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Representing the regions
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This chapter begins with a discussion of automatic thresholding and histogram methods for segmentation, followed by a discussion of techniques for representing regions Then more sophisticated techniques for region segmentation will be presented Edge detection techniques will be discussed in 5 In the following section, we will discuss techniques for region formation Thresholding is the simplest region segmentation technique After discussing thresholding, we will present methods to judge the similarity of regions using their intensity characteristics These methods may be applied after an initial region segmentation using thresholding It is expected that these algorithms will produce a region segmentation that corresponds to an object or its part Motion characteristics of points can also be used to form and refine regions Knowledge-based approaches may be used to match regions to object models The use of motion will be discussed in 14
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CHAPTER 3 REGIONS
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The segmentation problem, first defined in Section 21, is now repeated for ease of reference: Given a set of image pixels I and a homogeneity predicate P(), find a partition S of the image I into a set of n regions ~,
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The homogeneity predicate and partitioning of the image have the properties that any region satisfies the predicate P(~)
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for all i, and any two adjacent regions cannot be merged into a single region that satisfies the predicate P(~ U Rj)
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The homogeneity predicate P() defines the conformity of all points in the region ~ to the region model The process of converting a gray value image into a binary image is a simple form of segmentation where the image is partitioned into two sets The algorithms for thresholding to obtain binary images can be generalized to more than two levels The thresholds in the algorithm discussed in 2 were chosen by the designer of the system To make segmentation robust to variations in the scene, the algorithm should be able to select an appropriate threshold automatically using the samples of image intensity present in the image The knowledge about the gray values of objects should not be hard-wired into an algorithm; the algorithm should use knowledge about the relative characteristics of gray values to select the appropriate threshold This simple idea is useful in many computer vision algorithms
Automatic
Thresholding
To make segmentation more robust, the threshold should be automatically selected by the system Knowledge about the objects in the scene, the application, and the environment should be used in the segmentation algorithm in a form more general than a fixed threshold value Such knowledge may include
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32 REGION SEGMENTATION
Intensity characteristics of objects Sizes of the objects Fractions of an image occupied by the objects Number of different types of objects appearing in an image
A thresholding scheme that uses such knowledge and selects a proper threshold value for each image without human intervention is called an automatic thresholding scheme Automatic thresholding analyzes the gray value distribution in an image, usually by using a histogram of the gray values, and uses the knowledge about the application to select the most appropriate threshold Since the knowledge employed in these schemes is more general, the domain of applicability of the algorithm is increased Suppose that an image contains n objects 01, O2, , On, including the background, and gray values from different populations 71"1,, 7I"n ith prob w ability distributions Pl(Z), ,Pn(z) In many applications, the probabilities PI'' Pn of the objects appearing in an image may also be known Using this knowledge, it is possible to rigorously formulate the threshold selection problem Since the illumination geometry of a scene controls the probability distribution of intensity values Pi(Z) in an image, one cannot usually precompute the threshold values As we will see, most methods for automatic threshold selection use the size and probability of occurrence and estimate intensity distributions by computing histograms of the image intensities Many automatic thresholding schemes have been used in different applications Some of the common approaches are discussed in the following sections To simplify the presentation, we will follow the convention that objects are dark against a light background In discussing thresholds, this allows us to say that gray values below a certain threshold belong to the object and gray values above the threshold are from the background, without resorting to more cumbersome language The algorithms that we present in the following sections can easily be modified to handle other cases such as light objects against a dark background, medium gray objects with background values that are light and dark, or objects with both light and dark gray values against a medium gray background Some algorithms can be generalized to handle object gray values from an arbitrary set of pixel values
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