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Midterm Review
Image ProcessingCSE 166
Lecture 10
Image acquisition
CSE 166, Fall 2016 2
Digitization, line of image
CSE 166, Fall 2016 3
Digitization, whole image
CSE 166, Fall 2016 4
Geometric transformations
CSE 166, Fall 2016
CSE 166Transpose these matrices
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Interpolation
CSE 166, Fall 2016 6
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Intensity transformations
CSE 166, Fall 2016 7
Intensity transformations
CSE 166, Fall 2016 8
Negative transformation
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Gamma transformation
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Gamma transformation
CSE 166, Fall 2016
γ 1
Lightimage
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Piecewise‐linear transformations
• Contrast stretching• Intensity‐level slicing• Bit‐plan slicing
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Contrast stretching
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Intensity‐level slicing
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Bit‐plane slicing
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Bit‐plane slicing
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Histogram
CSE 166, Fall 2016
Similar to probability density function (pdf)
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Histogram equalization
CSE 166, Fall 2016 19
Histogram equalization
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Histogram equalization
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Histogram matching
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Local histogram equalization
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Spatial filtering
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Correlation and convolution (1D)
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Correlation and convolution (2D)
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Correlation and convolution (2D)
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Smoothing filters
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Smoothing filters
CSE 166, Fall 2016 31
Derivatives
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Sharpening filtersLaplacian (using second derivatives)
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Sharpening filters
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Gradient (first derivatives)
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Magnitude of gradient vector
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Combining spatial filtering and intensity transformations
CSE 166, Fall 2016
Laplacian
Sobel
Smooth
SharpenedMagnitudeof gradient
Smoothedmagnitudeof gradient
Noisereduced sharpened
“Sharpened”
Gamma37
Jean‐Baptiste Joseph Fourier1768‐1830
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Periodic functions can be represented as weighted sum of sines and cosines
CSE 166, Fall 2016
Fourier series
39
1D continuous Fourier transform
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Unit discrete impulse
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Impulse train
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Sampling
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Sampling
CSE 166, Fall 2016
Over‐sampled
Critically‐sampled
Under‐sampled
1/ΔT
Fourier transform of function
Fourier transforms of sampled function
44
The sampling theorem
CSE 166, Fall 2016
Critically‐sampled
Fourier transform of function
Fourier transform of sampled function
45
Recovering F(μ) from F(μ)
CSE 166, Fall 2016
~
Over‐sampled
Recovered
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Aliasing
CSE 166, Fall 2016
Under‐sampled
Will result in aliasing
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Aliasing
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Continuous Fourier transform
CSE 166, Fall 2016
1D
2D
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Unit discrete impulse
CSE 166, Fall 2016
1D
2D
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Impulse train
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1D
2D
51 CSE 166, Fall 2016
1D
2D
Over‐sampled
Under‐sampled
Fourier transform of sampled functionand extracting one period
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Aliasing
CSE 166, Fall 2016
1D
2D
Aliasing
Original
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Aliasing in real images
CSE 166, Fall 2016
AliasingOriginal No aliasing
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Centering the DFT
CSE 166, Fall 2016
1D
2D
In MATLAB, use fftshift and ifftshift
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Centering the DFT
CSE 166, Fall 2016
OriginalDFT(look at corners)
Shifted DFTLog of shifted DFT
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DFT of geometrically transformed images
CSE 166, Fall 2016
Translated
Rotatedabout center
Same as DFT of original
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Rectangle phase images
CSE 166, Fall 2016
Translated Rotated about centerOriginal
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Inverse DFT
CSE 166, Fall 2016
Phase
IDFT: Phase only
(zero magnitude)
IDFT: Magnitude
only (zero phase)
IDFT: Woman
magnitude and rectangle phase
IDFT: Rectangle
magnitude and woman phase59
Filtering using convolution theorem
CSE 166, Fall 2016
Filtering in spatial domain using
convolution
expectedresult
Filtering in frequencydomain using productwithout
zero‐padding
wraparounderror
60
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Filtering using convolution theorem
CSE 166, Fall 2016
Filtering in frequencydomain using productwith
zero‐padding
no wraparounderror
Gaussian lowpass filter in frequency domain
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Filtering using convolution theorem
CSE 166, Fall 2016
Filtering in spatialdomain using
convolution
Filtering in frequencydomain using
product
Identical results
DFT
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Filtering in the frequency domain
• Ideal lowpass filter (LPF)– Frequency domain
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Filtering in the frequency domain
• Ideal lowpass filter (LPF)– Spatial domain
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Filtering in the frequency domain
• Butterworth lowpass filter (LPF)
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Filtering in the frequency domain
• Gaussian lowpass filter (LPF)
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Filtering in the frequency domain
CSE 166, Fall 2016Ideal LPF Butterworth LPF Gaussian LPF
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Example: character recognition
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Highpass filter (HPF)Frequency domain
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Ideal HPF
Gaussian HPF
Butterworth HPF
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Highpass filter (HPF)Spatial domain
CSE 166, Fall 2016
Ideal HPF Butterworth HPF Gaussian HPF
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Filtering in the frequency domain
CSE 166, Fall 2016
Ideal HPF
Gaussian HPF
Butterworth HPF
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Filtering in the frequency domain
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1D
Lowpass filter Sharpening filter72
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Filtering in the frequency domain
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2D
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Filtering in the frequency domain
• Sharpening filter
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Bandreject and bandpass filters
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Jean‐Baptiste Joseph Fourier1768‐1830
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Model of image degradation, then restoration
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Noise modeled as different probability density functions
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Input image (free of noise)
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Adding noise from different models
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Adding noise from different models
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Histograms of sample patches
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Sample “flat” patches from images with noise
Identify closest probability density function (pdf) match82
Mean filters
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Additive Gaussian noise
Geometric mean filtered
Arithmetic mean filtered
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Mean filters
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Additivesaltnoise
Additivepeppernoise
Contraharmonicmean filtered
Contraharmonicmean filtered
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Order‐statistic filters
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Additivesalt and peppernoise
1x median filtered
3x median filtered
2x median filtered
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Order‐statistic filters
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Min filtered
Max filtered
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Comparing filters
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Additiveuniformnoise
Alpha‐trimmed mean filtered
Median filtered
Additiveuniform + salt and pepper
noise
Arithmetricmean filtered
Geometric mean filtered
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Adaptive filters
CSE 166, Fall 2016
AdditiveGaussiannoise
Arithmetricmean filtered
Geometric mean filtered
Adaptive noise reduction filtered
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Adaptive filters
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Additivesalt and pepper
noiseMedian filtered
Adaptive median filtered
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Periodic noise
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Example pair of conjugate impulses due to corruption
by (spatial) sinusoidal noise
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Bandreject filter
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Bandreject filters
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Notch pass filter
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Degraded image
Estimate of original image
DFT magnitude
Product of DFT magnitude and notch pass filter
Noise(result of notch reject filter)
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Notch reject filters
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Estimation of degradation function by experimentation
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Estimation of degradation function by mathematical modeling
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Atmospheric turbulence model
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Estimation of degradation function by mathematical modeling
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Motion blur model
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Image restoration
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Inverse filtering
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Image restoration
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Inverse filtering Wiener filtering
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Image restoration
CSE 166, Fall 2016
Inversefiltering
Wienerfiltering
Degraded image
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Image restoration
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Constrained least squares filtering
101
Electromagnetic spectrum
CSE 166, Fall 2016 102
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Separating light
CSE 166, Fall 2016 103
Human eye cones
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Mixing light
CSE 166, Fall 2016
Light
Pigment
Primary and secondary colors are swapped
Note that blue and cyan are not
accurate colors on this slide or in the book
105
RGB color model
CSE 166, Fall 2016
RGB coordinates
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XYZ color model andchromaticity coordinates
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Not actual colors
locations; just gives an idea
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Color gamuts
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Averageperson
Computermonitor
Printer
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HSI color model:Relationship to RGB color model
CSE 166, Fall 2016
All colors with cyan
hueRGB color cube rotated such that
line joining black and white (intensity axis) is vertical
109
HSI color model
CSE 166, Fall 2016
RGB color cube rotated such that line joining black and white
(intensity axis) is vertical
Viewed from the top down
Shape does not matter
110
HSI color model
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HS plane is orthogonal to intensity axis
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Color models
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HSI
RGB
CMYK
112
Intensity slicing
CSE 166, Fall 2016
Grayscale to 2 colors
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Intensity slicing
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Grayscale to 2 colors
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Intensity slicing
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Grayscale to 8 colors115
Intensity slicing
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Grayscale to 256 colors
Colorbar
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Intensity to color transformations
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Grayscale input image
RGBoutput image
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Intensity to color transformations
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Grayscale input image
“See through” explosive
RGB output image
Without explosive
With explosive
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Intensity to color transformations
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Multiple grayscale
input images
SingleRGB
output image
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Intensity to color transformations
CSE 166, Fall 2016
Multiple grayscale
input images
SingleRGB
output image
Near infrared
R G
B NIR
RGB NIRGB image 120
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Intensity to color transformations
CSE 166, Fall 2016
SingleRGB
output image
Multiple grayscale input images,
some outside of visible spectrum
Close upPhysical and chemical
processes likely to affect sensor response
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Full‐color image processing
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Spatial filtering: process each channel independently
122
Full‐color image processing
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All RGB channels
HSI intensity channel only
Spatial filtering: image smoothing
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Full‐color image processing
CSE 166, Fall 2016
All RGB channels
HSI intensity channel only
Spatial filtering: image sharpening
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Full‐color image processing
CSE 166, Fall 2016
Histogram equalization: do not process each channel independently
1. RGB to HSI2. Histogram equalize intensity3. HSI to RGB
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