Image Processing

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Image Processing Deconvolution in the TIR

• Lecture VEH4
• 09-16-03

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From last time
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Silicates
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Christiansen Feature in Silicates
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Pyroxenes
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Hamilton, 2000
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Hamilton, 2000
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Carbonates

• Fundamental vibrational modes dominated by C-O
  stretching and bending modes
• Generally in the 1600-1400, 900-850, and 400-300
  cm-1 regions (6-7, 11.5, and 25-30 µm)
• Carbonates are a solid solution series, so
  features shift as a function of composition

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Oxides/Hydroxides

• Fundamental absorptions dominated by metal-O
  modes
• Typically in the lt800 cm-1 (gt12 µm) region

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Halides and Sulfates

• Absorptions dominated by primary element-O modes
• Halides (halite, sylvite, fluorite) have VERY
  broad features in the IR
• Minerals are isometric and have strong ionic
  bonds that cause primary vibrations to be
  dominated by lattice vibrations as a whole rather
  than (e.g.,) Na-Cl modes
• Sulfate (gypsum, anhydrite) absorptions common
  around 1100-1200, 700-200 cm-1 (8-10, 15-50 µm)

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Halides
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Sulfates
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Native Elements

• Should they have IR spectral features?
• Why/not?

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Water Hydroxyl (not mineral groups, but
whatever)

• Fundamental modes of H2O at 2.9 and 6.1 µm only
  the bending mode is visible in TIR
• Visibility of 6.1 µm band in TIR depends on
  particle size (more on this later)
• OH- -bearing minerals (without H2O) display a 2.7
  µm band, but no 2.9 or 6.1 µm band

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Rocks Linear Mixing

• Rock spectra are simple linear combinations of
  component mineral spectra in proportion to
  abundance
• Areal mixtures (also called checkerboard)
• Comparable to looking at a rock in thin section

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Rock Spectra

• Christiansen feature position is no longer tied
  to a single optical constant
• CF migrates to longer wavelengths from felsic to
  ultramafic compositions - WHY?
• CF is correlated with bulk chemistry Lyon,
  1964 Salisbury and Walter, 1989 Walter and
  Salisbury, 1989

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CF Correlations
CF, µm
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Mixture Deconvolution

• Process of reverse engineering mixtures to
  determine components of a scene/spectrum and
  their relative/absolute abundances
• Components (A, B, C)
• Rocks (granite, basalt, quartzite)
• Minerals (kaolinite, calcite, olivine)
• Identification of rocks and minerals usually
  requires additional input information (e.g.,
  spectral library)

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Linear Mixing

• Band matching approach common in VNIR analyses
  is not appropriate in TIR
• Linear addition of spectra changes band shapes
  and positions
• Complex spectra must be linearly deconvolved

Note IR bands are NOT Gaussians
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Linear Deconvolution

• See Ramsey and Christensen 1998 and references
  therein for details
• Inputs
• Mixed spectrum (unknown)
• End member minerals (from spectral library)
• Spectral range desired
• Remove negative components?
• Outputs
• Best-fit modeled spectrum
• End members used in best fit and abundances
• RMS error

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End member selection

• Overall spectral shape can be used to generally
  identify a spectrums dominant mineralogy
• Mafic vs. felsic intrusive vs. extrusive
• End member sets can be tailored to expected
  mineralogy and common alteration/weathering
  products
• Number of end members depends on number of data
  points in spectrum and common sense
• 25-30 is reasonable, including solid solution
  phases
• Deconvolution is mathematics - theres nothing
  about geologic plausibility
• The geologist is an important part of the process

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Spectral range selection

• Keep the dominant mineralogy in mind and make
  sure that youre including all regions that may
  contain important features
• e.g., carbonate bands that fall outside the
  silicate wavelength range
• Dont include unnecessary regions that may
  confound your analysis due to measurement
  idiosyncrasies
• Strong water vapor absorptions may be fit by
  carbonates

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V. E. Hamilton TES Data Users Workshop
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Assessing the qualityof your fit

• RMS error
• Provided as a single number averaged over the
  entire spectrum, its not very valuable
• only good for judging multiple fits of a single
  unknown (i.e., with differing end member sets)
• does not reliably indicate major local errors if
  most of the spectrum is fit well
• Residual error spectrum
• Subtract model spectrum from measured spectrum
• useful for identifying local misfits
• Visual inspection
• Severe local misfits indicate missing or
  wrong phase

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Hamilton and Christensen 2000
V. E. Hamilton TES Data Users Workshop
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What should you believe?

• Geological plausibility of minor phases
• Minerals that should(nt) occur together
• Minerals that form in weird environments
• Detectability limits
• Detectability depends in large part on overall
  spectral contrast and band depth/width
• Laboratory
• Phases identified at gt5-10 vol. are usually
  believable in simple mixtures (i.e., standard
  rock)
• Remote Sensing (i.e., TES)
• Phases identified at gt10-15 vol. are usually
  believable
• Deconvolution is mathematics - tiny abundances
  may improve a fit, but may not be reasonable

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Spectral Contrast

• Differences in contrast between unknown and end
  members can be accommodated by including a
  blackbody end member
• e.g., differences between particle size of end
  member samples and unknown
• Carbonates and oxides may be included to reduce
  contrast if theres no blackbody end member
• Linearity of mixing persists to very fine
  particle sizes (10 - 20 µm)
• Need fine particulate end member spectra

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V. E. Hamilton TES Data Users Workshop
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On to images
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Image Data

• Data assembled as an image, in digital format
• Picture elements - pixel
• Arranged in regular order in x, y space
• Rows and columns
• Lines and samples
• Pixel contains EM energy intensity information as
  a numerical value called digital number, or DN
• Recorded in bits, with each bit as an exponent of
  base 2
• 8-bit 28 256 values on gray scale, with
  0black and 255white
• 8 bits 1 byte (a common format descriptor)
• Successive wavelength data are added in z
  dimension
• Image cube

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Image Cube
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Image Processing

• Image restoration
• Image enhancement
• Information extraction

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Image Processing

• Image restoration
• Geometric transforms correct for
• Distortion in imaging system
• motion of s/c or aircraft
• Topography
• Changes in viewing geometry
• Projection
• Restoration of data dropouts or striping
• Removal of random noise
• Corrections for atmospheric scattering

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MOC N/A
Geometrically corrected
As acquired
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THEMIS IR
Geometrically corrected
As acquired
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Image Processing

• Image restoration
• Geometric transforms correct for
• Distortion in imaging system
• motion of s/c or aircraft
• Topography
• Changes in viewing geometry
• Projection
• Restoration of data dropouts or striping
• Removal of random noise (FFT)
• Corrections for atmospheric scattering

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Datadropouts striping
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Image Processing

• Image enhancement
• Filters - usually for edge enhancement
• Boxcar (filter shape)
• a.k.a. Laplacian filter
• 3 x 3 pixels minimum, odd numbered
• non-directional
• Low pass/Gaussian (filter type)
• removes high frequency information, odd numbered
• High pass (filter type)
• removes low frequency information, also odd
  numbered
• difference of original data and low pass filter
• User-defined
• e.g., directional filter

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Boxcar (Laplacian) Filter
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Multiply each pixel by valuein corresponding
filter pixelsum the resulting value andcombine
with center pixel valueof original data new DN
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High pass
Low pass
Original
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Original
Horizontal
Vertical
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Image Processing

• Image enhancement, cont.
• Stretches
• Linear
• a.k.a. auto, auto-ends
• Improves contrast throughout scene, saturates at
  ends
• Gaussian
• Enhances contrast in tails of histogram
• Histogram equalization (a.k.a. uniform
  distribution)
• Enhances contrast in most populated DN range
• Density slicing

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linear 0.001
linear 0.01
linear 0.1
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Image Processing

• Information Extraction
• Colorization
• Principle components analysis decorrelation
  stretch
• Classifications
• Supervised
• Unsupervised
• Band ratios
• Mixing models

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Colorization
B1, B2, B3
Band 1
Band 2
Band 3
R153, G51, B204
B2, B3, B1
DN153
DN51
DN204
R51, G204, B153
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Colorization with Minerals
Assume a 5,3,1RGB image
R0.93, G0.5, B0.54
R0.66, G0.923, B0.985
Emissivity
Values (radiance, emissivity, etc.) in each band
can be converted to DN and combined to make an
RGB image
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PCA

• In multispectral images, DN values from band to
  band are usually highly correlated
• It is desirable to reduce this redundancy
• Principal-components analysis (PCA) calculates
  new coordinate system along (and perpendicular
  to) the axis of correlation between bands
• Can be applied to multispectral data w/many bands
• Each new coordinate is perpendicular to the last
  and in the direction of maximum pixel density
• For each pixel, new DNs are determined along the
  new axes for each band relative to the first
  principal component
• Each subsequent PC accounts for an increasingly
  small amount of variation in original data

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PCA
Combine PC bands as RGB PCA band 1 is commonly
dominated by temperature in IR,
brightness/shadowing in VNIR, both result from
topography
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Decorrelation Stretch
To enhance variation in PC images, apply stretch
to PC bands, rotate back to original axis and
display as image
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Band Ratios

• Divide values in one band by the values in
  another
• Can take this further by ratioing ratios
• Enhances spectral differences and eliminates
  illumination differences
• Takes advantage of spectral slopes
• Can combine ratio images to make RGB images
• Think of all the bands you could represent in
  three colors!
• Can be done in radiance, DN, emissivity, etc.
• Values can blow up (i.e., division by 0), so
  some scaling may be necessary to get best image
  quality
• Warning materials that are different but with
  similar slopes can be difficult to distinguish

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Classification

• Spectral, spatial, temporal
• Supervised
• Training areas defined by user
• Algorithm uses training areas to classify
  remaining pixels in image
• Many approaches minimum distance to means,
  parallelepiped, Gaussian maximum likelihood
• Unsupervised
• Algorithm defines classes in image commonly uses
  natural groupings/clusters within image to define

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Mixing Models

• Can be similar to linear deconvolution with
  spectral data
• Instead of blackbody, shade may be used
• All pixels may represent a mixture, but there are
  still pure pixels i.e., those that cannot be
  made from combinations of other pixel values