Lecture 4 : Stat 238 . Winter 2014 . B . Bonev ,
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چکیده
Image segmentation is the process of dividing an image into multiple segments (sets of pixels, also known as superpixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Meaningful in the sense that each segment will hopefully correspond to a part/subpart of an object (e.g, person, head) or background region (e.g, sky, road). Easier to analyze in the sense that the number of segments will be much smaller than the number of pixels and each segment would provide a richer description than a single pixel does. In this lecture we consider segmentation as an intermediate-level computer vision technique. Segmentation goes beyond low-level vision by grouping or dividing regions based on both local and global image properties. It is based on natural properties of the images, such as the assumption that there exist smooth or roughly homogeneous regions and they are compact to some extent. We consider a segmentation method which does not use any object-specific information. Thus, the segments produced serve as an input for a high-level computer vision method. For example, they can be used as candidate regions for object recognition techniques, see Figure 1. Segments can be both connected or disconnected, and they can form a single partition of the image or they can overlap, if there are multiple hypothesis about the image segmentation. This is the case of hierarchical image segmentation methods, which produce different segmentation levels with increasing (or decreasing) number of segments in each partition.
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Lecture Six - STAT 212a
Conversely, for every -packing subset t1, . . . , tn of T , the closed balls B(ti, /2), i = 1, . . . , n are disjoing and hence every /2-cover of T must have one point in each of the balls B(ti, /2). As a result, an /2-cover of T must have at least n points. This implies that M( /2, T ) ≥ N( , T ). Lemma 1.2 (Volumetric Argument). Let T = X denote the ball in R of radius Γ centered at the origi...
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