Chapter 10 Image Segmentation. Yinghua He

Transcription

1 Chapter 10 Image Segmentation Yinghua He

2 The whole is equal to the sum of its parts. -Euclid The whole is greater than the sum of its parts. -Max Wertheimer The Whole is Not Equal to the Sum of Its Parts: An Approach to Teaching the Research Paper. -by Mangum, Bryant

3 Detection of Discontinuities Edge Linking and Boundary Detection Thresholding Region-Based Segmentation Segmentation by Morphological Watersheds The Use of Motion in Segmentation

4 R = w z + w z w 9 z 9 = 9 i= 1 w i z i

5 Point Detection Line Detection Edge Detection

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7 Point Detection Line Detection Edge Detection

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10 Point Detection Line Detection Edge Detection

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14 Gradient operators The gradient of an image f(x,y) at location (x,y) is defined as the vector f = G G x y f = f x y An important quantity in edge detection is the magnitude of this vector, denoted f,where [ ] 2 2 G 1/ 2 x G f = mag( f ) = + y

15 The direction of the gradient vector also is an important quantity. Let α ( x, y) represent the direction angle of the vector f at (x,y). Then, from vector analysis, α( x, y) = tag 1 G G y x

16 Roberts cross-gradient operators: G x = ( z z5 ) 9 and G y = ( z z 8 6 )

17 An approach using masks of size 3*3 is given by and G x = ( z7 + z8 + z9 ) ( z1 + z2 + z3 ) G y = ( z3 + z6 + z9 ) ( z1 + z4 + z7 )

18 A slight variation of these two equations uses a weight of 2 in the center coefficient: and ) 2 ( ) 2 ( z z z z z z G y = ) 2 ( ) 2 ( z z z z z z G x =

19 An approach used frequently is to approximate the gradient by absolute values: f G + G x y

20 The Laplacian The Laplacian of a 2-D function f(x,y) is a second-order derivative defined as For a 3*3 region, one of the two forms encountered most frequently in practice is y f x f f + = ( ) z z z z z f =

21 A digital approximation including the diagonal neighbors is given by 2 5 ( z + z + z + z + z + z + z ) f = 8z + z

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30 Detection of Discontinuities Edge Linking and Boundary Detection Thresholding Region-Based Segmentation Segmentation by Morphological Watersheds The Use of Motion in Segmentation

31 Local Processing Global Processing via the Hough Transform Global Processing via Graph-Theoretic Techniques

32 An edge pixel with coordinates (x 0,y 0 ) in a predefined neighborhood of (x,y), is similar in magnitude to the pixel at (x,y) if f ( x, y) f ( x0, y0 ) E An edge pixel at (x 0,y 0 ) in the predefined neighborhood of (x,y) has an angle similar to the pixel at (x,y) if α x, y) α( x, y ) < ( 0 0 A

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34 Local Processing Global Processing via the Hough Transform Global Processing via Graph-Theoretic Techniques

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37 x cosθ + y sinθ = ρ

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39 ( ) 2 ( ) 2 x + = 2 c y c c 1 2 3

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42 Local Processing Global Processing via the Hough Transform Global Processing via Graph-Theoretic Techniques

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44 A sequence of nodes n 1,n 2,,n k, with each node n i being a successor of node n i-1, is called a path from n 1 to n k. The cost of the entire path is: c = k i= 2 c ( ) n i 1, n i

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48 Detection of Discontinuities Edge Linking and Boundary Detection Thresholding Region-Based Segmentation Segmentation by Morphological Watersheds The Use of Motion in Segmentation

49 Foundation The Role of Illumination Basic Global Thresholding Basic Adaptive Thresholding

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51 Based on the preceding discussion, thresholding may be viewed as an operation that involves tests against a function T of the form T = T x, y, p( x, y), f ( x, y) [ ] A thresholded image g(x,y) is defined as

52 A thresholded image g(x,y) is defined as g( x, y) = 1 0 if if f ( x, y) > T f ( x, y) T

53 Foundation The Role of Illumination Basic Global Thresholding Basic Adaptive Thresholding

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55 Taking the natural logarithm of this equation yields a sum: ), ( ), ( ), ( y x r y x i y x f = ), ( ), ( ), ( ln ), ( ln ), ( ln ), ( ' ' y x r y x i y x r y x i y x f y x z + = + = =

56 Foundation The Role of Illumination Basic Global Thresholding Basic Adaptive Thresholding

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58 The following algorithm can be used to obtain T automatically: Select an initial estimate for T; Segment the image using T. This will produce two groups of pixels: G 1 consisting of all pixels with grey level values>t and G 2 consisting of pixels with values <=T. Compute the average gray level values μ1 and μ2 for the pixels in regions G 1 and G 2. Compute a new threshold value: 1 T = ( μ 1 + μ 2 ) 2 Repeat steps 2 through 4 until the difference in T in successive iterations is smaller than a predefined parameter T o.

59 Foundation The Role of Illumination Basic Global Thresholding Basic Adaptive Thresholding

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62 Detection of Discontinuities Edge Linking and Boundary Detection Thresholding Region-Based Segmentation Segmentation by Morphological Watersheds The Use of Motion in Segmentation

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64 Region Growing Region Splitting and Merging

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69 Region Growing Region Splitting and Merging

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71 Split into four disjoint quadrants any region R i for which P(R i )=FALSE; Merge any adjacent regions R j and R k for which P( R j U Rk ) = TRUE. Stop when no further merging or splitting is possible.

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73 Detection of Discontinuities Edge Linking and Boundary Detection Thresholding Region-Based Segmentation Segmentation by Morphological Watersheds The Use of Motion in Segmentation

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80 Detection of Discontinuities Edge Linking and Boundary Detection Thresholding Region-Based Segmentation Segmentation by Morphological Watersheds The Use of Motion in Segmentation

81 Spatial Techniques Frequency Domain Techniques

82 d ij ( x, y) = 1 if f ( x, y, ti ) f ( x, y, t j ) > 0 otherwise T

83 and > + = otherwise y x A T k y x f y x R if y x A y x A k k k ), ( ),, ( ), ( 1 ), ( ), ( 1 1 > + = otherwise y x P T k y x f y x R if y x P y x P k k k ), ( ),, ( ), ( 1 ), ( ), ( 1 1 < + = otherwise y x N T k y x f y x R if y x N y x N k k k ), ( ),, ( ), ( 1 ), ( ), ( 1 1

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86 Spatial Techniques Frequency Domain Techniques

87 e ( x' + t ) Δt = [ 2πa ( x' + t) Δt] + j sin[ 2 a ( x' + t) Δt] cos 1 j2πa 1 1 π

88 The actural physical speed in the x-dirextion is

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