Most of previous semi-supervised methods that seek to obtain disentangled representations using variational autoencoders divide the latent representation into two components: the non-interpretable part and the disentangled part that explicitly models the factors of interest. With such models, features associated with high-level factors are not explicitly modeled, and they can either be lost, or at best entangled in the other latent variables, thus leading to bad disentanglement properties. To address this problem, we propose a novel conditional dependency structure where both the labels and their features belong to the latent space. We show using the CelebA dataset that the proposed model can learn meaningful representations, and we provide quantitative and qualitative comparisons with other approaches that show the effectiveness of the proposed method.

Whether in medical imaging, astronomy or remote sensing, the data are increasingly complex. In addition to the spatial dimension, the data may contain temporal or spectral information that characterises the different sources present in the image. The compromise between spatial resolution and temporal/spectral resolution is often at the expense of spatial resolution, resulting in a potentially large mixing of sources in the same pixel/voxel. Source separation methods must incorporate spatial information to estimate the contribution and signature of each source in the image. We consider the particular case where the position of the sources is approximately known thanks to external information that may come from another imaging modality or from a priori knowledge. We propose a spatially constrained dictionary learning source separation algorithm that uses e.g. high resolution segmentation map or regions of interest defined by an expert to regularise the source contribution estimation. The originality of the proposed model is the replacement of the sparsity constraint classically expressed in the form of an $\ell _{1}$ penalty on the localisation of sources by an indicator function exploiting the external source localisation information. The model is easily adaptable to different applications by adding or modifying the constraints on the sources properties in the optimisation problem. The performance of this algorithm has been validated on synthetic and quasi-real data, before being applied to real data previously analysed by other methods of the literature in order to compare the results. To illustrate the potential of the approach, different applications have been considered, from scintigraphic data to astronomy or fMRI data.

This paper compares several linear and non-linear multivariate models for the detection of abnormal patterns in neuroimaging data, when comparing a single subject to a normal control group. The proposed methods learn the manifold spanned by the normal controls using non-linear dimension reduction techniques. The image of a subject is projected on the control group manifold either via a standard projection or through an embedding/reconstruction scheme. A comparison of the reconstruction with the subject's original neuroimaging data allows for the detection of abnormal patterns by way of statistical tests on the residuals. The different abnormality detection methods are assessed on synthetic data and real (MRI) neuroimaging data. The importance of non-linear modeling of the manifold in the reduced-dimension subspace is highlighted, as well as robustness to large abnormalities.

Regularized pixel-based tomographic reconstruction techniques suffer from streaking artifacts when only few projection angles are available. Shape-based methods, that reconstruct objects by optimizing their boundaries typically enforce a length penalty on the evolving curve, which is not suited to all possible shapes or topologies. To overcome this limitation, we propose in this paper to introduce high-level shape priors in tomographic reconstruction using active contours. Our shape descriptor is moment-based-hence rather compact and hierarchical - and may be made invariant to geometric transformations up to affine ones. It can handle multiple references simultaneously to accommodate shape variations. Experimental results on synthetic data show the effectiveness of the prior, especially for small numbers of noisy projections.

This correspondence addresses the inversion of 3-D transformation fields, which is a problem that typically arises in image warping problems. A topology preserving parametric B-spline-based representation of the deformation field is considered. Topology preservation ensures that the transformation is a one-to-one mapping and consequently that it is invertible. Inverting such transformation fields amounts to solving a system of nonlinear equations. To tackle this problem, we rely on interval analysis techniques. The proposed algorithm yields a solution whose accuracy is user-controlled. This method may be extended to any dense transformation field and also to deformations defined on a grid of points, by considering a projection in the space of topology preserving B-spline-based deformation fields. The performance of the algorithm is illustrated on transformation fields coming from intersubject brain registration.

This communication deals with data reduction and regression. A set of high dimensional data (e.g., images) usually has only a few degrees of freedom with corresponding variables that are used to parameterize the original data set. Data understanding, visualization and classification are the usual goals. The proposed method reduces data considering a unique set of low-dimensional variables and a user-defined cost function in the multidimensional scaling framework. Mapping of the reduced variables to the original data is also addressed, which is another contribution of this work. Typical data reduction methods, such as Isomap or LLE, do not deal with this important aspect of manifold learning. We also tackle the inversion of the mapping, which makes it possible to project high-dimensional noisy points onto the manifold, like PCA with linear models. We present an application of our approach to several standard data sets such as the SwissRoll.

We present an original appearance model that generalizes the usual Gaussian visual subspace model to non-Gaussian and nonparametric distributions. It can be useful for the modeling and recognition of images under difficult conditions such as large occlusions and cluttered backgrounds. Inference under the model is efficiently solved using the mean shift algorithm.

This paper presents a novel statistical approach for the modeling and analysis of structured random processes observed through multiple event sequences: the hidden Markov multiple event sequence model (HMMESM). This model accounts for several features of these processes: (i) the hidden-observable aspect of the event sequences to be analyzed, (ii) the multiplicity of the observed event sequences, (iii) the non stationary, time-localized character of their events, (iv) the redundancy, complementarity, and strong asynchrony that exist between events across sequences. A first application of this model in functional MRI (fMRI) brain mapping is presented. The developed method shows high robustness to noise and variability of the active fMRI signals

We present a new way of constraining the evolution of a region-based active contour with respect to a reference shape. Minimizing a shape prior, defined as a distance between shape descriptors based on the Legendre moments of the characteristic function, leads to a geometric flow that can be used with benefits in a two-class segmentation application. The shape model includes intrinsic invariance with regard to pose and affine deformations.

This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of, which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts to solving a constrained optimization problem: The residual energy between the target image and the deformed source image is minimized under constraints on the Jacobian. Unlike the 2-D case, in which simple linear constraints are derived, the 3-D B-spline-based deformable mapping yields a difficult (until now, unsolved) optimization problem. In this paper, we tackle the problem by resorting to interval analysis optimization techniques. Care is taken to keep the computational burden as low as possible. Results on multipatient 3-D MRI registration illustrate the ability of the method to preserve topology on the continuous image domain.

In this paper, a novel functional magnetic resonance imaging (fMRI) brain mapping method is presented within the statistical modeling framework of hidden semi-Markov event sequence models (HSMESMs). Neural activation detection is formulated at the voxel level in terms of time coupling between the sequence of hemodynamic response onsets (HROs) observed in the fMRI signal, and an HSMESM of the hidden sequence of task-induced neural activations. The sequence of HRO events is derived from a continuous wavelet transform (CWT) of the fMRI signal. The brain activation HSMESM is built from the timing information of the input stimulation protocol. The rich mathematical framework of HSMESMs makes these models an effective and versatile approach for fMRI data analysis. Solving for the HSMESM Evaluation and Learning problems enables the model to automatically detect neural activation embedded in a given set of fMRI signals, without requiring any template basis function or prior shape assumption for the fMRI response. Solving for the HSMESM Decoding problem allows to enrich brain mapping with activation lag mapping, activation mode visualizing, and hemodynamic response function analysis. Activation detection results obtained on synthetic and real epoch-related fMRI data demonstrate the superiority of the HSMESM mapping method with respect to a real application case of the statistical parametric mapping (SPM) approach. In addition, the HSMESM mapping method appears clearly insensitive to timing variations of the hemodynamic response, and exhibits low sensitivity to fluctuations of its shape.

We present a 3D brain MRI segmentation method in which a high resolution label image evolves under the influence of multiple constraints. The constraints are expressed in a versatile energy minimization framework which allows for evolutions only at label boundaries, effectively making it a surface evolution system. Constraints are defined using atlas-mapped parameters. The atlas, composed of a reference image and parameter values, is mapped onto the source image using a multiresolution deformable image matching method. Variable scale image constraints are considered. The prior model currently includes: a relative distribution constraint, which gives the probability of observing a label at a given distance from another label, a thickness constraint and a surface regularization constraint. Issues related to partial volumes are addressed by the use of a high resolution label image and an accurate model of the acquisition process. High resolution segmentations are thus obtained from standard (eventually low resolution) MRIs.

In this paper, we present a novel approach for incorporating geometric shape priors in region-based active contours in order to provide more robustness to clutter, noise and occlusions. We define shape descriptors based on Legendre moments and embed them in a recent Eulerian formulation of region-based active contours, which enables a rigorous mathematical treatment. An evolution equation that minimizes a function of the distance between the active contour and a reference shape is derived. Experimental results show the ability of the geometric shape prior to constrain an evolving curve to resemble a target shape. We finally introduce the new shape prior into a two-class segmentation functional and show its benefits on segmentation results, in presence of occlusions and clutter.

We present a new robust algorithm for reconstructing images into a linear subspace using MAP estimation. The algorithm takes into account the a priori distribution of the subspace variables and the noise is robustly modeled to allow for occlusions. The subspace distribution is estimated using nonparametric density estimation techniques. An efficient optimization scheme based on the mean shift procedure D Comaniciu et al. (2002) and on half-quadratic theory [ D Geman et al. (1992), P Charbonnier et al. (1997)] is developed, making optimization of the MAP function feasible for high-dimensional images. Preliminary results on real images demonstrate the contribution of a priori distribution modeling of sub-space variables, with respect to standard reconstruction methods over linear subspaces.

Due to the piecewise stationarity assumption required for the observable process of a hidden Markov chain, the application of hidden Markov models (HMMs) to the analysis of event-based random processes remains intricate. For such processes, a new class of HMMs is proposed: the hidden semi-Markov event sequence model (HSMESM). In a HSMESM, the observable process is no more considered as segmental in nature but issued from a detection-characterization preprocessing step. The standard markovian formalism is adapted accordingly. Results obtained in functional MRI sequence analysis validate this novel statistical modeling approach while opening new perspectives in detection-recognition of event-based random processes.

Change detection in image sequences has mainly focused on the recovery of moving objects when the viewing system is static, or on the detection of simple production effects such as video shot boundaries or scene transitions. Camera motion is usually handled by the compensation of dominant motion, using motion estimation and segmentation schemes. We propose a novel statistical change detection method able to handle more complex events such as entering or exiting objects, or changes in object appearance, when the camera is moving. Temporal changes of objects are captured by analyzing the statistics of successive images. Considering an appropriate choice of image features, we show how it is possible to extract the statistics of changing objects from a pair of successive image histograms. Changing objects are then located by statistical backprojection techniques. The method is completely unsupervised and does not require any motion estimation or motion compensation. It is illustrated here on real world road scenes exhibiting large camera motion.

In this paper, we address the issue of topology preservation in deformable image matching. A novel constrained hierarchical parametric approach is presented, that ensures that the mapping is globally one-to one and thus preserves topology in the deformed image. The transformation between the source and target images is parameterized at different scales, using a decomposition of the deformation vector field over a sequence of nested (multiresolution) subspaces. The Jacobian of the mapping is controlled over the continuous domain of the transformation, ensuring actual topology preservation on the whole image support. The resulting fast nonlinear constrained optimization algorithm enables to track large nonlinear deformations while preserving the topology. Experimental results are presented both on simulated data and on real medical images.

A probabilistic deformable model for the representation of multiple brain structures is described. The statistically learned deformable model represents the relative location of different anatomical surfaces in brain magnetic resonance images (MRIs) and accommodates their significant variability across different individuals. The surfaces of each anatomical structure are parameterized by the amplitudes of the vibration modes of a deformable spherical mesh. For a given MRI in the training set, a vector containing the largest vibration modes describing the different deformable surfaces is created. This random vector is statistically constrained by retaining the most significant variation modes of its Karhunen-Loève expansion on the training population. By these means, the conjunction of surfaces are deformed according to the anatomical variability observed in the training set. Two applications of the joint probabilistic deformable model are presented: isolation of the brain from MRI using the probabilistic constraints embedded in the model and deformable model-based registration of three-dimensional multimodal (magnetic resonance/single photon emission computed tomography) brain images without removing nonbrain structures. The multi-object deformable model may be considered as a first step toward the development of a general purpose probabilistic anatomical atlas of the brain.

In this paper a robust pattern recognition system, using an appearance-based representation of colour images is described. Standard appearance-based approaches are not robust to outliers, occlusions or segmentation errors. The approach proposed here relies on robust M-estimators, involving non-quadratic and possibly non-convex energy functions. To deal with the minimisation of non-convex functions in a deterministic framework, we introduce an estimation scheme relying on M-estimators used in continuation, from convex functions to hard redescending nonconvex estimators. At each step of the robust estimation scheme, the non-quadratic criterion is minimized using the half-quadratic theory. This leads to a weighted least squares algorithm, which is easy to implement. The proposed robust estimation scheme does not require any user interaction because all necessary parameters are previously estimated. The method is illustrated on a road sign recognition application. Experiments show significant improvements with respect to standard estimation schemes.

This paper addresses the problem of describing the significant intra- and inter-variability of 3D deformable structures within 3D image data sets. In pursuing it, a 3D probabilistic physically based deformable model is defined. The statistically learned deformable model captures the spatial relationships between the different objects surfaces, together with their shape variations. The structures of interest in each volume are parameterized by the amplitudes of the vibration modes of a deformable spherical mesh. For a given 3D image in the training set, a vector containing the largest vibration modes describing the desired object is created. This random vector is statistically constrained by retaining the most significant variation modes of its Karhunen-Loeve (KL) expansion on the considered population. The surfaces of the modeled structures thus deform according to the variability observed in the training set. A preliminary application of a 3D multi-object model for the segmentation of 3D brain structures from MR images is presented.

We present a topology preserving image matching method, based on a hierarchical parametric model of the deformation map. The transformation is parameterized at different scales, using a decomposition of the deformation vector field over a sequence of nested subspaces, generated from a single compactly supported scaling function. To preserve topology, the positivity of the Jacobian of the continuous deformation is enforced. We establish that, for the proposed hierarchical parametric model, the Jacobian J may be easily constrained over the whole deformation field, by only constraining its values at a limited number of control points, yielding a fast topology preserving matching algorithm. Experimental results are presented both on simulated and real-world medical MR images.

In this paper, we present a novel morphological approach to image simplification by flat zones which, applied to a temporal image sequence, leads to a method for spatio-temporal segmentation. Our approach considers a sequence as a single 3D image, rather than as a succession of 2D images. An extension of recent tools of 2D mathematical morphology, to the spatio-temporal (2D+t) volume, allows a fast detection of moving objects, a tracking of moving regions across time as well as a classification of motion.

Noncasual Markov (or energy-based) models are widely used in early vision applications for the representation of images in high-dimensional inverse problems. Due to their noncausal nature, these models generally lead to iterative inference algorithms that are computationally demanding. In this paper, we consider a special class of nonlinear Markov models which allow one to circumvent this drawback. These models are defined as discrete Markov random fields (MRF) attached to the nodes of a quadtree. The quadtree induces causality properties which enable the design of exact, noniterative inference algorithms, similar to those used in the context of Markov chain models. We first introduce an extension of the Viterbi algorithm which enables exact maximum a posteriori (MAP) estimation on the quadtree. Two other algorithms, related to the MPM criterion and to Bouman and Shapiro's (1994) sequential-MAP (SMAP) estimator are derived on the same hierarchical structure. The estimation of the model hyper parameters is also addressed. Two expectation-maximization (EM)-type algorithms, allowing unsupervised inference with these models are defined. The practical relevance of the different models and inference algorithms is investigated in the context of image classification problem, on both synthetic and natural images.

A generic approach for the extraction and recognition of gesture using raw grey-level images is presented. The probabilistic visual learning approach, a learning method recently proposed by B. Moghaddam and A. Pentland (1997), is used to create a set of compact statistical representations of gesture appearance on low dimensional eigenspaces. The same probabilistic modeling framework is used to extract and track gesture and to perform gesture recognition over long image sequences. Gesture extraction and tracking are based on maximum likelihood gesture detection in the input image. Recognition is performed by using the set of learned probabilistic appearance models as estimates of the emission probabilities of a continuous density hidden Markov model (CDHMM). Although the segmentation and CDHMM-based recognition use raw grey-level images, the method is fast, thanks to the data compression obtained by probabilistic visual learning. The approach is comprehensive and may be applied to other visual motion recognition tasks. It does not require application-tailored extraction of image features, the use of markers or gloves. A real-time implementation of the method on a standard PC-based vision system is under consideration.

This paper presents a hierarchical framework to perform deformable matching of three dimensional (3D) images. 3D shape deformations are parameterized at different scales, using a decomposition of the continuous deformation vector field over a sequence of nested subspaces, generated from a single scaling function. The parameterization of the field enables to enforce smoothness and differentiability constraints without performing explicit regularization. A global energy function, depending on the reference image and the transformed one, is minimized via a coarse-to-fine algorithm over this multiscale decomposition. Contrary to standard multigrid approaches, no reduction of image data is applied. The continuous field of deformation is always sampled at the same resolution, ensuring that the same energy function is handled at each scale and that the energy decreases at each step of the minimization.

We present a statistical method for the motion-based segmentation of deformable structures undergoing nonrigid movements. The proposed approach relies on two models describing the shape of interest, its variability, and its movement. The first model corresponds to a statistical deformable template that constrains the shape and its deformations. The second model is introduced to represent the optical flow field inside the deformable template. These two models are combined within a single probability distribution, which enables to derive shape and motion estimates using a maximum likelihood approach. The method requires no manual initialization and is demonstrated on synthetic data and on a medical X-ray image sequence.

The registration of multimodal images remains an intricate issue, especially when the multimodal image pair shows non overlapping structures, missing data, noise or outliers. In this paper, we present a deformable model-based technique for the rigid registration of 2D and 3D multimodal images. The deformable model embeds a priori knowledge of the spatial correspondence and statistical variability of the different (eventually non overlapping) image features which are used in the registration procedure. The method is applied to the intrasubject registration of medical MR/SPECT images of the brain by constructing a deformable model incorporating information on both MR (head) and SPECT (brain) contours. In an off-line training procedure, the spatial relations between head and brain as well as the anatomical variations of these two structures are learned. The registration is performed by minimizing an objective function involving the contours of the MR and SPECT images.

We present a statistical method for the motion-based segmentation of deformable structures undergoing non-rigid movements. The proposed approach relies on two models describing the shape of interest, its variability and its movement. The first model corresponds to a statistical deformable template that constrains the shape and its deformations. The second model is introduced to represent the optical flow field inside the deformable template. These two models are combined within a single probability distribution which enables to derive optimal shape and motion estimates using a maximum likelihood approach. The method requires no manual initialization and is demonstrated on medical X-ray image sequences.

We describe a method for the temporal tracking of stochastic deformable models in image sequences. The object representation relies on a hierarchical statistical description of the deformations applied to a template. The optimal Bayesian estimate of deformations is obtained by maximizing nonlinear probability distributions using optimization techniques. The method may be sensitive to local maxima of the distributions and require an initial configuration close to the optimal solution. In our approach, the initialization is provided by a robust estimate of the rigid and statistically constrained nonrigid motions from the normal optical flow computed along the deformable contour. The approach is demonstrated on real-world sequences showing mouth movements and cardiac motions with missing data.

Using the causal Markov model defined on a quadtree we derive a multiresolution EM algorithm for unsupervised image classification. This algorithm is an efficient alternative to expensive or approximate EM algorithms associated with Markov random fields (MRFs). We show on synthetic and real images that our algorithm also provides good or even better results than those obtained by spatial MRF models.

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 previously to combine Markov random field (MRF) models and multiresolution algorithms in image analysis: renormalization group, subsampling of stochastic processes, MRFs 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 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 is studied by exhibiting a neighborhood structure with respect to which the restricted field is an MRF. Sufficient conditions for the new neighborhood structure to be "minimal" are derived. Several consequences of these general results related to various "multiresolution" MRF-based modeling approaches in image analysis are presented.

This paper presents a class of nonlinear hierarchical algorithms for the fusion of multiresolution image data in low-level vision. The approach combines nonlinear causal Markov models defined on hierarchical graph structures, with standard bayesian estimation theory. Two random processes defined on simple hierarchical graphs (quadtrees or "ternary graphs") are introduced to represent the multiresolution observations at hand and the hidden labels to be estimated. An optimal algorithm (inspired from the Viterbi algorithm) is developed to compute the bayesian estimates on the hierarchical graph structures. Estimates are obtained within two passes on the graph structure. This algorithm is non-iterative and yields a per pixel computational complexity which is independent of image size. This approach is compared to the multiscale algorithm proposed by (Bouman et al., 1994) for single-resolution image segmentation (that we have extended for multiresolution data fusion).>

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 correspondence, we present an unsupervised texture segmentation method that does not require 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 that enables dynamic creation of new regions during the optimization process. A Bayesian estimate of this map is computed using a deterministic relaxation algorithm. Results on real-world textured images are presented.

In this paper, we propose a new statistical framework for modeling and extracting 2D moving deformable objects from image sequences. The object representation relies on a hierarchical description of the deformations applied to a template. Global deformations are modeled using a Karhunen Loeve expansion of the distortions observed on a representative population. Local deformations are modeled by a (first-order) MarKov process. The optimal bayesian estimate of the global and local deformations is obtained by maximizing a non-linear joint probability distribution using stochastic and deterministic optimization techniques. The use of global optimization techniques yields robust and reliable segmentations in adverse situations such as low signal-to-noise ratio, non-gaussian noise or occlusions. Moreover, no human interaction is required to initialize the model. The approach is demonstrated on synthetic as well as on real-world image sequences showing moving hands with partial occlusions.>

We present a new algorithmic framework which enables making a full use of the large potential of data parallelism available on 2D processor arrays for the implementation of nonlinear multigrid relaxation methods. This framework leads to fast convergence towards quasi-optimal solutions. It is demonstrated on two different low-level vision applications.>

In this paper, comprehensive non-linear optimization algorithms for the minimization of global objective functions in image analysis tasks, are investigated. We explore several versions of the approach corresponding to different exploration strategies of the multiresolution structure. The efficiency of this general approach to global optimization in image processing is demonstrated on a highly non-linear MRF motion estimation model. We show, that, associated with a deterministic relaxation algorithm, very significant gains on the convergence speed and on the quality of the final solutions may be obtained.>

We describe a method for the temporal tracking of stochastic deformable models in long image sequences. The object representation relies on a hierarchical statistical description of the deformations applied to a template. A Bayesian estimate of the deformations is obtained by maximizing a highly non-linear joint probability distribution. Time consuming global (stochastic) optimization techniques are necessary to obtain optimal solutions unless a good initial guess is available. A good initialization is provided by a recursive temporal filtering of the parameters of the deformable template, combined with a detection of abrupt changes. This procedure yields robust segmentations and enables to track reliably complex deformable structures as is demonstrated here on real-world image sequences showing hand and mouth movements.>

The estimation of dense velocity fields from image sequences is basically an ill-posed problem, primarily because the data only partially constrain the solution. It is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches. In this paper, the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints. It is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances. The theoretical framework relies on Bayesian estimation associated with global statistical models, namely, Markov random fields. The constraints introduced here aim to address the following issues: optical flow estimation while preserving motion boundaries, processing of occlusion regions, fusion between gradient and feature-based motion constraint equations. Deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field. The algorithm is well suited to a multiresolution implementation which brings an appreciable speed-up as well as a significant improvement of estimation when large displacements are present in the scene. Experiments on synthetic and real world image sequences are reported.>

The authors investigate a new approach to multigrid image analysis based on Markov random field (MRF) models. The multigrid algorithms under consideration are based on constrained optimization schemes. The global optimization problem associated with MRF modeling is solved sequentially over particular subsets of the original configuration space. Those subsets consist of constrained configurations describing the desired resulting field at different scales. The constrained optimization can be implemented via a coarse-to-fine multigrid algorithm defined on a sequence of consistent multiscale MRF models. The proposed multiscale paradigm yields fast convergence toward high-quality estimates when compared to standard monoresolution or multigrid relaxation schemes.>

An approach to the problem of optic flow estimation and segmentation from image sequences is presented. It is shown that optic flow estimation and segmentation can be expressed, within a Bayesian decision framework, as a global estimation problem. The unknown process to be estimated corresponds to the 2D relative velocity field and to the motion boundaries. Several observations are used in the scheme, involving the spatiotemporal gradients of the image sequence and the output of an intensity edge detector. The unknown velocity field and motion discontinuities are modeled using a joint Markov random field, allowing the smoothing of the velocity field and the preservation of motion boundaries. Critical areas, such as occluding regions, are detected using a likelihood test and, in this case, a modified interaction model is applied. Results are presented on a real-world digital TV sequence involving complex 3D motions and occlusions.>

A multimodal approach to the problem of velocity estimation is presented. It combines the advantages of the feature-based and gradient-based methods by making them cooperate in a single global motion estimator. The theoretical framework is based on global Bayesian decision associated with Markov random field models. The proposed approach addresses, in parallel, the problem of velocity estimation and segmentation. Results on synthetic as well as on real-world image sequences are presented. Accurate motion measurement and detection of motion discontinuities with a surprisingly good quality have been obtained.>

The authors propose a novel approach to the problem of detecting events, i.e. significant differences between pictures of a given scene taken at different wavelengths or with different sensors. It is shown that event detection can be expressed, within a Bayesian decision framework, as a contextual estimation problem. The unknown process to be estimated corresponds to the significant interimage changes. A grey-level map assigned to the unknown event maximizes the a posteriori distribution of the event image, given the observed images. A Markov random field model is used to describe the spatial statistics of the unknown process. The authors present an application to the fine arts, that of finding an underpainting from a visible/X-ray pair of images of the same painting.>