Midterm Review. Image Processing CSE 166 Lecture 10

Transcription

1 Midterm Review Image Processing CSE 166 Lecture 10

2 Topics covered Image acquisition, geometric transformations, and image interpolation Intensity transformations Spatial filtering Fourier transform and filtering in the frequency domain Image restoration Color image processing CSE 166, Fall

3 Image acquisition CSE 166, Fall

4 Geometric transformations CSE 166, Fall

5 Intensity transformations Contrast stretching function Thresholding function CSE 166, Fall

6 Intensity transformations Some basic transformation functions CSE 166, Fall

7 Gamma transformation CSE 166, Fall

8 Gamma transformation Dark image γ < 1 CSE 166, Fall

9 Gamma transformation Light image γ > 1 CSE 166, Fall

10 Piecewise linear transformations Contrast stretching Intensity level slicing Bit plane slicing CSE 166, Fall

11 Contrast stretching CSE 166, Fall

12 Intensity level slicing CSE 166, Fall

13 Bit plane slicing CSE 166, Fall

14 Histogram Similar to probability density function (pdf) CSE 166, Fall

15 Histogram equalization CSE 166, Fall

16 Histogram equalization CSE 166, Fall

17 Histogram equalization CSE 166, Fall

18 Spatial filtering (2D) CSE 166, Fall

19 Correlation and convolution (2D) CSE 166, Fall

20 Smoothing kernels Average (box kernel) Weighted average (Gaussian kernel) CSE 166, Fall

21 Smoothing with box kernel Input image 3x3 11x11 21x21 CSE 166, Fall

22 Smoothing with Gaussian kernel Standard deviation σ Percent of total volume under surface Volume under surface greater than 3σ is negligible CSE 166, Fall

23 Smoothing with Gaussian kernel Input image σ = 3.5 σ = 7 21x21 43x43 CSE 166, Fall

24 Derivatives CSE 166, Fall

25 Sharpening filters CSE 166, Fall

26 Review Complex numbers CSE 166, Fall

27 Overview: Image processing in the frequency domain Image in spatial domain f(x,y) Fourier transform Image in frequency domain F(u,v) Image in spatial domain g(x,y) Jean Baptiste Joseph Fourier Inverse Fourier transform Frequency domain processing Image in frequency domain G(u,v) CSE 166, Fall

28 1D Fourier series Sines and cosines Period T Weighted by magnitude Shifted by phase Periodic function CSE 166, Fall

29 Sampling CSE 166, Fall

30 Sampling Fourier transform of function Fourier transforms of sampled function Over sampled Critically sampled 1/ΔT Under sampled CSE 166, Fall

31 The sampling theorem Fourier transform of function Fourier transform of sampled function Critically sampled CSE 166, Fall

32 Recovering F(μ) from ~ F(μ) Fourier transform of sampled function Over sampled Ideal lowpass filter Product of above Recovered CSE 166, Fall

33 Aliasing Continuous Discrete Under sampled Alias: a false identity Different Identical Over sampled Sampled at same rate CSE 166, Fall

34 Aliasing 1D Original 2D Aliasing CSE 166, Fall

35 Fourier transform of sampled function and extracting one period Over sampled Under sampled 1D 2D Recovered m max Footprint of a 2-D ideal lowpass (box) filter v max v ass Imperfect recovery v due to interference m CSE 166, Fall m

36 Centering the DFT 1D 2D In MATLAB, use fftshift and ifftshift CSE 166, Fall

37 Centering the DFT Original DFT (look at corners) Shifted DFT Log of shifted DFT CSE 166, Fall

38 Contributions of magnitude and phase to image formation Phase IDFT: Phase only (zero magnitude) IDFT: Magnitude only (zero phase) IDFT: Boy magnitude and rectangle phase IDFT: Rectangle magnitude CSE 166, Fall 2017 and boy phase 38

39 Filtering using convolution theorem Filtering in spatial domain using convolution expected result Filtering in frequency domain using product without zero padding wraparound error CSE 166, Fall

40 Filtering using convolution theorem Zero padding Filtering in frequency domain using product with zero padding Fourier transform Product no wraparound error Inverse Fourier transform CSE 166, Fall 2017 Gaussian lowpass filter in frequency domain 40

41 Filtering in the frequency domain Ideal lowpass filter (LPF) Frequency domain CSE 166, Fall

42 Filtering in the frequency domain Ideal lowpass filter (LPF) Spatial domain H(u,v) h(x,y) CSE 166, Fall

43 Filtering in the frequency domain Gaussian lowpass filter (LPF) CSE 166, Fall

44 Filtering in the frequency domain Butterworth lowpass filter (LPF) CSE 166, Fall

45 Filtering in the frequency domain Ideal LPF Gaussian LPF Butterworth LPF CSE 166, Fall

46 Highpass filter (HPF) Frequency domain Ideal HPF Gaussian HPF Butterworth HPF CSE 166, Fall

47 Highpass filter (HPF) Spatial domain Ideal HPF Gaussian HPF Butterworth HPF CSE 166, Fall

48 Filtering in the frequency domain Ideal HPF Gaussian HPF Butterworth HPF CSE 166, Fall

49 Filtering in the frequency domain H (u) H (u) Frequency domain 1D h(x) u h(x) u Spatial domain x x Lowpass filter Sharpening filter CSE 166, Fall

50 Filtering in the frequency domain Lowpass filter Highpass filter Offset highpass filter 2D CSE 166, Fall

51 Bandreject filters Ideal Gaussian Butterworth CSE 166, Fall

52 Model of image degradation, then restoration CSE 166, Fall

53 Histograms of sample patches Sample flat patches from images with noise Identify closest probability density function (pdf) match: Gaussian Rayleigh Uniform CSE 166, Fall

54 Mean filters X ray image Additive Gaussian noise Arithmetic mean filtered Geometric mean filtered CSE 166, Fall

55 Order statistic filters Additive salt and pepper noise 1x median filtered 2x median filtered 3x median filtered CSE 166, Fall

56 Comparing filters Additive uniform + salt and pepper noise Arithmetric mean filtered Geometric mean filtered Median filtered Alpha trimmed mean filtered CSE 166, Fall

57 Adaptive filters Additive Gaussian noise Arithmetric mean filtered Geometric mean filtered Adaptive noise reduction filtered CSE 166, Fall

58 Periodic noise DFT magnitude Additive sinusoidal noise Conjugate impulses CSE 166, Fall

59 Notch reject filters CSE 166, Fall

60 Notch reject filter Degraded image Conjugate impulses DFT magnitude Filter in frequency domain Conjugate impulses Estimate of original image CSE 166, Fall

61 Estimation of degradation function by experimentation Impulse of light Imaged (degraded) impulse CSE 166, Fall

62 Estimation of degradation function by mathematical modeling Atmospheric turbulence model CSE 166, Fall

63 Image restoration Inverse filtering CSE 166, Fall

64 RGB color model RGB color cube RGB coordinates CSE 166, Fall

65 HSI color model: Relationship to RGB color model RGB color cube rotated such that line joining black and white (intensity axis) is vertical CSE 166, Fall 2017 All colors with cyan hue 65

66 RGB color cube HSI color model HSI intensity axis RGB color cube rotated such that observer is on intensity axis, beyond white looking towards black Shape does not matter, only angle from red CSE 166, Fall

67 Color models CMYK CMY RGB HSI CSE 166, Fall

68 Intensity slicing Grayscale to 2 colors CSE 166, Fall

69 Intensity slicing Grayscale to 2 colors CSE 166, Fall

70 Intensity slicing Colorbar Grayscale to 256 colors CSE 166, Fall

71 Intensity to color transformations Grayscale input image RGB output image CSE 166, Fall

72 Intensity to color transformations X ray grayscale input image Without explosive With explosive RGB output images CSE 166, Fall 2017 Misses explosive 72

73 Intensity to color transformations Multiple grayscale input images Single RGB output image CSE 166, Fall

74 Intensity to color transformations Red (R) Green (G) Blue (B) Multiple satellite grayscale input images Near infrared (NIR) NIR,G,B as RGB Output RGB images R,NIR,B as RGB 74

75 Full color image processing Spatial filtering: process each channel independently CSE 166, Fall

76 Full color image processing Spatial filtering: image smoothing All RGB channels HSI intensity channel only CSE 166, Fall 2017 Difference 76

77 Full color image processing Spatial filtering: image sharpening All RGB channels HSI intensity channel only Difference CSE 166, Fall

78 Full color image processing Histogram equalization: do not process each channel independently 1. RGB to HSI 2. Histogram equalize HSI intensity 3. HSI to RGB 4. HSI saturation adjustment CSE 166, Fall