. A variety of computer vision problems can be optimally posed as Bayesian labeling in which the solution of a problem is defined as the maximum a posteriori (MAP) probability estimate of the true labeling. The posterior probability is usually derived from a prior model and a likelihood model. The latter relates to how data is observed and is problem domain dependent. The former depends on how various prior constraints are expressed. Markov Random Field Models (MRF) theory is a tool to encode contextual constraints into the prior probability. This paper presents a unified approach for MRF modeling in low and high level computer vision. The unification is made possible due to a recent advance in MRF modeling for high level object recognition. Such unification provides a systematic approach for vision modeling based on sound mathematical principles. 1 Introduction Since its beginning in early 1960's, computer vision research has been evolving from heuristic design of algorithms to syste...

Graphical techniques for modeling the dependencies of random variables have been explored in a variety of di erent areas including statistics, statistical physics, arti-cial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been developed relatively independently in these research communities. In this paper we explore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independence networks (PINs). The paper contains a self-contained review of the basic principles of PINs. It is shown that the well-known forward-backward (F-B) and Viterbi algorithms for HMMs are special cases of more general inference algorithms for arbitrary PINs. Furthermore, the existence of inference and estimation algorithms for more general graphical models provides a set of analysis tools for HMM practitioners who wish to explore a richer class of HMM structures. Examples of relatively complex models to handle sensor fusion and coarticulation in speech recognition are introduced and treated within the graphical model framework to illustrate the advantages of the general approach. 1

The general problem of unsupervised textured image segmentation remains a fundamental but not entirely solved issue in image analysis. Many studies have proven that statistical model-based texture segmentation algorithms yield good results provided that the model parameters and the number of regions be known a priori. In this paper, we present an unsupervised texture segmentation method which does not require a priori knowledge about the different texture regions, their parameters, or the number of available texture classes. The proposed algorithm relies on the analysis of local and global second and higher order spatial statistics of the original images. The segmentation map is modeled using an augmented-state Markov Random Field, including an outlier class which enables dynamic creation of new regions during the optimization process. A bayesian estimate of this map is computed using a deterministic relaxation algorithm. The whole segmentation procedure is controlled by one single p...

The emerging video coding standard MPEG-4 enables various content-based functionalities for multimedia applications. To support such functionalities, as well as to improve coding e#ciency, MPEG-4 relies on a decomposition of each frame of an image sequence into video object planes (VOP's). Each VOP corresponds to a single moving object in the scene. In this thesis, a new method for automatic segmentation of moving objects in image sequences is presented. We formulate the problem as graph labeling over a region adjacency graph (RAG), based on motion information. The label field is modeled as a Markov random field (MRF).

The association of statistical models and multiresolution data analysis in a consistent and tractable mathematical framework remains an intricate theoretical and practical issue. Several consistent approaches have been proposed recently to combine Markov Random Field (MRF) models and multiresolution algorithms in image analysis: renormalization group, subsampling of stochastic processes, MRF's defined on trees or pyramids, etc. For the simulation or a practical use of these models in statistical estimation, an important issue is the preservation of the local Markovian property of the representation at the different resolution levels. It is shown in this paper that this key problem may be studied by considering the restriction of a Markov random field (defined on some simple finite nondirected graph) to a part of its original site set. Several general properties of the restricted field are derived. The general form of the distribution of the restriction is given. "Locality" of the field...

We present a novel probabilistic model for the hierarchical structure of an image and its regions. We call this model spatial random tree grammars (SRTGs). We develop algorithms for the exact computation of likelihood and maximum a posteriori (MAP) estimates and the exact expectation-maximization (EM) updates for model-parameter estimation. We collectively call these algorithms the center-surround algorithm. We use the center-surround algorithm to automatically estimate the maximum likelihood (ML) parameters of SRTGs and classify images based on their likelihood and based on the MAP estimate of the associated hierarchical structure. We apply our method to the task of classifying natural images and demonstrate that the addition of hierarchical structure significantly improves upon the performance of a baseline model that lacks such structure.

The problem of image interpretation is one of inference with the help of domain knowledge. In this correspondence, we formulate the problem as the maximum a posteriori (MAP) estimate of a properly defined probability distribution function. We show that a Bayesian network can be used to represent this p.d.f. as well as the domain knowledge needed for interpretation. The Bayesian network may be relaxed to obtain the set of optimum interpretations.

This paper presents a Markov random field (MRF) model for object recognition in high level vision. The labeling state of a scene in terms of a model object is considered as an MRF or couples MRFs. Within the Bayesian framework, the optimal solution is defined as the maximum a posteriori (MAP) estimate of the MRF. The posterior distribution is derived based on sound mathematical principles from theories of MRF and probability, which is in contrast to heuristic formulations. An experimental result is presented. 1 Introduction In object recognition, an object is usually represented by a set of primitives or features. These features are attributed by their properties and are constrained to one another by contextual inter-relations. Two issues must be addressed for successful recognition: how to use contextual constraints effectively and how to deal with uncertainties. Markov random field (MRF) theory provides a way of encoding contextual constraints. Since 1980's, there has been considera...

In this paper we present a new energy function for MRF which is inspired by models of physics of disordered systems. This energy function presents two main advantages: it can be very easily applied to problems modeled by irregular sites because it considers the neighborhood system as fully connected; it does not require an algorithm for searching the absolute minima because those and their analytical properties are given by theory. We performed experiments on appearance-based object recognition, using the COIL 100 database; we achieve a recognition rate of 98.78%. 1 Introduction This contribution describes a new model that allows the use of Spin-Glass Theory (SGT, [14]) results in a Maximum A Posteriori-Markov Random Field (MAP-MRF, [12]) framework for 3D object recognition. Many vision problems can be posed as labeling problems; labeling is also a natural representation for the study of MRFs [12]. Two major tasks when modeling MRFs are how to define the neighborhood system for irreg...

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