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### lecture17

Course: CS 791, Fall 2009
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791E CS Computer Vision Instructor: Mircea Nicolescu Lecture 17 Region Merging Region merging using hypothesis testing - This approach considers whether or not to merge adjacent regions based on the probability that they will have the same statistical distribution of intensity values. - Assume that the gray-level values in an image region are drawn from Gaussian distributions. - We can estimate the parameters...

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791E CS Computer Vision Instructor: Mircea Nicolescu Lecture 17 Region Merging Region merging using hypothesis testing - This approach considers whether or not to merge adjacent regions based on the probability that they will have the same statistical distribution of intensity values. - Assume that the gray-level values in an image region are drawn from Gaussian distributions. - We can estimate the parameters of the Gaussian using MaximumLikelihood: 2 Region Merging Region merging using hypothesis testing cont. - Given two regions R1 and R2 with m1 and m2 pixels respectively, there are two possible hypotheses: - H0: Both regions belong to the same object. The intensities are all drawn from a single Gaussian distribution N(0, 0): - H1: The regions belong to different objects. The intensities of each region are drawn from separate Gaussian distributions N(1, 1) and N(2, 2): - The joint probability density under H0, assuming all pixels are independently drawn, is given by: 3 Region Merging Region merging using hypothesis testing cont. - The joint probability density under H1 is given by: - The likelihood ratio is defined as the ratio of the probability densities under the two hypotheses: - If the likelihood ratio is below a threshold value, there is strong evidence that there is only one region and the two regions may be merged. 4 Region Merging Region merging by removing weak edges - The idea is to combine two regions if the boundary between them is weak. - A weak boundary is one for which the intensities on either side differ by less than some threshold T1. - The length of the weak boundary (compared to the overall length of region boundaries) must be also considered. 5 Region Merging Region merging by removing weak edges cont. Approach 1 Merge adjacent regions R1 and R2 if W / S > T2 where W is the length of the weak part of the boundary, and S = min(S1, S2) is the minimum of the perimeter of the two regions. do not merge merge 6 Region Merging Region merging by removing weak edges cont. Approach 2 Merge adjacent regions R1 and R2 if W / S > T3 where W is the length of the weak part of the boundary, and S is common boundary between R1 and R2 do not merge merge 7 Region Splitting Region splitting operations add missing boundaries by splitting regions that contain parts of different objects. Splitting schemes begin with a partition satisfying condition (5), for example, the whole image. Then, they proceed to fulfill condition (4) by gradually splitting image regions. 8 Region Splitting Two main difficulties in implementing this approach: - Deciding when to split a region (e.g., use variance, surface fitting). - Deciding how to split a region. 9 Region Splitting and Merging Splitting or merging might not produce good results when applied separately. Better results can be obtained by interleaving merge and split operations. This strategy takes a partition that possibly satisfies neither condition (4) or (5) with the goal of producing a segmentation that satisfies both conditions. 10 Region Splitting and Merging 11 Region Splitting and Merging 12 Connected Components A set of pixels in which each pixel is connected all to other pixels is called a connected component. Definition: A pixel p S is said to be connected to q S if there is a path from p to q consisting entirely of pixels of S. A component labeling algorithm finds all connected components in an image and assigns a unique label to all points in the same component. 13 Connected Components Recursive algorithm - Assume that region pixels have the value 0 (black) and that background pixels have the value 255 (white). 14 Connected Components Sequential algorithm - Usually requires two passes over the image. - It works with only two rows of an image at a time. 15 Connected Components Region boundary - The boundary of a connected component S is the set of pixels of S that are adjacent to background. - In most applications, one wants to track pixels on the boundary of a region in a particular order (e.g., clockwise). 16 Connected Components Region boundary cont. 17 Region Representation Array Representation - The most basic representation for regions is to use an array of the same size as the original image with entries that indicate the region to which a pixel belongs. 18 Region Representation Hierarchical Representations - Hierarchical representations of images (or regions) allow representation at multiple resolutions. - In many applications, one can compute properties of images (or regions) first at a low resolution and then perform additional computations over a selected area of the image at a higher resolution. - Include: - Pyramids - Quad trees 19 Region Representation Pyramids - A pyramid representation of an n x n image contains the image and k reduced versions of the image. - Assuming n is a power of 2, the other images are: - A pixel at level l is obtained by combining information from several pixels in the image at level l + 1 (e.g., averaging). 20 Region Representation Pyramids cont. 21 Region Representatio...

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