Final Review. Image Processing CSE 166 Lecture 18

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1 Final Review Image Processing CSE 166 Lecture 18

2 Topics covered Basis vectors Matrix based transforms Wavelet transform Image compression Image watermarking Morphological image processing Segmentation CSE 166, Fall

3 General inverse transform using basis vectors CSE 166, Fall

4 Matrix based transforms Discrete Fourier transform (DFT) Discrete Hartley transform (DHT) Discrete cosine transform (DCT) Discrete sine transform (DST) Walsh Hadamard (WHT) Slant (SLT) Haar (HAAR) Daubechies (DB4) Biorthogonal B spline (BIOR3.1) CSE 166, Fall

5 Basis vectors of matrix based 1D transforms Example: DFT of f(x) = sin(2πx), N = 8 real part + imaginary part CSE 166, Fall

6 Basis vectors of matrix based 1D transforms N = 16 real part imaginary part Standard basis (for reference) CSE 166, Fall

7 Basis vectors of matrix based 1D transforms N = 16 basis dual Standard basis (for reference) CSE 166, Fall

8 Basis images of matrix based 2D transforms Standard basis images (for reference) 8 by 8 array of 8 by 8 basis images CSE 166, Fall

9 Basis images of matrix based 2D transforms Discrete Fourier transform (DFT) basis images real part imaginary part CSE 166, Fall

10 Basis images of matrix based 2D transforms Discrete Hartley transform (DHT) basis images CSE 166, Fall

11 Basis images of matrix based 2D transforms Discrete cosine transform (DCT) basis images CSE 166, Fall

12 Basis images of matrix based 2D transforms Discrete sine transform (DST) basis images CSE 166, Fall

13 Basis images of matrix based 2D transforms Walsh Hadamard transform (WHT) basis images CSE 166, Fall

14 Basis images of matrix based 2D transforms Slant transform (SLT) basis images CSE 166, Fall

15 Basis images of matrix based 2D transforms Haar transform (HAAR) basis images CSE 166, Fall

16 Wavelet transforms A scaling function is used to create a series of approximations of a function or image, each differing by a factor of 2 in resolution from its nearest neighboring approximations. Wavelet functions (wavelets) are then used to encode the differences between adjacent approximations. The discrete wavelet transform (DWT) uses those wavelets, together with a single scaling function, to represent a function or image as a linear combination of the wavelets and scaling function. CSE 166, Fall

17 Scaling function, multiresolution analysis 1. The scaling function is orthogonal to its integer translates. 2. The function spaces spanned by the scaling function at low scales are nested within those spanned at higher scales. 3. The only function representable at every scale (all ) is f(x) = All measureable, square integrable functions can be represented as CSE 166, Fall

18 Relationship between scaling and wavelet function spaces CSE 166, Fall

19 2D discrete wavelet transform Decomposition CSE 166, Fall

20 2D discrete wavelet transform 3 level wavelet decomposition CSE 166, Fall

21 Wavelet based edge detection Zero lowest scale approximation Edges Zero horizontal details Vertical edges CSE 166, Fall

22 Wavelet based noise removal Noisy image Threshold details Zero highest resolution details Zero details for all levels CSE 166, Fall

23 Data redundancy in images Coding redundancy Spatial redundancy Irrelevant information Does not need all 8 bits Information is unnecessarily replicated Information is not useful CSE 166, Fall

24 Fidelity criteria subjective (qualitative) CSE 166, Fall

Approximations Objective (quantitative) quality rms error (in intensity levels) 5.17 15.67 14.

25 Approximations Objective (quantitative) quality rms error (in intensity levels) Lower is better (a) (b) (c) Subjective (qualitative) quality, relative (a) is better than (b). (b) is better than (c) CSE 166, Fall

26 Compression system CSE 166, Fall

27 Compression methods Huffman coding Golomb coding Arithmetic coding Lempel Ziv Welch (LZW) coding Run length coding Symbol based coding Bit plane coding Block transform coding Predictive coding Wavelet coding CSE 166, Fall

28 Symbol based coding (0,2) (3,10) CSE 166, Fall

29 Block transform coding Encoder Decoder CSE 166, Fall

30 Block transform coding 4x4 subimages (4x4 basis images) Walsh Hadamard transform Discrete cosine transform CSE 166, Fall

31 8x8 subimages Block transform coding Fourier transform Walsh Hadamard transform cosine transform Retain 32 largest coefficients Error image rms error Lower is better CSE 166, Fall

32 Block transform coding Reconstruction error versus subimage size DCT subimage size: 2x2 4x4 8x8 CSE 166, Fall

33 JPEG uses block DCT based coding Compression reconstruction Scaled error image Zoomed compression reconstruction 25:1 Compression ratio 52:1 CSE 166, Fall

34 Predictive coding model Encoder Decoder CSE 166, Fall

35 Predictive coding Example: previous pixel coding Input image Histograms Prediction error image CSE 166, Fall

36 Wavelet coding Encoder Decoder CSE 166, Fall

37 Wavelet coding Detail coefficients below 25 are truncated to zero CSE 166, Fall

38 JPEG 2000 uses wavelet based coding Compression reconstruction Scaled error image Zoomed compression reconstruction 25:1 Compression ratio 52:1 CSE 166, Fall

39 JPEG 2000 uses wavelet based coding Compression reconstruction Scaled error image Zoomed compression reconstruction 75:1 Compression ratio 105:1 CSE 166, Fall

40 Visible watermark Watermark Watermarked image Original image minus watermark CSE 166, Fall

41 Invisible image watermarking system Encoder Decoder CSE 166, Fall

42 Invisible watermark Example: watermarking using two least significant bits Original image JPEG compressed Extracted watermark Two least significant bits Fragile invisible watermark CSE 166, Fall

43 Invisible watermark Example: DCT based watermarking Watermarked images Extracted robust invisible watermark CSE 166, Fall

44 Reflection and translation Reflection Translation CSE 166, Fall

45 Sets of pixels: objects and structuring elements (SEs) Border of background pixels around objects Tight border around SE CSE 166, Fall

46 Reflection about the origin Origin Don t care elements CSE 166, Fall

47 Erosion Example: square SE CSE 166, Fall

48 Erosion Example: elongated SE CSE 166, Fall

49 Erosion Shrinks 11x11 15x15 45x45 CSE 166, Fall

50 Dilation Examples Square SE Elongated SE CSE 166, Fall

51 Dilation Expands CSE 166, Fall

52 Opening Structuring element rolls along inner boundary CSE 166, Fall

53 Closing Structuring element rolls along outer boundary CSE 166, Fall

54 Opening and closing Erosion Opening Dilation Closing CSE 166, Fall

55 Morphological image processing Noisy input Erosion Opening Dilation Closing Dilation Erosion CSE 166, Fall

56 Boundary extraction Erosion Set difference CSE 166, Fall

57 Boundary extraction CSE 166, Fall

58 Hole filling Given point in hole CSE 166, Fall

59 Hole filling Given points in holes All holes filled CSE 166, Fall

60 Connected components Given point in A CSE 166, Fall

61 Connected components X ray image 15 connected components CSE 166, Fall

62 Image segmentation Input Edges Segmentation Edge based Region based CSE 166, Fall

63 Image derivatives CSE 166, Fall

64 Detection of isolated points Laplacian (second derivative) Threshold absolute value Input Segmentation CSE 166, Fall

65 Line detection Double lines Input Laplacian (second derivative) Threshold absolute value Threshold value CSE 166, Fall

66 Line detection, specific directions Spatial filters CSE 166, Fall

67 Line detection, specific directions +45 Negative values set to zero Threshold CSE 166, Fall

68 Edge models Step Ramp Roof edge CSE 166, Fall

69 Edge models Step Ramp Roof edge CSE 166, Fall

70 Ramp edge Two points First derivative Second derivative One point CSE 166, Fall

71 Noise and image derivatives Input First derivative Second derivative Noise CSE 166, Fall

72 Gradient and edge direction Gradient direction is orthogonal to edge direction CSE 166, Fall

73 Gradient operators Forward difference CSE 166, Fall

74 Gradients Input Magnitude of vertical gradient Magnitude of horizontal gradient Magnitude of gradient vector CSE 166, Fall

75 Gradients Smooth image prior to computing gradients. Results in more selective edges Input Magnitude of vertical gradient Magnitude of horizontal gradient Magnitude of gradient vector CSE 166, Fall

76 Edge detection Threshold magnitude of gradient vector Without smoothing With smoothing CSE 166, Fall

77 Advanced edge detection Input Magnitude of gradient vector (with smoothing) Marr Hildreth Canny See textbook for algorithms CSE 166, Fall

78 Thresholding Histograms Single threshold Dual threshold CSE 166, Fall

79 Noise and thresholding Noise CSE 166, Fall

80 Varying background and thresholding Input Intensity ramp Product of input and intensity ramp CSE 166, Fall

81 Basic global thresholding Input Intensity ramp Threshold CSE 166, Fall

82 Optimum global thresholding Input Histogram Basic global thresholding Optimum global thresholding using Otsu s method CSE 166, Fall

83 Image smoothing to improve global thresholding Otsu s method Without smoothing With smoothing CSE 166, Fall

84 Image smoothing does not always improve global thresholding Otsu s method Without smoothing With smoothing CSE 166, Fall

85 Edges to improve global thresholding Input Masked input Mask image (thresholded gradient magnitude) Optimum global thresholding using Otsu s method CSE 166, Fall

86 Edges to improve global thresholding Mask image (thresholded absolute Laplacian) Input Masked input Optimum global thresholding using Otsu s method CSE 166, Fall

87 Variable thresholding Input Global thresholding Local standard deviations Local thresholding using standard deviations CSE 166, Fall

88 Variable thresholding Input (spot shading) Global thresholding Local thresholding using moving averages CSE 166, Fall

89 Variable thresholding Input (sinusoidal shading) Global thresholding Local thresholding using moving averages CSE 166, Fall

90 Segmentation by region growing Input X ray image Initial seed image Final seed image Output image CSE 166, Fall

Difference image thresholded with the smallest of the

91 Segmentation by region growing Difference image Difference image thresholded using dual thresholds Difference image thresholded with the smallest of the dual thresholds Segmentation by region growing CSE 166, Fall

92 Advanced segmentation methods k means clustering Superpixels Graph cuts CSE 166, Fall

93 Segmentation using k means clustering Input Segmentation using k means, k = 3 CSE 166, Fall

94 Superpixels Input image of 480,000 pixels Image of 4,000 superpixels with boundaries Image of 4,000 superpixels CSE 166, Fall

95 Superpixels 1,000 superpixels 500 superpixels 250 superpixels CSE 166, Fall

96 Superpixels for image segmentation Input image of 301,678 pixels Segmentation using k means, k = 3 Superpixel image (100 superpixels) Segmentation using k means, k = 3 CSE 166, Fall

97 Images as graphs Stronger (greater weight) edges are darker Simple graph with edges only between 4 connected neighbors CSE 166, Fall

98 Graph cuts for image segmentation Cut the weak edges CSE 166, Fall

99 Graph cuts for image segmentation Input Smoothed input Graph cut segmentation CSE 166, Fall

Digital Image Processing

Digital Image Processing Third Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive PEARSON Prentice Hall Pearson Education International Contents Preface xv Acknowledgments