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## Image Segmentation

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**What 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-dependent**Outline**• Discontinuity Detection • Point, edge, line • Edge Linking and boundary detection • Thresholding • Region based segmentation • Segmentation by morphological watersheds • Motion segmentation**Point Detection**Apply detection mask, followed by threshold detection**Line Detection**Useful for detecting lines with width = 1.**Edge Detection**• Points and lines are special cases of edges. • Edge detection is difficult since it is not clear what amounts to an edge!**Edge Detection Operators**Figure 10.8, 10.9**Emphasizing Diagonal Edges**Use diagonal Sobel operator shown in figure 10.9(d)**Laplacian and Mexican Hat**LoG operator**Comparison of Edge Detection**Zero-crossing Threshold LoG original Sobel LoG • Gradient method: • suitable for abrupt gray level transition, sensitive to noise • 2nd order derivative: • good for smooth edges Laplacian operator Gaussian smooth operator**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 Boundary Extraction**Local Processing Edge Linking**An edge pixel will be linked to another edge pixel within its own neighborhood if they meet two criteria:**Global Processing Edge Linking: Hough Transform**Find 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 + b Then plot them on the parameter space (a, b): b = xi a + yi All 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.**To avoid infinity slope, use polar coordinate to represent a**line. Q points on the same straight line gives Q sinusoidal curves in (r, ) plane intersecting at the same (ri, i) cell. Hough Transform in (r, ) plane**Needs of Local Threshold**Properly and improperly segmented subimages from Fig. 10.30. Further division of the sub-image, and result of adaptive thresholding**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|zH0) = p1(z) p(z| z H1) = p2(z) Prior P1 = p(zH0) , P2 = p(zH1) 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 Threshold: Hypothesis Testing**Given**Set P1 p1(T) = P2 p2(T) and solve for T. Take log on both sides and simplify to AT2 + BT + C = 0 Uni-model Gaussian Example**Clustering Problem Statement**• Given a set of vectors {xk; 1 k K}, find a set of M clustering centers {w(i); 1 i c} such that each xk is assigned to a cluster, say, w(i*), according to a distance (distortion, similarity) measure d(xk, w(i)) such that the average distortion is minimized. • I(xk,i) = 1 if x is assigned to cluster i with cluster center w(I); and = 0 otherwise -- indicator function.**k-means Clustering Algorithm**Initialization: Initial cluster center w(i); 1 i c, D(–1)= 0, I(xk,i) = 0, 1 i c, 1 k K; Repeat (A) Assign cluster membership (Expectation step) Evaluate d(xk, w(i)); 1 i c, 1 k K I(xk,i) = 1 if d(xk, w(i)) < d(xk, w(j)), j i; = 0; otherwise. 1 k K (B) Evaluate distortion D: (C) Update code words according to new assignment (Maximization) (D) Check for convergence if 1–D(Iter–1)/D(Iter) < e , then convergent = TRUE,**x = {1, 2,0,2,3,4},**W={2.1, 2.3} Assign membership 2.1: {1, 2, 0, 2} 2.3: {3, 4} Distortion D = (1 2.1)2 + (22.1)2 + (0 2.1)2 + (2 2.1)2 + (3 2.3)2 + (4 2.3)2 3. Update W to minimize distortion W1 = (12+0+2)/4 = .25 W2 = (3+4)/2 = 3.5 4. Reassign membership .25: {1, 2, 0} 3.5: {2, 3, 4} 5. Update W: w1 = (1 2+0)/3 = 1 w2 = (2+3+4)/3 = 3. Converged. A Numerical Example**Thresholding Example**Threshdemo.m