Image acquisition. Midterm Review. Digitization, line of image. Digitization, whole image. Geometric transformations. Interpolation 10/26/2016

Transcription

1 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

2 Intensity transformations Intensity transformations 7 8 Negative transformation Gamma transformation 9 10 Gamma transformation Gamma transformation Dark image Light image γ < 1 γ >

3 Piecewise linear transformations Contrast stretching Contrast stretching Intensity level slicing Bit plan slicing Intensity level slicing Bit plane slicing Bit plane slicing Histogram Similar to probability density function (pdf)

4 Histogram equalization Histogram equalization Histogram equalization Histogram matching Local histogram equalization Spatial filtering

5 Correlation and convolution (1D) 25 Correlation and convolution (2D) 27 Correlation and convolution (2D) Smoothing filters

6 Smoothing filters Derivatives Sharpening filters Laplacian (using second derivatives) Sharpening filters Gradient (first derivatives) Magnitude of gradient vector

7 Combining spatial filtering and intensity transformations Laplacian Jean Baptiste Joseph Fourier 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 Unit discrete impulse Impulse train

8 Sampling Sampling Fourier transform of function Fourier transforms of sampled function Over sampled Critically sampled 1/ΔT Under sampled The sampling theorem Recovering F(μ) from ~ F(μ) Fourier transform of function Over sampled Fourier transform of sampled function Critically sampled Recovered Aliasing Aliasing Under sampled Will result in aliasing

9 Continuous Fourier transform Unit discrete impulse 1D 1D 2D 2D Impulse train Fourier transform of sampled function and extracting one period 1D 1D 2D 2D Under sampled Over sampled Aliasing Aliasing in real images 1D 2D Original Aliasing Original Aliasing No aliasing

10 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 DFT of geometrically transformed images Rectangle phase images Original Translated Rotated about center Translated Same as DFT of original Rotated about center 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

11 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 Filtering in the frequency domain Butterworth lowpass filter (LPF) Filtering in the frequency domain Gaussian lowpass filter (LPF)

12 Filtering in the frequency domain Example: character recognition Ideal LPF Butterworth LPF Gaussian LPF Ideal HPF Highpass filter (HPF) Frequency domain Highpass filter (HPF) Spatial domain Ideal HPF Butterworth HPF Gaussian HPF Butterworth HPF Gaussian HPF Filtering in the frequency domain Filtering in the frequency domain Ideal HPF Butterworth HPF 1D Gaussian HPF Lowpass filter Sharpening filter

13 Filtering in the frequency domain Filtering in the frequency domain Sharpening filter 2D Bandreject and bandpass filters Jean Baptiste Joseph Fourier Model of image degradation, then restoration Noise modeled as different probability density functions

14 Input image (free of noise) Adding noise from different models 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

15 Order statistic filters Order statistic filters Additive salt and pepper noise 1x median 2x median 3x median Max Min 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 Adaptive filters Periodic noise Additive salt and pepper noise Median Adaptive median Example pair of conjugate impulses due to corruption by (spatial) sinusoidal noise

16 Bandreject filter Bandreject filters 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) Estimation of degradation function by experimentation Estimation of degradation function by mathematical modeling Atmospheric turbulence model

17 Estimation of degradation function by mathematical modeling Image restoration Inverse filtering Motion blur model Image restoration Image restoration Degraded image Inverse filtering Wiener filtering Inverse filtering Wiener filtering Image restoration Electromagnetic spectrum Constrained least squares filtering

18 Separating light Human eye cones 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 XYZ color model and chromaticity coordinates Color gamuts Not actual colors locations; just gives an idea Average person Computer monitor Printer

19 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 HSI color model Color models HS plane is orthogonal to intensity axis CMYK RGB HSI Intensity slicing Intensity slicing Grayscale to 2 colors Grayscale to 2 colors

20 Intensity slicing Intensity slicing Colorbar Grayscale to 256 colors Grayscale to 8 colors 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

21 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 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 Full color image processing Histogram equalization: do not process each channel independently 1. RGB to HSI 2. Histogram equalize intensity 3. HSI to RGB