Optimal tilings and best basis search in large dictionaries

Abstract

Abstract-We develop a new framework of multitree dictionaries which include many previously proposed dictionaries as special cases. We show how to efficiently find the best object in a multitree dictionary using a recursive dynamic programming algorithm. We apply our framework to find the best rectangular tiling of an image domain.

Classification of images using spatial random trees

“…This process can be visualized as a tree where each production a → α is depicted as a node labeled a whose children are labeled with the elements of α. Following [6][7][8], we let a multitree dictionary D a (G) be the set of all such trees that can be produced by the grammar G, starting with the root symbol a. When there is no possibility of confusion, we will simply denote such a dictionary by D. We say that a grammar G = (A, S) is finite-depth if, for every a ∈ A, D a (G) is a finite set containing only finite-depth trees.…”

“…This problem can be solved using an efficient recursive algorithm for best tree search described in [6][7][8]. To illustrate this algorithm, we suppose that the only allowed split of the symbol a is: a → b 1 b 2 .…”

“…We first review the framework of multitree dictionaries [6][7][8] which we will use to develop our SRT image models. Multitree dictionaries are defined using grammar formalism [5,10].…”

“…We build upon our earlier research on stochastic grammars [11][12][13], and demonstrate a close relationship between SRTs and multitree dictionaries introduced in [6][7][8]. We show how to find the MAP estimate of both the tree structure and the tree states for an SRT model.…”

Optimal representations in multitree dictionaries with application to compression

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ABSTRACTWe generalize our results of [8,9] and propose a new framework of multitree dictionaries which include many previously proposed dictionaries as well as many new, very large, treestructured dictionaries. We present an efficient, globally optimal algorithm to find the best tree in such a dictionary.

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