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ECE/OPTI 531 – Image Processing Lab for Remote Sensing Fall 2005
Spectral Transforms
Reading: Chapter 5
Fall 2005Spectral Transforms 2
Spectral Transforms
• Feature Spaces• Spectral Band Ratios and VIs• Principal and Tasseled-Cap Components• Contrast Enhancement
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Fall 2005Spectral Transforms 3
Multispectral Data Spaces
• Three “spaces” associated with multispectralimages:– image space – the DNb(x,y) space, i.e. an “image” in
band b– spectral (data) space – the DN = (DN1, DN2, . . ., DNK)
vector space– feature space – derived from the image or spectral
space
Fall 2005Spectral Transforms 4
Feature Spaces
• Good features reduce effects that hinder theextraction of information
• Nonlinear spectral transform
– multispectral ratios are one example• Linear spectral transform
– corresponds to a coordinate rotation of the DN space tothe DN´ space
– principal components transform is an example
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Fall 2005Spectral Transforms 5
Spectral Transforms
• Feature Spaces• Spectral Band Ratios and VIs• Principal and Tasseled-Cap Components• Contrast Enhancement
• Vegetated scene– PCT extracts contrast between bands 3 and 4 (red and
NIR) due to the vegetation “red edge”
TM1 TM2 TM3
TM4 TM5 TM7
PC1 PC2 PC3
PC4 PC5 PC6
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Fall 2005Spectral Transforms 25
PCT Noise Detection
• PCT can isolate spectrally-uncorrelated noise
TM2 TM3 TM4
PC1 PC2 PC3
Fall 2005Spectral Transforms 26
PCT Drawbacks
• Why not use the PCT?– It is data-dependent
• W coefficients change from scene-to-scene• Makes consistent interpretation of PC images difficult
– Spectral details, particularly in small areas, may be lostif higher-order PCs are ignored
– Computationally expensive for large images or formany spectral bands
• Calculation of covariance matrix is the culprit
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Fall 2005Spectral Transforms 27
Tasseled-Cap Components
• Linear spectraltransform like the PCT
• In this case, the WTCmatrix is fixed for agiven sensor
Tasseled-cap components for MSS and TM
Fall 2005Spectral Transforms 28
TCT Benefits
• Why use the TCT?– It is a fixed reference
• Same reference for everyimage from a given sensorpermits consistentinterpretation
– Components are related togeophysical properties ofthe scene
• First component is “soilbrightness”
• Second component is“greeness”
Brightness
Greeness
DN3
DN4PC2
PC1
TCT axes alignbetter with thesoil and vegetationdirections
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Fall 2005Spectral Transforms 29
TCT Drawbacks
• Why not use the TCT?– Nonoptimal compression of data– Derivation of WTC requires multitemporal data for each
sensor
PC1 PC2 PC3
PC4 PC5 PC6
TC1 TC2 TC3
TC4 TC5 TC6
Comparison of PC and TC images
Fall 2005Spectral Transforms 30
Spectral Transforms
• Feature Spaces• Spectral Band Ratios and VIs• Principal and Tasseled-Cap Components• Contrast Enhancement
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Fall 2005Spectral Transforms 31
Contrast Enhancement
• Two problems– Most images do not fill the dynamic range of the sensor
– Most images also do not fill the dynamic range of the displaysystem
• Contrast enhancement means “stretching” the data rangeto fill the display system range GL = T(DN)– Parameters of transformation T based on global or local
image statistics
signal rangerequired at
A/D input for fullrange DN output
ab
eb
anticipated range
optional high gainb
offsetb
all scenes
standard gainb
of detected signals low radiance scenes
Fall 2005Spectral Transforms 32
Global Single-Band Transforms
• Linear stretch– min-max
• scale range of image DNs to range of display GLs• sensitive to outliers
– saturation• scale a smaller range of DNs to range of display GLs• saturation of 1–3% pixels at each end usually acceptable
• Nonlinear stretch– piecewise-linear
• different contrast “gain” over different DN ranges– histogram equalization
• use scaled CDF of original image as the transformation
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Fall 2005Spectral Transforms 33
DN-to-GL Transformations
Fall 2005Spectral Transforms 34
Contrast Stretch Examples
original min-max
3% saturation 8% saturation
piecewise linear histogram equalization
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original min-max
3% saturation 8% saturation
piecewise linear histogram equalization
Application to GOES image of North America
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Fall 2005Spectral Transforms 35
Normalization Stretch
• Linear scale of DN mean and sigma to specifiedvalues, followed by saturation
• Consistent behavior (robust) over wide range ofimages
original µ = 128, σ = 32
µ = 128, σ = 64µ = 128, σ = 48
Fall 2005Spectral Transforms 36
Reference Stretch
• Match the CDF of the image being processed to areference CDF, for example from another image– useful for
• multitemporal or multisensor radiance matching• matching image to reference contrast
DN
0
1
CDF
DNref
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CDFref
Reference stretch is a double transformation
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Fall 2005Spectral Transforms 37
Multitemporal Normalization
0 100
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DN0 12763
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TM band 3, Dec 31, 1982 TM band 3, Aug 12, 1983
dark-light targetlinear stretch
CDF referencestretch
Reference
CDF reference stretch
dark-light linear stretch
Dec 31, 1982 Aug 12, 1983
Fall 2005Spectral Transforms 38
Thresholding
• Binary “clipping” of DNs to low and high values– Useful for
• segmentation of certain images, e.g. clouds/water,land/water
DNT = 50
DNT = 100 DNT = 150
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Fall 2005Spectral Transforms 39
Formulas
Mathematical formulas for contrast enhancement techniques
Fall 2005Spectral Transforms 40
Color Images
• Techniques used for single-band imagery can beextended to color, but . . .– Sensitivity of the human vision system to shifts in color
and saturation require special attention• Min-max stretch
– Stretch the DNs in each band over their respective min-max range
– Good news:• Easy to calculate and implement• No data lost by saturation
– Bad news:• Sensitive to outlier DNs• Color balance can change unpredictably
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Fall 2005Spectral Transforms 41
Color Normalization
• Normalization stretch– “Standardized” stretch– Good news:
• Average color is grey• Contrast controlled by
single parameter, thedesired outputstandard deviation
– Bad news:• Some data are lost in
saturation
Normalization Stretch
Linearly stretch each band to same DN mean ( typically 128) and same DN standard deviation (typically 32 – 48)
Clip to [0,255]
RGB RGB
linear stretchto µ, !
clip at [0,255]
linear stretchto µ, !
clip at [0,255]
linear stretchto µ, !
clip at [0,255]
Fall 2005Spectral Transforms 42
Color Decorrelation
• Decorrelation stretch– Enhance small spectral
deviations in highly-correlated spectralbands
– Commonly used ingeology
– Good news:• Decorrelates bands• Emphasizes differences
among bands• Can be applied to any
number of bands– Bad news:
• Produces highlysaturated colors
Decorrelation Stretch
PCT transform
Stretch each PC component to equalize variances
Inverse PCT transform
Clip to [0,255]
image data space PC space
PCT
PCT-1clip at [0,255]
equalizevariances
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Fall 2005Spectral Transforms 43
Color Spaces
• HSI color coordinate system• Hexcone model
– similar to a cylindrical coordinatesystem, but based on RGB color cube
– value = max(R,G,B) used instead ofintensity
– efficient CST from RGB to Hue-Saturation-Value (HSV)
intensity
saturation
hue
I
S
H
whiteblack
P
red
yellow
green
cyan
blue
magenta
(255,0,0)
(0,255,0)
(0,0,255)
yellow
magenta
cyan
red
greenblue
black
white
GL3
GL2
GL1
project subcube faces onto orthogonal planeintersection at the vertex of subcube
cylindrical coordinates
Fall 2005Spectral Transforms 44
Color-Space Transforms
• Color-space transforms– Human vision system
perceives hue (H),saturation (S) andintensity (I), not RGB
– Therefore, control overcolor appearance is bestdone in HSI space