|Stochastic Systems Group|
Ilya Pollak, Ph.D
School of Electrical and Computer Engineering
In this talk, we will introduce a new class of hierarchical stochastic models for multidimensional signals, called spatial random trees (SRTs). Compared to previous efforts which model images with stochastic processes on quadtrees, our key innovation is that the tree structure itself is random, and is generated by a probabilistic context-free grammar. We develop exact procedures for likelihood calculation, MAP estimation of the processes, and parameter estimation. These recursive algorithms, collectively called the center-surround algorithm, can be applied to learning the hierarchical structure of a set of images, as well as to image parsing and classification. In addition, these algorithms can be adapted to solve certain best-basis search problems where a dictionary of orthogonal bases is given and the task is to find the basis that represents a given signal the best according to some cost.
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