Angiographic imaging is a crucial domain of medical imaging. In particular, Magnetic Resonance Angiography (MRA) is used for both clinical and research purposes. This article presents the first framework geared toward the design of virtual MRA images from real MRA images. It relies on a pipeline that involves image processing, vascular modeling, computational fluid dynamics and MR image simulation, with several purposes. It aims to provide to the whole scientific community (1) software tools for MRA analysis and blood flow simulation; and (2) data (computational meshes, virtual MRAs with associated ground truth), in an open-source/open-data paradigm. Beyond these purposes, it constitutes a versatile tool for progressing in the understanding of vascular networks, especially in the brain, and the associated imaging technologies. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper aims at classifying changed from unchanged pattern in multi-acquisition data using kernel based support vector data description (SVDD). Indeed, SVDD is a well known method allowing to map the data into a high dimensional features space where an hypersphere encloses most patterns belonging to the ”un-changed” class. In this work, we propose a new kernel function which combines the characteristics of basic kernel functions with new information about features distribution and then dependency between samples through copula theory that will be used for the first time to our knowledge in the SVDD framework. The effectiveness of the method is demonstrated on synthetic and real data sets.

In this paper, we present a robust method to estimate parameters of hidden Markov chains (HMC) in order to segment brain MR images. Indeed, parameter estimation can be very sensitive to the presence of outliers in the data. We propose to use the trimmed likelihood estimator (TLE) to extract such outliers and to accurately estimate the parameters of different tissue classes in a robust way. Moreover neighborhood information is included in the model by using hidden Markov chains. Experimental results on 2D synthetic data and on 3D brain MRI are included to validate this approach.

This paper proposes a new method to detect multiple sclerosis (MS) lesions on 3D multimodal brain MR images. MS lesions are detected as voxels that are not well explained by a statistical model for normal brain images. These outliers are extracted using the trimmed likelihood estimator (TLE). Spatial regularization is performed using a hidden Markov chain (HMC) model. Tests on real brain MR images with MS lesions have been carried out and results have been compared to manual expert segmentation to validate the proposed method.

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.

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

Magnetic resonance angiography (MRA) is currently used for cerebral flowing blood visualization. Many segmentation methods have been proposed for brain vessel segmentation, in order to help analyzing the huge data (generally more than 10/sup 7/ voxels) provided by MRA acquisitions. Recently, a new family of segmentation algorithms, involving high level anatomical knowledge, has been studied. These new algorithms require a way to model and store this knowledge. An efficient and general approach to reach that goal consists in using atlases. In this paper a method is proposed to create vascular atlases of the brain, containing information useful for vessel segmentation purpose. This atlas creation process, designed for phase-contrast MRA (PC-MRA), is composed of four steps: segmentation, quantification, registration and data fusion. It uses a region-growing algorithm for vessel segmentation, a skeleton and vessel size determination algorithm, based on discrete geometry, for determination of quantitative properties, and a topology preserving non-rigid registration method to fuse the information. This method, which has been applied to a 18 PC-MRA database, enables to create vascular atlases containing information on brain vessels position, density, size and orientation. The generated atlases are essentially devoted to segmentation purpose but can also be used for anatomical description or pathology detection.

Reliable segmentation of 3D magnetic resonance angiography (MRA) is fundamental for planning and performing neurosurgical procedures, but also for detecting vascular pathologies. We propose here a method for brain vessel segmentation based on mathematical morphology tools. This method, devoted to phase-contrast MRA (PC-MRA) performs vessel segmentation by applying an adaptive set of grey-level hit-or-miss operators on each point of the MR data. High level anatomical knowledge modeled by a vascular atlas is used in order to adapt the parameters of these operators (number, size, and orientation) to the current position. The method has been performed on 30 PC-MRA cases composed of both phase and magnitude images. The results have been validated and compared to segmented data obtained by applying a region-growing algorithm on the same database. They tend to prove that the method is reliable for brain vessel detection and additionally provides information on vessel size and orientation without requiring any post-processing step.

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.

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.

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.

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.

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.

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.