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Hyperspectral Imagery (HSI) Dimensionality Reduction. Ronald G. Resmini, Ph.D. 18 July 2005 Institute for Pure and Applied Mathematics (IPAM) v: 703-735-3899 • [email protected]. Outline. Introduction to HSI HSI Dimensionality HSI Dimensionality Reduction (DR) - PowerPoint PPT Presentation
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Hyperspectral Imagery (HSI)
Dimensionality Reduction
Hyperspectral Imagery (HSI)
Dimensionality Reduction
Ronald G. Resmini, Ph.D.Ronald G. Resmini, Ph.D.18 July 200518 July 2005
Institute for Pure and Applied Mathematics (IPAM)Institute for Pure and Applied Mathematics (IPAM)
v: 703-735-3899 v: 703-735-3899 •• [email protected] [email protected]
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OutlineOutline
• Introduction to HSI
• HSI Dimensionality
• HSI Dimensionality Reduction (DR)
Do We Need DR?
• HSI Algorithms
• What Can You Do? How ShouldYou Do It?
• Introduction to HSI
• HSI Dimensionality
• HSI Dimensionality Reduction (DR)
Do We Need DR?
• HSI Algorithms
• What Can You Do? How ShouldYou Do It?
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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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Electromagnetic EnergyElectromagnetic Spectrum
Electromagnetic EnergyElectromagnetic Spectrum
Electromagnetic SpectrumElectromagnetic Spectrum
WavelengthWavelength
(nm)(nm)
Cosmic Cosmic RaysRays
Gamma Gamma RaysRays
X X RaysRays
Microwaves Microwaves (Radar)(Radar)
Radio & Radio & Television WavesTelevision WavesUVUV
101055 101066 101077 101088 101099 10101010 10101111 1010121210101110101010-1-11010-2-21010-3-31010-4-41010-5-5
Shorter WavelengthsHigh Energy
Shorter WavelengthsHigh Energy
Longer WavelengthsLow Energy
Longer WavelengthsLow Energy
V / NIR / SWIR / V / NIR / SWIR / MWIR / LWIRMWIR / LWIR
Optical RegionOptical Region
400400 1400014000
400
0.4
400
0.4
14000
14.0
14000
14.0
1500
1.5
1500
1.5
3000
3.0
3000
3.0
5000
5.0
5000
5.0
700
0.7
700
0.7
NIRNIR MWIRMWIRSWIRSWIRRRGG LWIR LWIR BB LWIRLWIRWavelength
(nm)(m)
Emitted Emitted EnergyEnergy
Reflected Reflected EnergyEnergy
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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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Sampling the SpectrumSampling the Spectrum
NIR SWIR MWIR LWIR
400 nm400 nm 700700 15001500 30003000
RRBB
50005000 14000 nm
GG
Panchromatic: one very wide bandPanchromatic: one very wide bandLOW
Multispectral: several to tens of bandsMultispectral: several to tens of bandsMED
Hyperspectral: hundreds of narrow bandsHyperspectral: hundreds of narrow bandsHIGH
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Interaction of energy and objectsInteraction of energy and objects
Transmitted EnergyTransmitted Energy
Absorbed EnergyAbsorbed Energy
Reflected EnergyReflected EnergyV-MWIRV-MWIR
Emitted EnergyEmitted EnergyMW-LWIRMW-LWIR
Energy Balance Equation: EI () = ER() + EA() + ET() Energy Balance Equation: EI () = ER() + EA() + ET()
Incident EnergyIncident 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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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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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)
MultispectralMultispectral
(10’s of bands)
MultispectralMultispectral
(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.
(...beyond scope for a discussion on DR; but...)
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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
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 ReflectanceAngle 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
WavelengthWavelength
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
WavelengthWavelength
No Detection
Background
Gas
WavelengthWavelength
Absorption
Background (Warm)
Gas (Cool)
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d1ehc2dMM
1
kT
hc52
0
432
445
Thc15
Tk2
Stefan-Boltzmann Law:
Two surfaces radiating at each other:
View Factor Algebra and Radiant Exchange...
1
11TTA
q
21
42
41
12
...from Welty, Wicks, and Wilson (1984)
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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
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
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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• Spatial Resolution
• Radiometric Resolution
• Temporal Resolution
• Spatial Resolution
• Radiometric Resolution
• Temporal Resolution
ResolutionsResolutions
(...beyond scope for a discussion on DR; but...)
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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.
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
DR?
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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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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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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
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.4 0.8 1.2 1.6 2.0 2.4
Wavelength (m)
Ref
lect
ivity
,
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Four (A-D) Equivalent Notations/Representations
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
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,
(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
, Band a
, 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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Defining HSI Dimensionality• “Curse of dimensionality”
for Gaussian distribution......for a given classification accuracy# of training samples grows quadraticallybased on exploitation methodology; e.g.:
Mahalanobis Distance:
i1Ti
2i mxmxm,xd
Maximum Likelihood:
i1i
Tii
2i mxmxlnm,xd
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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
0.40
400
0.40
1500
1.50
1500
1.50
3000
3.00
3000
3.00
700
0.70
700
0.70
NIRNIR SWIRSWIRRRGGBB
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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Estimating HSI Dimensionality
• Eigenvalues of the covariance principal components analysis (PCA)/aka KL optimal, least squares sense
• Eigenvalues of the correlation matrix
• Visual—based on eigenvalues
• Continuous significant linear dimensionality CSD; eigenvalues (next slide...)
Umaña-Díaz, A., and Vélez-Reyes, M., (2003). Determining the dimensionality of hyperspectral imagery for unsupervised band selection. Proceedings of the SPIE, S.S Shen and P.E. Lewis, eds., v. 5093, pp. 70-81. (...and references cited therein.)
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n
ii,minCSD
1
1
m
ii
p
ii
Var%
1
1100
where: i are the eigenvalues
i
Tyy mymyECovariance Matrix:
Find the eigenvalues of the covariance(or correlation) matrix and then...
or:
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0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
45000000
50000000
0 20 40 60 80 100 120 140
Band Number
Eig
enva
lue
Virginia City Probe-1 HSI Data
Eigenvalues from a PCA
116 bands out of 128
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0
200000
400000
600000
800000
1000000
1200000
0 50 100 150 200
Band Number
Eig
enva
lue
Eigenvalues from a PCA
162 bands out of 210
Urban Scene HYDICE HSI Data
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0
10000
20000
30000
40000
50000
60000
70000
80000
0 20 40 60 80 100 120 140
Band Number
Eig
enva
lue
Eigenvalues from a PCA
128 bands out of 128
Mormon Mesa SEBASS HSI Data
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Estimating HSI Dimensionality
• Wavelet basis
• Nonlinear dimension estimationNear neighbor method of PettisFukunaga and Olsen’s KL-related methodFractal dimension
o Hausdorff dimensiono Box-counting methodo Correlation integral/dimension (next slide...)
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rln
rvlnlimDr
B 10
rln
rClnlimD m
r 0
Box Counting:
Correlation Dimension:
where: r is box size (DB) or radius of a hypersphere (D)
N
j,iji
Nm xxrH
NlimrC
12
1
Correlation Function:
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HSI Dimensionality Reduction• Techniques
Principal components analysis (PCA)Minimum noise fraction (MNF)Vector quantization (VQ)Projection pursuit (PP)The universe of data compression
o lossless/lossy (when/why?)o discrete cosine transformation (DCT)o wavelets-based compression
Best bands selection/band averaging
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Best-Bands SelectionBest-Bands Selection
2.0 m to 2.5 m – SWIR, Only
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Other Means of DR
• Spectral mixture analysis (SMA)basis vectors
• Analysis of filter vectors (OSP algorithms...)• Wavelet-based feature selection• On-board processing
transmit productadvanced computationquantum computation?
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Other Means of DR
• Transmit only bands of interestbest-bands selection/band averaging......perhaps after atmos. comp.
• Spectral parameterizations• Derivative spectroscopy• Binary encoding
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0.6
0.7
0.8
0.9
1.0
3 4 5 6 7 8 9 10 11 12 13 14
Wavelength (micrometers)
Quartz Primary Lobe 2Band Depth
(QP2)Quartz Primary Lobe 1 Slope
(QP1 Slope)
Primary Carbonate AbsorptionBand Depth(MWIR CO3)
Spectral Parameterization:Spectral Metrics (1 of 2)
Soil Spectrum
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Desert Soil (Malpais)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.00 0.10 0.20 0.30 0.40 0.50
3.5 - 4.17 microns Band 2 FWHM
3.5
- 4.
17
mic
rons
Ban
d 1
Dep
th
Disturbed Soil
Pristine Soil
Vehicle Treads
Spectral Parameterization:Spectral Metrics (2 of 2)
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The Need For DR• Is there a need for DR?• Is there a “curse of dimensionality”?• Well...it depends...• Not with today’s (and tomorrow’s) computers• Not with many capable HSI algorithms• Structure of HSI in n-D space
linear mixing trends mixed pixels; spectral endmembers are these clusters?
• Yes...if using traditional MSI classification
techniques...
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Mahalanobis Distance
i1Ti
2i mxmxm,xd
Maximum Likelihood
i1i
Tii
2i mxmxlnm,xd
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dxw|xpw|xpJ
2
x
jiij
Jeffries-Matusita (JM) Distance
Bij e12J
21
j21
i
ji
ji
1
jiTji
2
2
1mm
2mm
8
1B
Where B is the Bhattacharyya distance
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HSI Algorithms
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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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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, , 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
2T11
ss
sscos T1s
2s
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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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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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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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#UUIP
T1T# UUUU
PnPdPr p
PnxPdxPrx Tp
TT
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xPPx
xPPddxmax
xPnnPEx
xdPdxmax
TT
TTT
x2
2p
TTT
T2p
T
xmax
xAxB 1
TTPPddA
TPPB
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Pdq TT
This is equivalent to Unconstrained SMA
The value of xT which maximizes is given by xT = dT
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)= xMx2
1exp(M2 1T2
12J
J = # of Bands
H1: p1(x)= bxMbx2
1exp(M2 1T2
12J
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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xMx2
1exp(M2
bxMbx2
1exp(M2
ln)x(l1T2
12J
1T212J
xMx2
1exp(
bxMbx21
exp(ln
1T
1T
xMx
bxMbx1T
1T
Some algebra...
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A trick...recast as a univariable problem:
2
2
2
2
1T
1T
xbx
2
1exp
xMx21
exp(
bxMbx21
exp(
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
01T
1T ln2
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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What Should You Do?How Should You Do It?
• Join the fray!...HSI is a big tent• Dump Lena/girl...
the spectrum is the fundamental datum
• Conduct honest, rigorous comparisons with
existing, current best-practices HSI techniques• Apply techniques to multiple, large, diverse data sets• Team with HSI expert(s) and subject-matter expert(s)• Seek peer-reviews from HSI experts
I’m happy to be a reviewer...
• Learn about/care about the field; be relevant be more than buzz words we’re more than an opportunity for statistical analyses
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Contact Information
Ron Resmini
The Boeing Company (Associate Technical Fellow);
The National Geospatial-Intelligence Agency (NGA); and
School of Computational Sciences, George Mason University
v: 703-735-3899
e-mail(1): [email protected]
e-mail(2): [email protected]
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Backup SlidesBackup Slides
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• Remote Sensing of Environment
• International Journal of Remote Sensing
• IEEE Transactions on Geoscience and Remote Sensing
• Journal of Geophysical Research• Solid Earth, Planets, Oceans and Atmospheres
• Icarus
• Remote Sensing Reviews
• Photogrammetric Engineering and Remote Sensing
• Applied Optics
• Journal of the Optical Society of America
• Many others, too!
Resources: Peer-Reviewed Journals
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Resources: Non-Reviewed Journals
• Published conference proceedings:
• SPIE
• your library may subscribe to SPIE
• abstract services
• AVIRIS (NASA) conference
• IEEE/IGARSS
• Proceedings of the ASPRS
• Many others, too!
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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.