EOS 740 Algorithms: Introduction

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EOS 740 Algorithms Introduction
Ron Resmini v 703-735-3899 ronald.g.resmini_at_boein
g.com Office hours by appointment
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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

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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
• 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...and SAM...

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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
• 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
Where B is the Bhattacharyya distance
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• The mixed pixel
• a basis concept a very important
  conceptdescription of a mixed pixel
• determining quantity of material
• building a mixed pixel - spectral math
• building a mixed pixel - MS Excel
• mixing trends in hyperspace

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

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• 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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• Unmixing inversion
• interpretation of results
• RMS, RSS, algebraic and geometricinterpretations
• are RMS, RSS, etc. the best measures?
• residual correlation analysis (RCA)
• band residual cube
• can we build a band residual cubewith ENVI?

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• iterative process
• the inversion in Matlab a closer lookat the
  math
• fraction-plane color-composites
• change detection with fraction planes
• constraints on inversion
• is it a linear mixture?

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• application strategies (i.e., in-scenespectra/lib
  rary spectra)
• directed search? anomaly detection?
• Shade/shadow
• shade endmember
• shade removal
• Other...
• objective endmember determinationTompkins et al.

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• Non-linear spectral mixture analysis
• checker-board mixtures
• intimate mixtures
• building a non-linear mixture
• spectral transformations (e.g., SSA)and use of
  ENVI

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A linear equation...
x
A
b
5 endmembers in a 7-band spectral data set
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Prelude to Other Algorithms Statistical Spectral
Matched Filters OSP OBS

• 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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• 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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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 (ITT/RSI)

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Last Class of Algorithms

• Spectral feature fitting/derivative spectroscopy
• 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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• References/Resources
• Books
• Journals
• ATBDs (MODIS, other)
• SPIE, IEEE, other

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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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