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A new segmentation strategy based on a fusion procedure is presented for achieving a reliable and accurate segmentation result by combining several segmentation maps. Findings reveal that the proposed segmentation strategy is simple, fast and easily parallelizable.

This paper introduces a simple algorithm for tomographic reconstruction based on the use of a complexity regularization term. The regularization is formulated in the discrete cosine transform (DCT) domain by promoting a low-noise reconstruction having a high sparsity in the frequency domain. The resulting algorithm simply alternates between a maximum-likelihood (ML) expectation-maximization (EM) update and a decreasing sparsity constraint in the DCT domain. Applications to SPECT reconstruction and comparisons with a classical estimator using the best available regularization terms are given in order to illustrate the potential of our reconstruction technique. Index Terms--Discrete cosine transform (DCT), expectation-maximization (EM), reconstruction, SPECT tomography.

Most statistical background subtraction techniques are based on the analysis of temporal color/intensity distribution. However, learning statistics on a series of time frames can be problematic, especially when no frame absent of moving objects is available or when the available memory is not sufficient to store the series of frames needed for learning. In this letter, we propose a spatial variation to the traditional temporal framework. The proposed framework allows statistical motion detection with methods trained on one background frame instead of a series of frames as is usually the case. Our framework includes two spatial background subtraction approaches suitable for different applications. The first approach is meant for scenes having a nonstatic background due to noise, camera jitter or animation in the scene (e.g.,waving trees, fluttering leaves). This approach models each pixel with two PDFs: one unimodal PDF and one multimodal PDF, both trained on one background frame. In this way, the method can handle backgrounds with static and nonstatic areas. The second spatial approach is designed to use as little processing time and memory as possible. Based on the assumption that neighboring pixels often share similar temporal distribution, this second approach models the background with one global mixture of M Gaussians. Index Terms--Background detection, motion detection.

The article describes a fusion framework that blends together the region map and an application label field. The main merit of the framework is that it uses a simple and fast deterministic optimizer for admitting a natural implementation on a parallel architecture.

In this paper, we present a new model for deformations of shapes. A pseudolikelihood is based on the statistical distribution of the gradient vector field of the gray level. The prior distribution is based on the Probabilistic Principal Component Analysis (PPCA). We also propose a new model based on mixtures of PPCA that is useful in the case of greater variability in the shape. A criterion of global or local object specificity based on a preliminary color segmentation of the image is included into the model. The localization of a shape in an image is then viewed as minimizing the corresponding Gibbs field. We use the Exploration/Selection (E/S) stochastic algorithm in order to find the optimal deformation. This yields a new unsupervised statistical method for localization of shapes. In order to estimate the statistical parameters for the gradient vector field of the gray level, we use an Iterative Conditional Estimation (ICE) procedure. The color segmentation of the image can be computed with an Exploration/Selection/Estimation (ESE) procedure. Index Terms--Shape localization, statistical model, stochastic optimization, Exploration/Selection (E/S) algorithm, Probabilistic Principal Component Analysis (PPCA).

A spatial denoising method is proposed that is based on an averaging process performed on a set of Markhov Chain Monte-Carlo simulations of region partition maps constrained to be spatially piecewise uniform for each estimated constant-value regions. The results have shown that the method performs competitively and better than the best existing wavelet-based denoising methods in benchmark tests.

A Hidden Markov Random Field (HMRF) data-fusion model based on Julesz ensembles is presented and applied to the segmentation of natural images. The corresponding Exploration/Selection/Estimation (ESE) procedure for the estimation of the parameters is presented.

An original inhomogenous restoration (deconvolution) model is proposed under the Bayesian framework for observed images degraded by space-invariant blur and additive Gaussian noise. In this model, regularization is achieved during the iterative restoration process with a segmentation-based a priori term, while the experiments demonstrate that the discussed method performs competitively and sometimes better than the existing advanced methods in benchmark tests.

This paper presents a new and accurate three-dimensional (3-D) reconstruction technique for the scoliotic spine from a pair of planar and conventional (postero-anterior with normal incidence and lateral) calibrated radiographic images. The proposed model uses a priori hierarchical global knowledge, both on the geometric structure of the whole spine and of each vertebra. More precisely, it relies on the specification of two 3-D statistical templates. The first, a rough geometric template on which rigid admissible deformations are defined, is used to ensure a crude registration of the whole spine. An accurate 3-D reconstruction is then performed for each vertebra by a second template on which nonlinear admissible global, as well as local deformations, are defined. Global deformations are modeled using a statistical modal analysis of the pathological deformations observed on a representative scoliotic vertebra population. Local deformations are represented by a first-order Markov process. This unsupervised coarse-to-fine 3-D reconstruction procedure leads to two separate minimization procedures efficiently solved in our application with evolutionary stochastic optimization algorithms. In this context, we compare the results obtained with a classical genetic algorithm (GA) and a recent Exploration Selection (ES) technique. This latter optimization method with the proposed 3-D reconstruction model, is tested on several pairs of biplanar radiographic images with scoliotic deformities. The experiments reported in this paper demonstrate that the discussed method is comparable in terms of accuracy with the classical computed-tomography-scan technique while being unsupervised and while requiring only two radiographic images and a lower amount of radiation for the patient. Index Terms--Biplanar radiographies, energy function minimization, hierarchical statistical modeling, medical imaging, scoliosis, shape model, stochastic optimization, 3-D reconstruction model, 3-D/2-D registration.

In this paper, we present an original method for the three-dimensional (3-D) reconstruction of the scoliotic rib cage from a planar and a conventional pair of calibrated radiographic images (postero-anterior with normal incidence and lateral). To this end, we first present a robust method for estimating the model parameters in a mixture of probabilistic principal component analyzers (PPCA). This method is based on the stochastic expectation maximization (SEM) algorithm. Parameters of this mixture model are used to constrain the 3-D biplanar reconstruction problem of scoliotic rib cage. More precisely, the proposed PPCA mixture model is exploited for dimensionality reduction and to obtain a set of probabilistic prior models associated with each detected class of pathological deformations observed on a representative training scoliotic rib cage population. By using an appropriate likelihood, for each considered class-conditional prior model, the proposed 3-D reconstruction is stated as an energy function minimization problem, which is solved with an exploration/selection algorithm. The optimal 3-D reconstruction then corresponds to the class of deformation and parameters leading to the minimal energy. This 3-D method of reconstruction has been successfully tested and validated on a database of 20 pairs of biplanar radiographic images of scoliotic patients, yielding very promising results. As an alternative to computed tomography-scan 3-D reconstruction this scheme has the advantage of low radiation for the patient, and may also be used for diagnosis and evaluation of deformity of a scoliotic rib cage. The proposed method remains sufficiently general to be applied to other reconstruction problems for which a database of objects to be reconstructed is available (with two or more radiographic views). Index Terms--Biplanar radiographies, medical imaging, mixtures of probabilistic principal component analyzers, reduction of dimensionality, scoliosis, shape model, stochastic optimization, 3-D reconstruction model, 3-D/2-D registration.

A new stochastic algorithm is proposed for computing useful Bayesian estimators of hidden Markov random field (HMRF) models that is called exploration/selection/estimation (ESE) procedure. This framework replaces the mechanism of the split-and-merge of regions that could be used in the context of image segmentation.

In this paper, we describe a statistical model for the gradient vector field of the gray level in images validated by different experiments. Moreover, we present a global constrained Markov model for contours in images that uses this statistical model for the likelihood. Our model is amenable to an Iterative Conditional Estimation (ICE) procedure for the estimation of the parameters; our model also allows segmentation by means of the Simulated Annealing (SA) algorithm, the Iterated Conditional Modes (ICM) algorithm, or the Modes of Posterior Marginals (MPM) Monte Carlo (MC) algorithm. This yields an original unsupervised statistical method for edge-detection, with three variants. The estimation and the segmentation procedures have been tested on a total of 160 images. Those tests indicate that the model and its estimation are valid for applications that require an energy term based on the log-likelihood ratio. Besides edge-detection, our model can be used for semiautomatic extraction of contours, localization of shapes, non-photo-realistic rendering; more generally, it might be useful in various problems that require a statistical likelihood for contours. Index Terms--Contours in images, edge-detection, parameter estimation, unsupervised statistical segmentation, Markov Random Field model.

This paper investigates the use of a nonparametric regularization energy term for devising a example-based rendering and segmentation technique. We have stated this problem in the multiresolution energy minimization framework and exploited the multiscale structure proposed by Wei and Levoy for the texture synthesis problem. In this nonparametric energy minimization framework, we also propose a computationally efficient coarse-to-fine recursive optimization method to minimize the cost function related to this hierarchical model. In this context, the formulation of our example-based regularization term also allows to directly infer an intuitive dissimilarity measure between two contour shapes. This measure is herein exploited to define an efficient shape descriptor for the contour-based shape recognition and indexing problem. Index Terms--Nonparametric multiscale energy-based (or multiresolution example-based) model, inpainting, Non-Photorealistic Rendering (NPR), segmentation, contour-based shape recognition, shape indexing.