,...,,,,,,,)pixelor(Spectrum rrrrrrrr
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0.9
1.0
0.4 0.8 1.2 1.6 2.0 2.4
Wavelength (mm)
Ref
lect
ivity
, r
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Four (A-D) Equivalent Notations/Representations
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1.00
0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
Wavelength (micrometers)
Re
flect
an
ce, r
(0.11, 0.23, 0.30, 0.25, 0.16, 0.27, 0.31, 0.37,...,)
...p.o.n.m.l.k.j.i. 370310270160250300230110
r, Band a
r, B
and
b
Spectrum s1
...imagine an n-Dhyperspace...
A B
C
D
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Some HSI Scatter Plots; Spectra as Points in ‘Hyperspace’
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SAM: n-D Geometry
A 2D scatterplot with 2 spectra:
Band a
Ban
d b
Spectrum s1
Spectrum s2
Angular Distance Metric (Spectral Angle Mapper or SAM)
Assume a two band spectral remote sensing system. Each two point‘spectrum’ is a point in Band b vs. Band a space.
The angle, q, between the two
lines connecting each spectrum
(point) to the origin is the angular
separation of the two spectra.
Smaller angular separations in-
dicate more similar spectra.
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SAM: The Math
• Chang (2003), ch. 2, pp. 20-21; and...• Assume two 5-band spectra as shown:
21
2T
11
ss
sscos T1s
2s
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e2e1d2d1c2c1b2b1a2a12T
1 ssssssssssss
• Let the 5 bands have band names a, b, c, d, and e:
1T
1e1e1d1d1c1c1b1b1a1a11 sssssssssssss
2T
2e2e2d2d2c2c2b2b2a2a22 sssssssssssss
2T
222
22
22
22
222 ssssssss
• The output units are radians
• ENVI does all this for you
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• Invariant to albedo...why:
A 2D scatterplot with 2 spectra:
Band a
Ban
d b
Spectrum s1
Spectrum s2
Move s1 towards origin...angle does not change
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• Application strategiesRadiance, reflectanceScaled values
• A few comments on SAM and
mixed pixels
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Euclidean Distance: n-D Geometry
A 2D scatterplot with 2 spectra:
Band a
Ban
d b
Spectrum s1
Spectrum s2
Whole-Pixel Distance Metric in n-D Hyperspace
Assume a two band spectral remote sensing system. Each two point‘spectrum’ is a point in Band b vs. Band a space.
Euclidean Distance
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Euclidean Distance: n-D Geometry
A 2D scatterplot with 2 spectra:
Band a
Ban
d b
Spectrum s1
Spectrum s2
Whole-Pixel Distance Metric in n-D Hyperspace
Assume a two band spectral remote sensing system. Each two point‘spectrum’ is a point in Band b vs. Band a space.
Euclidean Distance
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Euclidean Distance: The Math
It’s the Pythagorean Theorem
A 2D scatterplot with 2 spectra:
Band a
Ban
d b
Spectrum s1
Spectrum s2
a
b
c
c = Euclidean Distancec2 = a2 + b2
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T1s
2s
Euclidean Distance: More Math
As with SAM, assume two five-band spectra.
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21
2e2e1
2d2d1
2c2c1
2b2b1
2a2a1 ssssssssssc
• Let the 5 bands have band names a, b, c, d, and e:
• The output units are reflectance
• ENVI does all this for you
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• Application strategiesRadiance, reflectanceScaled values
• A few comments on Euclidean distance
and mixed pixels
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Linear Spectral Unmixing
The reflectance of an image pixel is a linear combination of
reflectances from (typically) several “pure” substances (or
endmembers) contained within the ground-spot sampled by the
remote sensing system:
n
jii,jji rMfR
1
where: Ri is the reflectance of a pixel in band i,
fj is the fractional abundance of endmember j in the pixel,
Mj,i is the reflectance of endmember substance j in band i,
ri is the unmodeled reflectance for the pixel in band i, and
n is the number of endmembers.
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Spectral Mixture Analysis (SMA)
• An area of ground of, say 1.5 m by 1.5 m may contain 3 materials: A, B, and C.• An HSI sensor with a GSD of 1.5 m would measure the ‘Mixture’ spectrum• SMA is an inversion technique to determine the quantities of A, B, and C
in the ‘Mixture’ spectrum• SMA is physically-based on the spectral interaction of photons of light and matter• SMA is in widespread use today in all sectors utilizing spectral remote sensing• Variations include different constraints on the inversion; linear SMA; nonlinear SMA
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0.90
1.00
0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40
Wavelength (micrometers)
Re
flect
an
ce
A
B
C
Mixture
‘Mixture’ = 25%A + 35%B + 40%C
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A linear equation...
7 x 5 5 x
1
7 x
1
5 endmembers in a 7-band spectral data set
A
x
b
bAAAx TT 1bAx
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Linear Spectral Unmixing Theory
Spectral unmixing theory states that the reflectance of an image pixel is a
linear combination of reflectances from the (typically) several “pure”
substances (or endmembers) contained within the ground-spot sampled by
the remote sensing system. This is indicated below:
n
jii,jji rMfR
1
where: Ri is the reflectance of a pixel in band i, f j is the fractional abundance of substance (or
endmember) j in the pixel, and Mj,i is the reflectance of endmember substance j in band i. r i is
the band-residual or unmodeled reflectance for the pixel in band i, and n is the number of
endmembers. A spectral unmixing analysis results in n fraction-plane images showing the
quantitative areal distribution of each of the endmember substances and one root mean
squared (RMS) image showing an overall or global goodness of fit of the suite of
endmembers for each pixel. The RMS image is formed, on a pixel-by-pixel basis, by:
n
j
in
rRMS1
2Objects may also be detected as
anomalies in the RMS image.
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y,xny,xMy,xr
d,uuuM 1pi1
1pi1 uuuU
nUdr p
OSP/LPD/DSR: Scene-Derived Endmembers
(Harsanyi et al., 1994; see also ch. 3 of Chang, 2003)
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This is equivalent to Unconstrained SMA
Some math happens to generate a vector called q...
Pdd
PxdT
T
p
scalary,xrqT
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Statistical Characterization of the Background(LPD/DSR)
0
nUr
q
1i
Tiir rr
q
1
(Harsanyi et al., 1994)
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VV rT
r
#VVIP~
P~
dw TT
scalary,xrwT
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Constrained Energy Minimization (CEM)• The description of CEM is similar to that of OSP/DSR (previous slides)• Like OSP and DSR, CEM is an Orthogonal Subspace Projection (OSP)
family algorithm• CEM differs from OSP/DSR in the following, important ways:
CEM does not simply project away the first n eigenvectors The CEM operator is built using a weighted combination of the
eigenvectors (all or a subset)• Though an OSP algorithm, the structure of CEM is equally readily observed by
a formal derivation using a Lagrange multiplier
• CEM is a commonly used statistical spectral matched filter• CEM for spectral remote sensing has been published on for over 10 years• CEM has a much longer history in the multi-dimensional/array signal
processing literature• Just about all HSI tools today contain CEM or a variant of CEM• If an algorithm is using M-1d as the heart of its filter kernel (where M is the
data covariance matrix and d is the spectrum of the target of interest), then
that algorithm is simply a CEM variant
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Hº: pº(x)= )xMxexp(M TJ 1212
2
12
J = # of Bands
H1: p1(x)= )bxMbxexp(M TJ 1212
2
12
Form the log-likelihood ratio test of Hº and H1:
Xp
xpln)x(l
0
1
Stocker, A.D., Reed, I.S., and Yu, X., (1990). Multi-dimensional signal processing for electro-Optical target detection. In: Signal and Data Processing of Small Targets 1990, Proceedingsof the SPIE, v. 1305, pp. 218-231.
Derivation taken from:
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)xMxexp(M
)bxMbxexp(Mln)x(l
TJ
TJ
1212
1212
2
12
2
12
)xMxexp(
)bxMbxexp(ln
T
T
1
1
21
21
xMx
bxMbx1T
1T
Some algebra...
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A trick...recast as a univariable problem:
2
2
2
2
1
1
2
1
21
21
xbxexp
)xMxexp(
)bxMbxexp(
T
T
After lots of simple algebra applied to the r.h.s:
2
2
2 2
bbxexp
Now, go back to matrix-vector notation:
0
1T1T
2
bMbxMbexp
a scalar threshold
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Take the natural log:
sxMb 1T ...a scalar for each pixel
{ {
FilterKernel
Pixel
0
1T1T ln
2
bMbxMb
Threshold, T
{
>T for H1; <T for H0
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xQQbxMb TTT 11
“The vector: QTx is a projection of the original spectral
data onto the eigenvectors of the covariance matrix, M,
which corresponds to the principal axes of clutter
distribution.” Stocker et al., 1990.
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“Further SCR gain is obtained by forming the optimum
weighted combination of principal components using
the weight vector:”
1QbT
From Stocker et al., 1990.
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Today’s HSI algorithms can also benefit from
1) spatial and spectral subsetting; 2) hierarchical
application of techniques; 3) other...
Its Important to Note That...
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A Day at the Office with HSI and ENVI•Given:See/have thoroughly completed actions (most) on next 3 slidesChecklists (data and sensor)
•You’re given an HSI cube; the fun begins!•Open it/import it in ENVI•Look at the data; spectra, animation, interactive stretching, statistics•Apply a PCA and/or MNF; inspect results, link, mouse about•What are you to do with the data? Devise a strategy.•Gather ancillary information; build/acquire spectral library(ies)•Apply atmospheric compensation; this may be (is!) iterative•Look at the data; spectra, animation, interactive stretching, statistics•Apply algorithms: SAM, MF, SMA, other; this is iterative; link; mouse aboutIn-scene spectra, library spectra
•Apply fusion with ancillary data and information•Problem not solved? May have to resort to other techniques...•Build products/reports
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• The entire remote sensing problem:• Problem analysis• Reason(s) for RS measurements• Planning (inc. costs/budget)• Tasking• Ground-truth• Logistics/persmissions/trespassing/etc...• Shipping to/from Field• Collection platform(s)• Ancillary data (e.g., DEM)• HSI data (now the fun begins!)• Archiving/Including metadata• Distribution
• A good RS report:• RS products
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Properties of the Data Cube
• # of samples, lines, bands• Headers, preline, postline, footers, etc.• Data type• Interleaving• Byte order• Wavelengths, FWHM• Bad bands list• Band names (very optional)• The logical and physical data cube• History file (it doesn’t exist) – keep notes!
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• What you need to know about your data; a check-list:
• Date, time, location, ground elevation, platform elevation,
heading, GSD, be able to calculate where the sun is;
i.e., all RS angles (geometry)
• On-going sensor characterization; know what it is; ask for it!
• Spatial sampling; spatial resolution
• Spectral sampling; SRF; spectral resolution
• NESR, NEDr, NED , NEDT
• Issues: smile, keystone, FPA misregistration, vibration,
parallax, scattered light, self-emission, platform
motion/imaging distortions, etc.
There’s More to Know...
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Introduction to RadiativeTransfer Theory
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Introduction to Radiative Transfer (RT) Theory
• The RT equation
• Simplified expressions get you >90% of what
you need to know…
• Radiometry and radiation propagation; this
discussion is largely from Schott (1997), ch. 4
• Coordinates; frames of reference; principal plane, etc.
• Illumination angle, direction
• View angle, direction
• Phase angle
• Azimuth, relative/absolute
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The Geometry of Remote Sensing
http://rst.gsfc.nasa.gov/Front/tofc.html
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The Radiative Transfer Equation
cos( , )
( , )( )
( , ) ( , , )' ' '
II
wI p d
4 4
Jw
p i T
( )( , , ) exp( cos ) ( , )
4 0
Eq. 7.21 on pg. 156 of Hapke (1993).
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Some Simplified RT Expressions
Schott, J.R., (1997). Remote Sensing: The Image Chain Approach. Oxford University Press, New York, 394 p.
This discussion is largely taken from:
• RT can be (and in practice is) viewed as an accounting
of terms based on radiance interactions in the RS scenario
• Bear in mind, however, that there is a link between the
terms in the accounting and solutions to the RT equation
• The accountings can be as simple or as complicated as
necessary to address the RS question(s)/scenario(s)
• i.e., add terms, delete/ignore terms
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,LLm.sr.m/WL u2r2
s
u2davgbd
d1''
s LrLF1r
FEr
cosE
u2d
d1''
ss Lr
Er
cosEL
For a horizontal surface:
u2T2d
d1''
ss LLr
Er
cosEL
Now, add a thermal emission term:
Solar/Reflective RS:
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uus2dbbsd
ddsT1''
s LLrLLF1r
EEFLr
cosEL
The “Big Equation”
FCHGEBDA LLLLLLLLL
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FCHGEBDA LLLLLLLLL
2d
ds2T21''
s
rFEL
rcosEL
LA LD LB
uus2db2dbs2d
d LLrLF1rLF1r
FE
LE LG LH LC LF
The “Big Equation” (continued)
There’s an LI, too; it’s the adjacency effect—and it’s sometimes
included in the LC term.
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Some ReferencesAdams, J.B., and Gillespie, A.R., (2006). Remote Sensing of Landscapes with Spectral
Images: A Physical Modeling Approach. Cambridge University Press, 362 p. Campbell, J.B., (2007). Introduction to Remote Sensing, 4th edition. The Guilford Press,
New York, NY, 626 p. Hapke, B., (1993). Theory of Reflectance and Emittance Spectroscopy. Cambridge
University Press, 455 p. Hecht, E., (1987). Optics, 2nd Edition. Addison-Wesley Publishing Company, Reading,
Massachusetts, 676 p. Jensen, J.R., (2007). Remote Sensing of the Environment: An Earth Resource
Perspective. 2nd edition. Prentice Hall Series in Geographic Information Science, 608 p. Jensen, J.R., (2005). Introductory Digital Image Processing. 3rd edition. Prentice Hall Series
in Geographic Information Science, 544 p. Landgrebe, D.A., (2003). Signal Theory Methods in Multispectral Remote Sensing. Wiley-
Interscience, John Wiley and Sons, New Jersey, 508 p. Richards, J.A., and Jia, X., (1999). Remote Sensing Digital Image Analysis, An Introduction,
3rd, Revised and Enlarged Edition. Springer, Berlin, 363 p. Sabins, F.F., (2007). Remote Sensing: Principles and Interpretation, 3rd Edition. Waveland
Pr. Inc., 512 p. Schott, J.R., (1997). Remote Sensing: The Image Chain Approach. Oxford University Press,
New York, 394 p. Solé, J.G., Bausá, L.E., and Jaque, D., (2005). An Introduction to the Optical Spectroscopy of
Inorganic Solids. John Wiley & Sons, Ltd., 283 p.