In recent years, multiscale Bayesian approaches have attracted increasing attention for use in image segmentation. Generally, these methods tend to offer improved segmentation accuracy with reduced computational burden. Existing Bayesian segmentation methods use simple models of context designed to encourage large uniformly classified regions. Consequently, these context models have a limited ability to capture the complex contextual dependencies that are important in applications such as document segmentation. In this paper, we propose a multiscale...

We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach provides a practical method for learning high-order Markov random field (MRF) models with potential functions that extend over large pixel neighborhoods. These clique potentials are modeled using the Product-of-Experts framework that uses nonlinear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field-of-Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with specialized techniques.

We consider the problems of image segmentation and classification, and image restoration when the true image is made up of a small number of (unordered) colors. Our emphasis is on both performance and speed; speed has become increasingly important for analyzing large images and multispectral images with many bands, processing large image databases, real-time or near real-time image analysis, and the online analysis of video. Bayesian image analysis (Geman and Geman...

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Abstract—We propose a new stochastic algorithm for computing useful Bayesian estimators of hidden Markov random field (HMRF) models that we call exploration/selection/estimation (ESE) procedure. The algorithm is based on an optimization algorithm of O. François, called the exploration/selection (E/S) algorithm. The novelty consists of using the a posteriori distribution of the HMRF, as exploration distribution in the E/S algorithm. The ESE procedure computes the estimation of the likelihood parameters and the optimal number of region classes, according to global constraints, as well as the segmentation of the image. In our formulation, the total number of region classes is fixed, but classes are allowed or disallowed dynamically. This framework replaces the mechanism of the split-and-merge of regions that can be used in the context of image segmentation. The procedure is applied to the estimation of a HMRF color model for images, whose likelihood is based on multivariate distributions, with each component following a Beta distribution. Meanwhile, a method for computing the maximum likelihood estimators of Beta distributions is presented. Experimental results performed on 100 natural images are reported. We also include a proof of convergence of the E/S algorithm in the case of nonsymmetric exploration graphs. Index Terms—Bayesian estimation of hidden Markov random field (HMRF) models, color model, exploration/selection (E/S) algorithm, image segmentation, maximum likelihood (ML) estimation of Beta distributions. I.

To segregate overlapping objects into depth layersrequ(Xfi the integration of local occluzYA cuu distribu(Y over the entire image into a global percept. We propose to model this process ussA hierarchical Markov random field (HMRF), andsuA))w a broader view that cliqu potentials in MRF models can beu)( to encode any local decision ruisi Atopology-dependent muHL(H)A. hierarchy isuA) to intro duA long range interaction. The operations within each level are identical across the hierarchy. Thecliqu parameters that encode the relative importance of these decisionruis are estimatedutim an optimization techniqu called learning from rehearsals based on 2-object training samples. We find that this model generalizes sueralizesA to 5-object test images, and that depth segregation can be completed within two traversals across the hierarchy. ThiscompufiHXA.HL framework therefore provides an interesting platform foru to investigate the interaction of local decision ruis and global representations, as well as to reason ab the rationales utionales some of recent psychological andneu)wfi ysiological findings related tofiguHfizA.Hzw segregation. 1

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose here to use an inhomogeneous model. We use the Maximum Likelihood Estimator (MLE) to estimate its parameters and we demonstrate that the MLE computed on the corrupted image is not suitable for image deconvolution, because it is not robust to noise. Then we show that the estimation is correct only if it is made from the original image. As this image is unknown, we need to compute an approximation of su#ciently good quality to provide useful estimation results.

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Homogeneous regularization models do not provide sufficiently satisfactory results, since real satellite data show spatially variant characteristics. We propose

Abstract. Previous work [5] has shown how Ising spatial priors [1] can be incorported into fMRI analysis in a principled manner by using Mutual Information as a statistic for protocol-related activity. The activation image with maximum a posteriori (MAP) probability can then be computed exactly in polynomial time by reduction to a Min-Cut/Max-Flow Problem [4]. In this work, we show that an Ising prior can be applied in the same manner using a standard, linear activation model. 1

With the development of remote sensing techniques, a vast amount of SAR sea