EOS 740 Hyperspectral Imaging Systems

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EOS 740 Hyperspectral Imaging Systems
February 25, 2005 Week 5
Ron Resmini v 703-735-3899 ronald.g.resmini_at_boein
g.com Office hours by appointment
Put EOS740 in the subject line of e-mails to
me...Thanks!
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Outline

• Review/context
• Picking thresholds in SAM
• Atmospheric compensation
• ELM
• Algorithm overview
• HSI analysis and exploitation with ENVI

Our first guest lecturer will be next week.
Topic HSI hardware. Pleasebe prepared to ask
questions!
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Four (A-D) Equivalent Notations/Representations
(0.11, 0.23, 0.30, 0.25, 0.16, 0.27, 0.31,
0.37,...,)
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Physics of Imaging Spectroscopy - Review

• Origin of spectral features
• Electronic, vibrational, vibrational/rotational,
  etc
• Materials reflect/scatter, transmit, absorb,
  light
• Optical constants
• index of refraction, n
• imaginary part of refractive index, k
• ...related to absorption absorption coefficient
  isa 4pk/l
• aka complex refractive index, m nik
• This is really a convenience for solving PDEsof
  electromagnetic theory

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• Sensors measure radiance (spectral radiance)
• Materials interact with light
• m nik
• Radiance to reflectance or emissivity
• The propagation of light
• Electromagnetic theory
• Solution of Maxwells Equations
• The Fresnel equations (pages from Hapke, 1993)
• BTW...Huygens Principle
• Snells Law/Law of Reflection
• Fermats Principle
• Polarization (not today...)
• What do you need to know?

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• For RS The types of scattering e.g.
• diffuse, specular idealized and
  reality(Schott, 1997 pg. 100) all describable
  withFresnel equations (and other...)
• Complicated, real surfaces and materials
• Minerals/rocks/mixtures (BTW...isotropic,uniaxial
  , biaxial)
• Vegetation
• Soils
• Water
• All real surfaces/materials!
• Its complicated but we have spectral libraries...
• Mixed pixels (briefly more later in semester)
• The atmosphere(!)

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• So, can HSI (or any RS) help you? You must ask
• Is there a signature?
• How much is expected to be exposed/present?
• Other physical, chemical, radiative
  transferconsiderations
• E.g., littoral zone RS of coral under a turbid
  watercolumn that is under a turbid
  atmosphere...yikes!

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Radiative Transfer (RT) Theory Review

• Simplified RT expressions get you gt90 of
  whatyou need to know
• Radiometry and radiation propagation
  ourdiscussion was 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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Some Simplified RT Expressions

• RT can be (and in practice is) viewed as an
  accountingof terms based on radiance
  interactions in the RS scenario
• Bear in mind, however, that there is a link
  between theterms in the accounting and solutions
  to the RT equation
• The accountings can be as simple or as
  complicated asnecessary to address the RS
  question(s)/scenario(s)
• i.e., add terms, delete/ignore terms

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Solar/Reflective RS
For a horizontal surface
Now, add a thermal emission term
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The Big Equation
Each interaction may be assigned a term and
accounted for in the RT expression.
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The Big Equation (continued)
Theres an LI, too its the adjacency effectand
its sometimes included in the LC term.
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A Day at the Office with HSI and ENVI

• Given
• See/have thoroughly completed actions (most) on
  Slides 3 and 4
• Checklists (data and sensor see next 3
  slides...)
• Youre 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 about
• In-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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Checklist (1 of 2)

• Some practical information you should know
• Kind of dispersion
• Prisms, gratings, interference (FTS)
• Push-broom whisk-broom other (e.g., FTS)
• What you need to know about your data a
  check-list
• Date, time, location, ground elevation, platform
  elevation,heading, GSD, of samples, of
  lines, of bands,band centers, band FWHM, band
  interleaving,byte order be able to calculate
  where the sun isi.e., all RS angles (geometry),
  scale factors

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Checklist (2 of 2)

• Radiometric and spectral calibration
• How theyre accomplished
• When ideally with every collection event
• On-going sensor characterization ask for it!
• Spatial sampling spatial resolution
• Spectral sampling SRF spectral resolution
• NESR, NEDr, NEDe, NEDT
• Issues smile, keystone, FPA misregistration,
  vibration,parallax, scattered light,
  self-emission, platformmotion/imaging
  distortions, etc
• Buyer beware - know the roles of the data
  providerand the data analyst

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There may be other items that shouldbe on the
checklist(s) and/or someitems on the list(s)
that are notshow-stoppers if you dont know them.
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Information Content and Extraction Context

• 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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• Algorithm types, classes, categoriesan
  introduction and overview
• Angular Metrics
• SAM
• Distance Metrics
• w/, w/o statistics
• Data transformations
• PCA, MNF, ICA
• SMA/OSP/DSR/CEM/SMF
• Derivative Spectroscopy/other Parameterization
  Methods

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The Atmosphere!
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The Empirical Line Method (ELM)

• You must have two or more calibration panels in
  your HSI cube
• You must have ground-truth reflectance spectra of
  those panels
• You must have calibrated at-aperture radiance
  data
• For each band in your HSI data set, construct the
  following plot

This example showssix (6) calibration
panels (there are 6 points)
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ELM - continued

• Fit a line to the points
• Obtain slope and intercept of that line
• Intercept is the additive or scattering term
• Intercept has units of radiance
• Gain is the multiplicative term (solar input and
  t)
• Gain has units of (radiance/reflectance)

Slope
Intercept
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ELM - continued

• If you have an n-band cube, you now have
• n pairs of (slope, intercept) one for each band
• Apply (slope, intercept) coefficients to the
  originalcalibrated at-aperture radiance data
• Radiance minus intercept followed by
• Division by gain
• (Radiance intercept) / gain
• ENVI does most of this for you

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Working with ENVI

• Spectral libraries in ENVI (continued)
• Building libraries
• Exporting images for building products
• Band math, spectral math a review
• Euclidean distance a review
• Empirical Line Method (ELM)
• Principal Components Analysis (PCA)
• A brief introduction
• Spectral matching SAM, ED, and now...
• Spectral Matched Filter
• A brief introduction

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Euclidean Distance nD Geometry A Review
Whole-Pixel Distance Metric in nD Hyperspace
Assume a two band spectral remote sensing system.
Each two point spectrum is a point in Band b
vs. Band a space.
A 2D scatterplot with 2 spectra
Spectrum s2
Band b
Spectrum s1
Band a
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SAM nD Geometry A Review
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.
A 2D scatterplot with 2 spectra
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 A Review

• Chang (2003), ch. 2, pp. 20-21 (see .pdf
  file) and...
• Assume two 5-band spectra as shown

BTW...read Sec. 2.2 to Sec. 2.2.2 on pp. 20-21
fair game material for the mid-term.
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• Let the 5 bands have band names a, b, c, d, and e

• 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
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Assignment 3 Due the Week of 11 Mar., 2005

• Read portion of chapter on principal components
  analysis(provided to you).
• Read chapter 3 in Chang (2003).Just glance at
  eqs. 3.6, 3.10, 3.11.Do NOT panic if this
  stuffs completely opaque to you tryto wade
  through it.

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How are your projects going?