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13
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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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.
SPARSE ORTHONORMAL TRANSFORMS FOR IMAGE COMPRESSION
"... We propose a blockbased transform optimization and associated image compression technique that exploits regularity along directional image singularities. Unlike established work, directionality comes about as a byproduct of the proposed optimization rather than a built in constraint. Our work class ..."
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Cited by 14 (2 self)
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We propose a blockbased transform optimization and associated image compression technique that exploits regularity along directional image singularities. Unlike established work, directionality comes about as a byproduct of the proposed optimization rather than a built in constraint. Our work classifies image blocks and uses transforms that are optimal for each class, thereby decomposing image information into classification and transform coefficient information. The transforms are optimized using a set of training images. Our algebraic framework allows straightforward extension to nonblock transforms, allowing us to also design sparse lapped transforms that exploit geometric regularity. We use an EZW/SPIHT like entropy coder to encode the transform coefficients to show that our block and lapped designs have competitive ratedistortion performance. Our work can be seen as nonlinear approximation optimized transform coding of images subject to structural constraints on transform basis functions. Index Terms — Sparse orthonormal transforms, sparse lapped transforms, image coding, directional transforms 1.
SpaceFrequency Quantization for Image Compression with Directionlets
 IEEE Trans. Image Processing
"... Abstract—The standard separable 2D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1D discontinuities, like edges or contours. These features, being elongated and ..."
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Cited by 13 (3 self)
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Abstract—The standard separable 2D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions, called directionlets. In this paper, we show how to design and implement a novel efficient spacefrequency quantization (SFQ) compression algorithm using directionlets. Our new compression method outperforms the standard SFQ in a ratedistortion sense, both in terms of meansquare error and visual quality, especially in the lowrate compression regime. We also show that our compression method, does not increase the order of computational complexity as compared to the standard SFQ algorithm. Index Terms—Directional transforms, directional vanishing moments (DVMs), image coding, image orientation analysis, image segmentation, multiresolution analysis, nonseparable transforms, wavelet transforms (WTs). I.
Conditional density estimation by penalized likelihood model selection and applications. ArXiv 1103.2021
, 2011
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 10 (3 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
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.
Conditional Density Estimation by Penalized Likelihood Model Selection and Applications
, 2011
"... In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a KullbackLeibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a bes ..."
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In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a KullbackLeibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a best model within a collection. We give a general condition on penalty choice that leads to oracle type inequality for the resulting estimate. This construction is applied to two examples of partitionbased conditional density models, models in which the conditional density depends only in a piecewise manner from the covariate. The first example relies on classical piecewise polynomial densities while the second uses Gaussian mixtures with varying mixing proportion but same mixture components. We show how this last case is related to an unsupervised segmentation application that has been the source of our motivation to this study.
Conditional Density Estimation by Penalized Likelihood Model Selection and Applications
, 2012
"... In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a KullbackLeibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a be ..."
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In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a KullbackLeibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a best model within a collection. We give a general condition on penalty choice that leads to oracle type inequality for the resulting estimate. This construction is applied to two examples of partitionbased conditional density models, models in which the conditional density depends only in a piecewise manner from the covariate. The first example relies on classical piecewise polynomial densities while the second uses Gaussian mixtures with varying mixing proportion but same mixture components. We show how this last case is related to an unsupervised segmentation application that has been the source of our motivation to this study. 1
A Novel Image Compression Algorithm Based on Multitree Dictionary and Perceptualbased RateDistortion Optimization
"... This paper presents a novel blockbased image coding algorithm which applies a treestructured multitree dictionary and a perceptualbased rate distortion optimization scheme. While multitree dictionary is employed to support a very large number of different tilings, perceptualbased rate distortion ..."
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This paper presents a novel blockbased image coding algorithm which applies a treestructured multitree dictionary and a perceptualbased rate distortion optimization scheme. While multitree dictionary is employed to support a very large number of different tilings, perceptualbased rate distortion optimization utilizes the SSIM metric, instead of popular MSE metric, to allocate bit rate according to human visual system. Experimental results show that our proposed method outperforms many existing techniques in both subjective and objective image quality measures.
Optimal Tiling Algorithms for Interframe Video Compression.
"... We propose the use of large dictionaries of tilings for video compression and develop fast algorithms to select the optimal tiling for both the motion compensation and transform stages of a video coder. We illustrate the effectiveness of this approach by showing that our tiling selection method resu ..."
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We propose the use of large dictionaries of tilings for video compression and develop fast algorithms to select the optimal tiling for both the motion compensation and transform stages of a video coder. We illustrate the effectiveness of this approach by showing that our tiling selection method results in up to 23 % savings in bit rate as compared to the H.264/AVC tiling selection, for several standard video sequences. Index Terms Large treestructured dictionaries, motion compensation, transform, H.264/AVC.
IEEE TRANSACTIONS ON IMAGE PROCESSING 1 On the Number of Rectangular Tilings
"... Abstract — Adaptive multiscale representations via quadtree splitting and 2D wavelet packets, which amount to space and frequency decompositions, respectively, are powerful concepts that have been widely used in applications. These schemes are direct extensions of their 1D counterparts, in particula ..."
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Abstract — Adaptive multiscale representations via quadtree splitting and 2D wavelet packets, which amount to space and frequency decompositions, respectively, are powerful concepts that have been widely used in applications. These schemes are direct extensions of their 1D counterparts, in particular, by coupling of the two dimensions and restricting to only one possible further partition of each block into four subblocks. In this paper, we consider more flexible schemes that exploit more variations of multidimensional data structure. In the meantime, we restrict to treebased decompositions that are amenable to fast algorithms and have low indexing cost. Examples of these decomposition schemes are anisotropic wavelet packets, dyadic rectangular tilings, separate dimension decompositions, and general rectangular tilings. We compute the numbers of possible decompositions for each of these schemes. We also give bounds for some of these numbers. These results show that the new rectangular tiling schemes lead to much larger sets of 2D space and frequency decompositions than the commonlyused quadtreebased schemes, therefore bearing the potential to obtain better representation for a given image. Index Terms — Number of bases, wavelet packets, quadtree decompositions, rectangular tilings, multiscale representations, anisotropic bases, best basis. I.