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Image SegmentationWhat is Image Segmentation?OutlinePoint DetectionLine DetectionEdge DetectionSlide 7Impact of NoiseFirst & Second Derivatives of EdgesEdge Detection OperatorsApproximate Gradient with L1 NormEffects of SmoothingEmphasizing Diagonal EdgesLaplacian and Mexican HatComparison of Edge DetectionBoundary ExtractionLocal Processing Edge LinkingGlobal Processing Edge Linking: Hough TransformHough Transform in (r, ) planeExampleSlide 21Threshold SegmentationEffect of Illumination on ThresholdingThreshold ExampleNeeds of Adaptive ThresholdNeeds of Local ThresholdThreshold: Hypothesis TestingUni-model Gaussian ExampleClustering Problem Statementk-means Clustering AlgorithmA Numerical ExampleThresholding Example© 2002-2003 by Yu Hen Hu1ECE533 Digital Image ProcessingImage Segmentation© 2002-2003 by Yu Hen Hu2ECE533 Digital Image ProcessingWhat is Image Segmentation?Segmentation: »Split or separate an image into regions»To facilitate recognition, understanding, and region of interests (ROI) processingIll-defined problem»The definition of a region is context-dependent20 40 60204060© 2002-2003 by Yu Hen Hu3ECE533 Digital Image ProcessingOutlineDiscontinuity Detection»Point, edge, lineEdge Linking and boundary detectionThresholdingRegion based segmentationSegmentation by morphological watershedsMotion segmentation© 2002-2003 by Yu Hen Hu4ECE533 Digital Image ProcessingPoint DetectionApply detection mask, followed by threshold detection© 2002-2003 by Yu Hen Hu5ECE533 Digital Image ProcessingLine DetectionUseful for detecting lines with width = 1.© 2002-2003 by Yu Hen Hu6ECE533 Digital Image ProcessingEdge DetectionPoints and lines are special cases of edges. Edge detection is difficult since it is not clear what amounts to an edge!© 2002-2003 by Yu Hen Hu7ECE533 Digital Image ProcessingEdge Detection© 2002-2003 by Yu Hen Hu8ECE533 Digital Image ProcessingImpact of Noise© 2002-2003 by Yu Hen Hu9ECE533 Digital Image ProcessingFirst & Second Derivatives of Edgesgradient, ofdirection :tan),(gradient of magnitude ://122xyyxyxyxGGyxGGGGyfxfGGff© 2002-2003 by Yu Hen Hu10ECE533 Digital Image ProcessingEdge Detection OperatorsFigure 10.8, 10.9© 2002-2003 by Yu Hen Hu11ECE533 Digital Image ProcessingApproximate Gradient with L1 Norm© 2002-2003 by Yu Hen Hu12ECE533 Digital Image ProcessingEffects of Smoothing© 2002-2003 by Yu Hen Hu13ECE533 Digital Image ProcessingEmphasizing Diagonal EdgesUse diagonal Sobel operator shown in figure 10.9(d)© 2002-2003 by Yu Hen Hu14ECE533 Digital Image ProcessingLaplacian and Mexican Hat   22222/4222/2222222)(rrererhyfxffLoG operator© 2002-2003 by Yu Hen Hu15ECE533 Digital Image ProcessingComparison of Edge Detectionoriginal Sobel LoGThreshold LoGZero-crossingGaussian smooth operatorLaplacian operatorGradient method: suitable for abrupt gray level transition, sensitive to noise2nd order derivative: good for smooth edges© 2002-2003 by Yu Hen Hu16ECE533 Digital Image ProcessingBoundary ExtractionEdge detection classifies individual pixels to be on an edge or not. Isolated edge pixels is more likely to be noise rather than a true edge.Adjacent or connected edge pixels should be linked together to form boundary of regions that segment the image.Edge linking methods:»Local processing »Hough transform»Graphic theoretic method»Dynamic programming© 2002-2003 by Yu Hen Hu17ECE533 Digital Image ProcessingLocal Processing Edge LinkingAn edge pixel will be linked to another edge pixel within its own neighborhood if they meet two criteria:( , ) ( , )( , ) ( , )o oo of x y f x y Ex y x y Aa a�-ѣ- �© 2002-2003 by Yu Hen Hu18ECE533 Digital Image ProcessingGlobal Processing Edge Linking: Hough TransformFind a subset of n points on an image that lie on the same straight line.Write each line formed by a pair of these points as yi = axi + bThen plot them on the parameter space (a, b):b = xi a + yiAll points (xi, yi) on the same line will pass the same parameter space point (a, b).Quantize the parameter space and tally # of times each points fall into the same accumulator cell. The cell count = # of points in the same line.© 2002-2003 by Yu Hen Hu19ECE533 Digital Image ProcessingHough Transform in () planeTo avoid infinity slope, use polar coordinate to represent a line.Q points on the same straight line gives Q sinusoidal curves in () plane intersecting at the same (ii) cell. sincos yx© 2002-2003 by Yu Hen Hu20ECE533 Digital Image ProcessingExample© 2002-2003 by Yu Hen Hu21ECE533 Digital Image ProcessingExample© 2002-2003 by Yu Hen Hu22ECE533 Digital Image ProcessingThreshold Segmentation© 2002-2003 by Yu Hen Hu23ECE533 Digital Image ProcessingEffect of Illumination on Thresholding© 2002-2003 by Yu Hen Hu24ECE533 Digital Image ProcessingThreshold Example© 2002-2003 by Yu Hen Hu25ECE533 Digital Image ProcessingNeeds of Adaptive Threshold© 2002-2003 by Yu Hen Hu26ECE533 Digital Image ProcessingNeeds of Local ThresholdProperly and improperly segmented subimages from Fig. 10.30. Further division of the sub-image, and result of adaptive thresholding© 2002-2003 by Yu Hen Hu27ECE533 Digital Image ProcessingThreshold: Hypothesis TestingQuestion: »Does this pixel with intensity z belong to a region (edge) or not?Hypothesis»H0: Null. It does not»H1: Alt. It doesLikelihood»p(z|zH0) = p1(z)»p(z| z H1) = p2(z)Prior»P1 = p(zH0) , »P2 = p(zH1) Maximum likelihood: »Pixel z belongs to a region if p(z|H1) > p(z|H0) Bayesian: P2 p(z|H1) > P1 p(z|H0) Sufficient statistic:z > T© 2002-2003 by Yu Hen Hu28ECE533 Digital Image ProcessingUni-model Gaussian ExampleGiven Set P1 p1(T) = P2 p2(T) and solve for T.Take log on both sides and simplify to AT2 + BT + C = 0 222exp21)(iiizzp 12212212121122221212222212122212221ln2 then, Ifln22PPTPPCBA© 2002-2003 by Yu Hen Hu29ECE533 Digital Image ProcessingClustering Problem Statement Given a set of vectors {xk; 1  k  K}, find a set of M clustering centers {w(i); 1  i  c} such


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UW-Madison ECE 533 - Image Segmentation

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