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Hierarchical stochastic image grammars for classification and segmentation
 IEEE Trans. Image Processing
, 2006
"... Abstract—We develop a new class of hierarchical stochastic image models called spatial random trees (SRTs) which admit polynomialcomplexity exact inference algorithms. Our framework of multitree dictionaries is the starting point for this construction. SRTs are stochastic hidden tree models whose l ..."
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Cited by 19 (4 self)
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Abstract—We develop a new class of hierarchical stochastic image models called spatial random trees (SRTs) which admit polynomialcomplexity exact inference algorithms. Our framework of multitree dictionaries is the starting point for this construction. SRTs are stochastic hidden tree models whose leaves are associated with image data. The states at the tree nodes are random variables, and, in addition, the structure of the tree is random and is generated by a probabilistic grammar. We describe an efficient recursive algorithm for obtaining the maximum a posteriori estimate of both the tree structure and the tree states given an image. We also develop an efficient procedure for performing one iteration of the expectationmaximization algorithm and use it to estimate the model parameters from a set of training images. We address other inference problems arising in applications such as maximization of posterior marginals and hypothesis testing. Our models and algorithms are illustrated through several image classification and segmentation experiments, ranging from the segmentation of synthetic images to the classification of natural photographs and the segmentation of scanned documents. In each case, we show that our method substantially improves accuracy over a variety of existing methods. Index Terms—Dictionary, estimation, grammar, hierarchical model, image classification, probabilistic contextfree grammar, segmentation, statistical image model, stochastic contextfree grammar, tree model. I.
Anisotropic 2D wavelet packets and rectangular tiling: theory and algorithms
 In Proc. SPIE, Wavelets: Appl. Signal Image Process
, 2003
"... We propose a new subspace decomposition scheme called anisotropic wavelet packets which broadens the existing definition of 2D wavelet packets. By allowing arbitrary order of row and column decompositions, this scheme fully considers the adaptivity, which helps find the best bases to represent an i ..."
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Cited by 14 (4 self)
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We propose a new subspace decomposition scheme called anisotropic wavelet packets which broadens the existing definition of 2D wavelet packets. By allowing arbitrary order of row and column decompositions, this scheme fully considers the adaptivity, which helps find the best bases to represent an image. We also show that the number of candidate tree structures in the anisotropic case is much larger than isotropic case. The greedy algorithm and doubletree algorithm are then presented and experimental results are shown.
New algorithms for best local cosine basis search
 In Proc. ICASSP2004
, 2004
"... We propose a best basis search algorithm for local cosine dictionaries. We improve upon the classical best local cosine basis selection based on a dyadic tree [2], by considering a larger dictionary of bases. This results in more compact representations, lower costs, and approximate shiftinvariance ..."
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Cited by 9 (8 self)
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We propose a best basis search algorithm for local cosine dictionaries. We improve upon the classical best local cosine basis selection based on a dyadic tree [2], by considering a larger dictionary of bases. This results in more compact representations, lower costs, and approximate shiftinvariance. We also provide a version of our algorithm which is strictly shiftinvariant. 1.
OPTIMAL REPRESENTATIONS IN MULTITREE DICTIONARIES WITH APPLICATION TO COMPRESSION.
"... We 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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Cited by 1 (0 self)
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We 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. We describe a novel block image coder based on our framework, which is an improvement over our image coder presented in [8]. 1. INTRODUCTION. This paper focuses on optimal representation problems: given a signal, a dictionary of representations, and a cost function, the aim is to select the representation from the dictionary which minimizes the cost for the given signal.
TimeFrequency Analysis with Best Local Cosine Bases
"... We propose new best basis search algorithms for local cosine dictionaries. We provide several algorithms for dictionaries of various complexity. Our framework generalizes the classical best local cosine basis selection based on a dyadic tree [1]. ..."
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We propose new best basis search algorithms for local cosine dictionaries. We provide several algorithms for dictionaries of various complexity. Our framework generalizes the classical best local cosine basis selection based on a dyadic tree [1].