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Section 6.2  Pooled Texture Representations by Discovering Textons  175





































                            FIGURE 6.10: Pattern elements can also be identified by vector quantizing vectors obtained
                            by reshaping an image window centered on each pixel. Here we show the top 50 pattern
                            elements (or textons), obtained using this strategy from all 1,000 images of the collection
                            of material images described in Figure 6.2. Each subimage here illustrates a cluster center.
                            For some cluster centers, we show the closest 25 image patches. To measure distance, we
                            first subtracted the average image intensity, and we weighted by a Gaussian to ensure that
                            pixels close to the center of the patch were weighted higher than those far from the center.
                            This figure shows elements of a database collected by C. Liu, L. Sharan, E. Adelson, and
                            R. Rosenholtz, and published at http: // people. csail. mit. edu/ lavanya/ research_
                            sharan. html . Figure by kind permission of the collectors.


                               • Assume the cluster centers are known and, allocate each point to the closest
                                 cluster center.
                               • Assume the allocation is known, and choose a new set of cluster centers. Each
                                 center is the mean of the points allocated to that cluster.
                            We then choose a start point by randomly choosing cluster centers, and then iterate
                            these stages alternately. This process eventually converges to a local minimum of
                            the objective function (the value either goes down or is fixed at each step, and
                            it is bounded below). It is not guaranteed to converge to the global minimum of
                            the objective function, however. It is also not guaranteed to produce k clusters,
                            unless we modify the allocation phase to ensure that each cluster has some nonzero
                            number of points. This algorithm is usually referred to as k-means (summarized in
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