Digital Image Processing COSC 6380/4393

Transcription

1 Digital Image Processing COSC 6380/4393 Lecture 21 Nov 16 th, 2017 Pranav Mantini Ack: Shah. M

2 Image Processing Geometric Transformation Point Operations Filtering (spatial, Frequency) Input Restoration/ Reconstruction Color Image Processing... Semantic meaning Output

3 Edge Detection Edge Detection Identify pixels that represent edges in the image

4 Why detect edges 1. Visual system The importance of using edges is also supported by nature The visual systems of mammals contain cells with gradient-based Gabor-like response. Initial stages of mammalian vision systems involve detection of edges and local features 2. Computer vision algorithms for Object detection and recognition Object recognition, stereo, texture analysis, motion analysis, image enhancement, image compression

5 Edge Formation

6 Edge Detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded in the edges Source: D. Lowe

7 What is an Edge? Discontinuity of intensities in the image Edge models

8 Characterizing edges An edge is a place of rapid change in the image intensity function Slide Credit: James Hays

9 Characterizing edges An edge is a place of rapid change in the image intensity function Slide Credit: James Hays

10 Effects of noise Consider a single row or column of the image Plotting intensity as a function of position gives a signal

11 Effects of noise Consider a single row or column of the image Plotting intensity as a function of position gives a signal Where is the edge?

12 Solution: smooth first

13 Solution: smooth first

14 Derivative theorem of convolution Differentiation is convolution, and convolution is associative:

15 Derivative theorem of convolution

16 Derivative theorem of convolution

17 Tradeoff between smoothing and localization Smoothed derivative removes noise, but blurs edge. Also finds edges at different scales.

18 Derivative in Two-Dimensions Definition Approximation Convolution kernels

19 Image Derivatives

20 Edge Detection Goals

21 Edge Detection Goals 1. Good detection: Low false alarm rate and low false dismissal rate: maximize S/ N ratio 2. Good localization: Mark point closest to center of true edge: minimize distance between marked point and center 3. Uniqueness: Only one response to a single edge 4. Good property measurement: Orientation, contrast, etc.

22 1D Edge Detection An ideal edge is a step function 22

23 1D Edge Detection The first derivative of I (x) has a peak at the edge The second derivative of I (x) has a zero crossing at the edge 23

24 Edge Detectors First order derivative based Second order derivative based

25 Edge Detectors First order derivative based Prewit Sobel Second order derivative based Marr-Hildreth (Laplacian of Gaussian ) Canny (Gradient of Gaussian)

26 First order edge detectors 1. Compute derivatives In x and y directions 2. Find gradient magnitude 3. Threshold gradient magnitude

27 Prewit: Compute derivatives In x directions Image Average smoothing in Y direction Smooth image Gradient in X direction Edges in X

28 Prewit: Compute derivatives In x and y directions Image Image Average smoothing in Y direction Average smoothing in X direction Smooth image Smooth image Gradient in X direction Gradient in Y direction Edges in X Edges in Y

29 Sobel : Compute derivatives In x and y directions Image Image Average smoothing in Y direction Average smoothing in X direction Smooth image Smooth image Gradient in X direction Gradient in Y direction Edges in X Edges in Y

30 Sobel Edge Detector

31 Pros: 1. Quick and simple Prewitt and Sobel Cons: 1. Detection: sensitive to noise 2. Uniqueness: Multiple responses (dependent on smoothing) 3. Requires tuning to define threshold

32 Second Order Derivative Edge Detection Methods Marr Hildreth Edge Detector 1. Smooth image by Gaussian filter S 2. Apply second order derivative to S 2 S (Laplacian) 3. Find zero crossings Scan along each row, record an edge point at the location of zero-crossing. Repeat above step along each column

33 Marr Hildreth Edge Detector Gaussian smoothing Find Laplacian

34 Marr Hildreth Edge Detector Laplacian of Gaussian (LoG)

35 Finding Zero Crossings 1. Four cases of zero-crossings : {+,-} {+,0,-} {-,+} {-,0,+} 2. Slope of zero-crossing {a, -b} is a+b. 3. To mark an edge compute slope of zero-crossing Apply a threshold to slope

36 Example

37 Marr Hildreth Edge Detector 1. Apply LoG to the Image 2. Find zero-crossings from each row 3. Find slope of zero-crossings 4. Apply threshold to slope and mark edges

38 Quality of an Edge

39 Quality of an Edge

40 Quality of an Edge

41 Quality of an Edge

42 Canny Edge Detector Criterion 1: Good Detection: The optimal detector must minimize the probability of false positives as well as false negatives. Criterion 2: Good Localization: The edges detected must be as close as possible to the true edges. Single Response Constraint: The detector must return one point only for each edge point.

43 Canny Edge Detector Steps 1. Smooth image with Gaussian filter

44 Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image

45 Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image 3. Find magnitude and orientation of gradient

46 Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image 3. Find magnitude and orientation of gradient 4. Apply Non-maximum Suppression

47 Canny Edge Detector Steps 1. Smooth image with Gaussian filter 2. Compute derivative of filtered image 3. Find magnitude and orientation of gradient 4. Apply Non-maximum Suppression 5. Apply Hysteresis Threshold

48 Smoothing Canny Edge Detector First Two Steps Derivative

49 Canny Edge Detector Derivative of Gaussian

50 Canny Edge Detector Derivative of Gaussian

51 Canny Edge Detector Derivative of Gaussian

52 Canny Edge Detector First Two Steps

53 Canny Edge Detector First Two Steps

54 Canny Edge Detector First Two Steps

55 Canny Edge Detector Third Step Gradient magnitude and gradient direction

56 Canny Edge Detector Third Step Gradient magnitude and gradient direction

57 Canny Edge Detector Third Step Gradient magnitude and gradient direction

58 Example

59 Derivative of Gaussian filter

60 Compute Gradients (DoG)

61 Edge Direction Vs Gradient Direction Gradient is maximum in the direction perpendicular to the edge Edge direction Maximum gradient direction Edge

62 Get Orientation at Each Pixel Threshold at minimum level Get orientation theta = tan 1 gy/gx

63 Canny Edge Detector Fourth Step Non maximum suppression

64 Canny Edge Detector Fourth Step Non maximum suppression

65 Canny Edge Detector Non-Maximum Suppression Suppress the pixels in S which are not local maximum

66 Canny Edge Detector Non-Maximum Suppression Suppress the pixels in S which are not local maximum

67 Canny Edge Detector Non-Maximum Suppression

68 Canny Edge Detector Hysteresis Thresholding If the gradient at a pixel is above High, declare it as an edge pixel below Low, declare it as a non-edge-pixel between low and high Consider its neighbors iteratively then declare it an edge pixel if it is connected to an edge pixel directly or via pixels between low and high.

69 Connectedness Canny Edge Detector Hysteresis Thresholding

70 Connectedness Canny Edge Detector Hysteresis Thresholding

71 Connectedness Canny Edge Detector Hysteresis Thresholding

72 Canny Edge Detector Hysteresis Thresholding

73 Canny Edge Detector Hysteresis Thresholding

74 Canny Edge Detector Hysteresis Thresholding

75 Canny Edge Detector Hysteresis Thresholding

76 Canny Edge Detector Hysteresis Thresholding Scan the image from left to right, topbottom.

77 Canny Edge Detector Hysteresis Thresholding Scan the image from left to right, topbottom. The gradient magnitude at a pixel is above a high threshold declare that as an edge point

78 Canny Edge Detector Hysteresis Thresholding Scan the image from left to right, topbottom. The gradient magnitude at a pixel is above a high threshold declare that as an edge point Then recursively consider the neighbors of this pixel. If the gradient magnitude is above the low threshold declare that as an edge pixel.

79 Canny Edge Detector Hysteresis Thresholding

80 Canny Edge Detector Hysteresis Thresholding

81 Before Non-max Suppression Slide

82 Before Non-max Suppression Slide

83 Hysteresis thresholding Threshold at low/high levels to get weak/strong edge pixels Do connected components, starting from strong edge pixels

84 Final Canny Edges

85 Effect of σ (Gaussian kernel spread/size) The choice of σ depends on desired behavior large σ detects large scale edges small σ detects fine features

86 Digital Image Processing

87 1. Pin hole camera Image Acquisition

88 Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE

89 Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE 3. OPTICAL IMAGING GEOMETRY light source (point source) emitted rays image object sensing plate, emulsion, etc focal length lens reflected rays

90 Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE 3. OPTICAL IMAGING GEOMETRY 4. Image Sampling and Quantization

91 Image Acquisition 1. Pin hole camera 2. OPTICS OF THE EYE 3. OPTICAL IMAGING GEOMETRY 4. Image Sampling and Quantization 5. Spatial and Intensity Resolution 6. Resampling

92 Digital Image Processing

93 BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM

94 BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING

95 BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS

96 BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS 4. BLOB COLORING

97 BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS 4. BLOB COLORING 5. BINARY MORPHOLOGY

98 BINARY IMAGES Processing 1. GRAY-LEVEL IMAGE HISTOGRAM 2. THRESHOLDING 3. LOGICAL OPERATIONS 4. BLOB COLORING 5. BINARY MORPHOLOGY 6. Binary image Compression

99 Digital Image Processing

100 Image Enhancement and Filtering 1. Linear Point operations

101 Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping

102 Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations

103 Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations 4. DFT

104 Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations 4. DFT 5. Spatial filtering

105 Image Enhancement and Filtering 1. Linear Point operations 2. Histogram shaping 3. Algebraic Operations 4. DFT 5. Spatial filtering 6. Convolution Theorem 7. Frequency Filtering

106 Digital Image Processing

107 1. Degradation model Image Restoration

108 Image Restoration 1. Degradation model 2. Modelling and estimating Noise

109 Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise

110 Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise 4. Mean and order statistic filters

111 Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise 4. Mean and order statistic filters 5. Model degradation functions

112 Image Restoration 1. Degradation model 2. Modelling and estimating Noise 3. Statistical and periodic noise 4. Mean and order statistic filters 5. Model degradation functions 6. Inverse filtering

113 Digital Image Processing

114 Color Image Processing 1. Color Fundamentals

115 Color Image Processing 1. Color Fundamentals 2. Color Models

116 Color Image Processing 1. Color Fundamentals 2. Color Models 3. Psuedo color image processing

117 Color Image Processing 1. Color Fundamentals 2. Color Models 3. Psuedo color image processing 4. Full color image processing

118 Digital Image Processing

119 1. Edge Formation Edge Detection

120 Edge Detection 1. Edge Formation 2. Characterizing edges

121 Edge Detection 1. Edge Formation 2. Characterizing edges 3. First order Derivatives 4. Second order derivatives 5. Canny edge detector

122 Digital Image Processing ~