Thresholding Otsu’s Thresholding Method Threshold Detection Methods Optimal Thresholding Multi-Spectral Thresholding 6.2. Edge-based Segmentation Edge Relaxation Border Tracing Hough Transforms 6.3. Region-based Segmentation Watershed segmentation 6.4. Matching 6.5. Evaluation Issues in Segmentation Chapter 6 – Segmentation I

1 Objective: Divide an image into separate regions that are homogeneous wrt some properties e.g., brightness, color, reflectivity, texture. Categories of segmentation techniques: Thresholding, Edge-based, Region-based Mathematically, image segmentation = set partition

2 6.1 Thresholding (A) Global Thresholding – threshold T is determined from the whole image f, i.e., T = T(f) Input image High thresholdLow threshold How to determine a threshold?

33 Otsu’s Thresholding Method Describe the histogram as a probability distribution by

44 Let t be the determined threshold value Define Find t such that

55 (B) Local Thresholding – position dependent e.g., Adaptive (or variable) thresholding – Threshold values vary over the image as a function of local image characteristics, i.e., (i) Divide image into strips (ii) Apply global thresholding methods to each strip

66 D: a set of gray values (C) Modifications: (i) Band Thresholding: (ii) Multiple Thresholding: (iii) Semi-thresholding:

7 。 P-tile Thresholding – The percentage of foreground and background after segmentation is known a priori e.g., In a printed text sheet, we know that characters of text cover 1/p of the sheet area 。 Mode Method – Find local maxima; then detect minima between them as thresholds Threshold Detection Methods

88 。 Histogram Transformation – build a histogram with a better peak-to-valley ratio e.g., (a) Weight histogram in favor of pixels with high image gradients (b) Uses only high-gradient pixels to build the histogram (unimodal) 。 Histogram concavity analysis method, 。 Entropic method, 。 Relaxation method, 。 Multi-thresholding

Optimal Thresholding 。 MOG Fitting Method - approximate the histogram of an image with a mixture of Gaussian. Histogram F of an image Fitting Gaussian distributions Fitted Gaussian distributions

10 。 Iterative Threshold Selection

Multi-Spectral Thresholding e.g. Color images

Edge-Based Segmentation (2) Thresholding Problems: over-threshold, under-threshold (1) Edge detection

13 (3) Given directional information of edges Problems: cluttered by noise

14 (4) Hysteresis approach

Edge Relaxation - For continuous border construction Crack edges: edges located between pixels Vertex types Edge types Direction

16 Edge relaxation iteratively updates edge confidences c(e) of edges until converge either to 0 or to 1 The initial is defined as a normalized edge magnitude

17 Given confidence, determine edge type. where a, b, c are values of incident crack edges, (i) First, determine vertex type. and q a constant. (ii) Edge type is then determined as a concatenation of vertex types.

18 Edge confidence is modified as follows. 0-0 (isolated edge): Negative influence on edge confidence 0-1 (uncertain): Weak positive, or no influence on edge confidence 0-2, 0-3 (dead end): Negative influence on edge confidence 1-1 (continuation): Strong positive on edge confidence 1-2, 1-3 (continuation to border intersection): Medium positive on edge confidence 2-2, 2-3, 3-3 (bridge between borders): No influence on edge confidence

19 Increase: Decrease: where is a constant. Additional stop criterion.

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Border Tracing Categories of border: Inner border, Outer border, Extended border - Find region borders

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Border Detection as Graph Searching

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Border Detection as Dynamic Programming

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Hough Transforms Edge magnitude image Thresholding Thinning

○ Line equation: y = ax + b A point on the line Rewrite as Another point on the line Parameter space

○ Line equation: Accumulator array:

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○ Circle equation:

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49 ○ Generalized Hough Transform: 1. Select a reference point inside the sample region 2. Construct a line starting at aiming region border 3. Find the edge direction at the intersection 4. Construct R-table Assume the shape, size and orientation of the desired region are known

For each, compute potential reference points by

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Border Detection Using Border Location Information

Region Construction from Borders

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Region-based Segmentation

56 1. Equally divide the input image into 4 sub-images 2. Compute the characteristics of each sub-image 3. Repeatedly divide sub-images into sub-sub-images if their characteristics are significantly different 4. Repeatedly merge adjacent sub-images if their characteristics are similar enough Steps:

57 Split

58 Merge Image characteristics: Intensity, Color, Texture

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60 Input Image Segmentation Region Boundary

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Watershed Segmentation Image data may be interpreted as a topographic surface.

69 Idea: Catchment basin of the topographic surface are homogeneous in the sense that all pixels belonging to the same catchment basin are connected with the basin’s region of minimum altitude by a simple path of pixels that have monotonically decreasing altitude along the path. Such catchment basins represent the regions of the segmented image Approach 1: Steps: 1. Finding a downstream path from each pixel to a local minimum of image surface altitude; 2. A catchment basin is defined as the set of pixels for which their downstream paths all end up in the same altitude minimum.

70 Approach 2 (Vincent and Soille, IEEE PAMI, 13(6), 1991): Idea: Imagine that the topographic surface is immersed in water. The water starts filling all catchment basins, minima of which are under the water level. If two catchment basins are to merge, a dam is built all the way to the highest surface altitude and the dam represents the watershed line.

71 2. Flooding step: i, E very pixel having grey level <= k has been assigned a catchment basin label. ii, A pixel having grey level k+1 belongs to a label l if at least one of its neighbors carries this label. iii, Geodesic influence zones are computed for all determined catchment basins. 1. Sorting step: i, compute brightness histogram ii, create a list of pointers to pixels of each grey level h

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Matching

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Evaluation Issues in Segmentation

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