EOS 840 Hyperspectral Imaging Applications

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EOS 840 Hyperspectral Imaging Applications
October 13, 2004 Week 7
Ron Resmini v 703-735-3899 ronald.g.resmini_at_boein
g.com Office hours by appointment
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Outline

• Spectral libraries
• Reading for next week
• Review/context/a thread...
• Thinking about spectra (a review)
• Algorithms
• My semester project status
• Your semester project status

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Review/Context/A Thread...

• HSI RS is based on the measurement of a physical
  quantityas a function of wavelength its
  spectroscopy
• HSI is based on discerning/measuring the
  interaction oflight (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
  targetsof interest in a scene
• There are complex interactions between light,
  targets ofinterest, and the atmosphere
• Theres a lot (lots!) of information in the
  spectra

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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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• Collections of spectra in hyperspace
• Resmini (2003)
• Density
• Volume
• Orientation
• Clustering/ of clusters/cluster spacing
• Mixing trends (binary, ternary, linear,
  non-linear)
• Eigenvectors/eigenvalues
• etc...
• Still vastly uncharted territory with lots of
  potential for understanding HSI...imho

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Algorithms
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• Algorithm "classes"/overview
• Distance Metrics
• Angular Metric
• SMA/OSP/DSR/CEM
• Derivative Spectroscopy/other Parameterization
  Methods
• Spectra in hyperspace
• Some real scatter plots
• Use ENVI to view scatter plots

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• Real data show very complicatedscatter plots
• blobs, elongated blobs, etc...
• binary, ternary mixing trends
• Radiance, reflectance, emissivity
• which to use? when?

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• Whole pixel/single-pixel, non-statistical
  distance metrics
• Distance between points (spectra) in hyperspace
• Spectra as vectors
• Absolute difference/absolute difference squared
• Derivative difference/derivative difference
  squared
• Euclidean distance
• Relative difference
• BE/Hamming distance (see Jia and Richards, 1999)
• There are others, too...
• ENVI...
• Application strategies (i.e., in-scene
  spectra/library spectra)
• Mixed pixels...

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• Spectra as vectors
• Angular separation of vectors (spectra)
• Spectral Angle Mapper (SAM)
• Invariant to albedo
• Running SAM in ENVI
• Application strategies(i.e., in-scene
  spectra/library spectra)
• Mixed pixels...

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• Statistical distance metrics
• (essentially preprocessing for supervisedclassifi
  cation)
• Minimum distance
• Mahalanobis distance
• Maximum likelihood distance
• Parallelpiped
• Jeffries-Matusita distance/Bhattacharyya distance
• Spectral divergence (see sec. 10.2.2 of Richards
  and Jia, 1999)
• Other...
• Application strategies (i.e., in-scene spectra)
• Mixed pixels...

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Minimum Distance
Mahalanobis Distance
Maximum Likelihood
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Jeffries-Matusita (JM) Distance
...the distance between a pair of probability
distributions is... from p. 244 of Richards and
Jia (1999)
Where B is the Bhattacharyya distance
See sec. 10.2.3 of Richards and Jia (1999).
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• The mixed pixel
• Building a mixed pixel - ENVI, MS Excel
• Linear spectral mixture analysis
• Determining quantity of material
• Endmember selection
• Manual
• Convex hull
• Pixel-Purity Index (PPI)
• Adaptive/updating/pruning...
• Other (e.g., N-FINDR, ORASIS, URSSA, etc...)
• Wild outliers

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• Spectral mixture analysis
• applications
• scene characterization
• material mapping
• anomaly detection
• other...

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A linear equation...
x
A
b
5 endmembers in a 7-band spectral data set
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• Unmixing inversion
• Interpretation of results
• RMS, RSS, algebraic and geometricinterpretations
  (pg. 155 of Strang, 1988)
• Band residual cube
• Iterative process
• Fraction-plane color-composites
• Change detection with fraction planes
• Inversion constraints?...
• Application strategies (i.e., in-scenespectra/lib
  rary spectra)

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• application strategies (continued)
• directed search? anomaly detection?
• Shade/shadow
• shade endmember
• shade removal
• Other...
• objective endmember determinationTompkins et al.

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• Is the mixing linear?
• Non-linear spectral mixture analysis
• Checker-board mixtures
• Intimate mixtures
• Spectral transformations (e.g., SSA)and use of
  ENVI

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...Recap Where have we been? Where are we
going? BTW...Always do the math!

• More on the statistical characterizationof
  multi-dimensional data
• Covariance matrices
• Eigenvectors of the covariance matrix
• Geometric interpretation
• Half-way to PCA...
• Statistics with ENVI

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• Orthogonal Subspace Projection (OSP)
• Derivation in detail (next several slides...)
• Application of the filter
• Endmembers
• Statistics
• Interpretation of results
• OSP w/endmembers unconstrained SMA
• Different ways to apply the filter/application
  strategies(i.e., in-scene spectra/library
  spectra)

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OSP/LPD/DSR Scene-Derived Endmembers
(Harsanyi et al., 1994)
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The value of xT which maximizes l is given by xT
dT
This is equivalent to Unconstrained SMA
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Statistical Characterization of the
Background (LPD/DSR)
(Harsanyi et al., 1994)
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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 theeigenvectors (all or a subset)
• Though an OSP algorithm, the structure of CEM is
  equally readily observed bya 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 signalprocessing
  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 thedata covariance
  matrix and d is the spectrum of the target of
  interest), thenthat algorithm is simply a CEM
  variant

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• The statistical spectral matched filter (SSMF)
• Derivation in detail
• Application of the filter
• Statistics
• Endmembers (FBA/MCEM)
• Interpretation of results
• Many algorithms are actually the basic SSMF
• Different ways to apply the filter/application
  strategies(i.e., in-scene spectra/library
  spectra)
• Matched filter in ENVI

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Derivation taken from
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.
J of Bands
Form the log-likelihood ratio test of Hº and H1
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Some algebra...
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A trick...recast as a univariable problem
After lots of simple algebra applied to the r.h.s
Now, go back to matrix-vector notation
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Take the natural log
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Constrained Energy Minimization (CEM)
(Harsanyi et al., 1994)
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An Endnote...

• Previous techniques exploit shape and albedo
• this can cause problems...
• Sub-classes of algorithms developed to mitigate
  this
• shape, only, operators
• MED, RSD of ASIT, Inc.
• MTMF of ENVI

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Last Class of Algorithms

• Spectral feature fitting/derivativespectroscopy
• Spectral parameterizations
• Wavelets
• Band depth/band depth mapping
• Application strategies (i.e., in-scenespectra/lib
  rary spectra)
• Mixed pixels...

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Another Endnote...

• Performance prediction/scoring/NP-Theory, etc...
• Hybrid techniques
• still some cream to be skimmed...
• Caveat emptor...
• lots of reproduction of work already accomplished
• who invented what? when?
• waste of resources
• please do your homework!read the lit.!

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My Semester Project Status

• Tools/approach
• 1D and 2D analytical solutions to heat equation
• FlexPDE finite element modeling
• Data analysis with ENVI
• Analytical solutions to 1D and 2D heat equation
• Additional TIMS data analysis in ENVI
• TES on going (this is a challenge)
• Literature research on-going
• Additional modeling with FlexPDE
• Dealing with (as yet) unconstrained parameters

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Surface Temperature vs. Lava Tube Roof Thickness
Tenviron 0º C TLava 1200º C
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Numerical 2D Modeling
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Analytical solution to
On the following
(Tenviron 0º C)
Y 0
Radiative boundary condition added
Y D
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The Solution
and
D Lava tube roof thickness
Solve with a root-finding algorithm
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Another Approach...
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X0
XL
Y0

YD
X0
XL
Y0
Y0

YD
YD
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The Solution
Technique Principle of superposition and
separation of variables
Evaluate the boundary condition at y D
Evaluate the coefficients
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The B.C. at Y D
At y D
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My Semester Project Issues

• Constraining the value of h
• What should the diameter of the lava tube be?
• Distinguishing sky lights from unbroken tube roof
• Widely ranging surface temperatures in the data
• Validity of B.C.s used in modeling
• Radiative upper B.C.?
• Mapping/contouring roof thickness throughoutthe
  entire TIMS Kilauea scene
• Need to double-check my math!
• Other...

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Your Semester Project Status
A Few More Project Challenges For You

• A matched filter algorithm based on a
  distribution other than normal
• Compare the technique of sec. 13.5.2 in textbook
  with a spectralmixture analysis approach to data
  classification
• Can/should the technique of 13.5.2 be used to
  build an adaptivespectral matched filter
  algorithm?
• Implant signatures in HSI cubes with ENVI. Run
  algorithms to findthe signatures record
  results. Remove one or more bands andrepeat.
  Is there a Hughes Phenomenon?
• Compare various lossy compression algorithms for
  tolerable limitsof information loss
• Compare exploitation based on log residuals with
  exploitationbased on ELM or other atmospheric
  compensation

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Backup Slides
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Lagrange Multiplier Derivation of CEM Filter
Minimizing E is equivalent to minimizing each yi2
(for k 1, 2, 3, ... )
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In Matrix Notation
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