Image acquisition Midterm Review Image Processing CSE 166 Lecture 10 2 Digitization, line of image Digitization, whole image 3 4 Geometric transformations Interpolation CSE 166 Transpose these matrices 5 6 1
Intensity transformations Intensity transformations 7 8 Negative transformation Gamma transformation 9 10 Gamma transformation Gamma transformation Dark image Light image γ < 1 γ > 1 11 12 2
Piecewise linear transformations Contrast stretching Contrast stretching Intensity level slicing Bit plan slicing 13 14 Intensity level slicing Bit plane slicing 15 16 Bit plane slicing Histogram Similar to probability density function (pdf) 17 18 3
Histogram equalization Histogram equalization 19 20 Histogram equalization Histogram matching 21 22 Local histogram equalization Spatial filtering 23 24 4
Correlation and convolution (1D) 25 Correlation and convolution (2D) 27 Correlation and convolution (2D) Smoothing filters 29 30 5
Smoothing filters Derivatives 31 32 Sharpening filters Laplacian (using second derivatives) Sharpening filters 33 34 Gradient (first derivatives) Magnitude of gradient vector 35 36 6
Combining spatial filtering and intensity transformations Laplacian Jean Baptiste Joseph Fourier 1768 1830 Sobel Smoothed magnitude of gradient Noise reduced sharpened Smooth Sharpened Magnitude of gradient Sharpened 37 Gamma 38 Periodic functions can be represented as weighted sum of sines and cosines 1D continuous Fourier transform Fourier series 39 40 Unit discrete impulse Impulse train 41 42 7
Sampling Sampling Fourier transform of function Fourier transforms of sampled function Over sampled Critically sampled 1/ΔT Under sampled 43 44 The sampling theorem Recovering F(μ) from ~ F(μ) Fourier transform of function Over sampled Fourier transform of sampled function Critically sampled Recovered 45 46 Aliasing Aliasing Under sampled Will result in aliasing 47 48 8
Continuous Fourier transform Unit discrete impulse 1D 1D 2D 2D 49 50 Impulse train Fourier transform of sampled function and extracting one period 1D 1D 2D 2D Under sampled Over sampled 51 52 Aliasing Aliasing in real images 1D 2D Original Aliasing Original Aliasing No aliasing 53 54 9
Centering the DFT Centering the DFT 1D Original DFT (look at corners) 2D Shifted DFT Log of shifted DFT In MATLAB, use fftshift and ifftshift 55 56 DFT of geometrically transformed images Rectangle phase images Original Translated Rotated about center Translated Same as DFT of original Rotated about center 57 58 Inverse DFT Phase Filtering using convolution theorem IDFT: Magnitude only (zero phase) IDFT: Phase only (zero magnitude) IDFT: Woman magnitude and rectangle phase Filtering in spatial domain using convolution Filtering in frequency domain using product without zero padding IDFT: Rectangle magnitude and woman phase 59 expected result wraparound error 60 10
Filtering using convolution theorem Filtering using convolution theorem DFT Filtering in frequency domain using product with zero padding Filtering in spatial domain using convolution Filtering in frequency domain using product no wraparound error Gaussian lowpass filter in frequency domain 61 Identical results 62 Filtering in the frequency domain Ideal lowpass filter (LPF) Frequency domain Filtering in the frequency domain Ideal lowpass filter (LPF) Spatial domain 63 64 Filtering in the frequency domain Butterworth lowpass filter (LPF) Filtering in the frequency domain Gaussian lowpass filter (LPF) 65 66 11
Filtering in the frequency domain Example: character recognition Ideal LPF Butterworth LPF Gaussian LPF 67 68 Ideal HPF Highpass filter (HPF) Frequency domain Highpass filter (HPF) Spatial domain Ideal HPF Butterworth HPF Gaussian HPF Butterworth HPF Gaussian HPF 69 70 Filtering in the frequency domain Filtering in the frequency domain Ideal HPF Butterworth HPF 1D Gaussian HPF Lowpass filter Sharpening filter 71 72 12
Filtering in the frequency domain Filtering in the frequency domain Sharpening filter 2D 73 74 Bandreject and bandpass filters Jean Baptiste Joseph Fourier 1768 1830 75 76 Model of image degradation, then restoration Noise modeled as different probability density functions 77 78 13
Input image (free of noise) Adding noise from different models 79 80 Adding noise from different models Histograms of sample patches Sample flat patches from images with noise 81 Identify closest probability density function (pdf) match 82 Mean filters Mean filters Additive Gaussian noise Additive pepper noise Additive salt noise Arithmetic mean Geometric mean Contraharmonic mean Contraharmonic mean 83 84 14
Order statistic filters Order statistic filters Additive salt and pepper noise 1x median 2x median 3x median Max Min 85 86 Comparing filters Adaptive filters Additive uniform noise Arithmetric mean Median Additive uniform + salt and pepper noise Geometric mean Alpha trimmed mean Additive Gaussian noise Geometric mean Arithmetric mean Adaptive noise reduction 87 88 Adaptive filters Periodic noise Additive salt and pepper noise Median Adaptive median Example pair of conjugate impulses due to corruption by (spatial) sinusoidal noise 89 90 15
Bandreject filter Bandreject filters 91 92 Notch pass filter Notch reject filters Degraded image DFT magnitude Product of DFT magnitude and notch pass filter Estimate of original image Noise (result of notch reject filter) 93 94 Estimation of degradation function by experimentation Estimation of degradation function by mathematical modeling Atmospheric turbulence model 95 96 16
Estimation of degradation function by mathematical modeling Image restoration Inverse filtering Motion blur model 97 98 Image restoration Image restoration Degraded image Inverse filtering Wiener filtering Inverse filtering Wiener filtering 99 100 Image restoration Electromagnetic spectrum Constrained least squares filtering 101 102 17
Separating light Human eye cones 103 104 Mixing light RGB color model Light Primary and secondary colors are swapped Pigment Note that blue and cyan are not accurate colors on this slide or in the book RGB coordinates 105 106 XYZ color model and chromaticity coordinates Color gamuts Not actual colors locations; just gives an idea Average person Computer monitor Printer 107 108 18
HSI color model: Relationship to RGB color model RGB color cube rotated such that line joining black and white (intensity axis) is vertical HSI color model Viewed from the top down RGB color cube rotated such that line joining black and white (intensity axis) is vertical All colors with cyan hue Shape does not matter 109 110 HSI color model Color models HS plane is orthogonal to intensity axis CMYK RGB HSI 111 112 Intensity slicing Intensity slicing Grayscale to 2 colors Grayscale to 2 colors 113 114 19
Intensity slicing Intensity slicing Colorbar Grayscale to 256 colors Grayscale to 8 colors 115 116 Intensity to color transformations Intensity to color transformations Without explosive With explosive Grayscale input image Grayscale input image RGB output image 117 RGB output image See through explosive 118 Intensity to color transformations Intensity to color transformations R B G NIR Multiple grayscale input images Near infrared Multiple grayscale input images Single RGB output image Single RGB output image 119 RGB NIRGB image 120 20
Intensity to color transformations Full color image processing Multiple grayscale input images, some outside of visible spectrum Single RGB output image Spatial filtering: process each channel independently Physical and chemical processes likely to affect sensor response Close up 121 122 Full color image processing Full color image processing Spatial filtering: image smoothing Spatial filtering: image sharpening All RGB channels HSI intensity channel only All RGB channels HSI intensity channel only 123 124 Full color image processing Histogram equalization: do not process each channel independently 1. RGB to HSI 2. Histogram equalize intensity 3. HSI to RGB 125 21