Cardiac fibers, as well as their local arrangement in laminar sheets, have a complex spatial variation of their orientation that has an important role in mechanical and electrical cardiac functions. In this paper, a statistical atlas of this cardiac fiber architecture is built for the first time using human datasets. This atlas provides an average description of the human cardiac fiber architecture along with its variability within the population. In this study, the population is composed of ten healthy human hearts whose cardiac fiber architecture is imaged ex vivo with DT-MRI acquisitions. The atlas construction is based on a computational framework that minimizes user interactions and combines most recent advances in image analysis: graph cuts for segmentation, symmetric log-domain diffeomorphic demons for registration, and log-Euclidean metric for diffusion tensor processing and statistical analysis. Results show that the helix angle of the average fiber orientation is highly correlated to the transmural depth and ranges from -41° on the epicardium to +66° on the endocardium. Moreover, we find that the fiber orientation dispersion across the population (±13°) is lower than for the laminar sheets (±31°) . This study, based on human hearts, extends previous studies on other mammals with concurring conclusions and provides a description of the cardiac fiber architecture more specific to human and better suited for clinical applications. Indeed, this statistical atlas can help to improve the computational models used for radio-frequency ablation, cardiac resynchronization therapy, surgical ventricular restoration, or diagnosis and followups of heart diseases due to fiber architecture anomalies.

Simulated annealing (SA) and deterministic continuation are well-known generic approaches to global optimization. Deterministic continuation is computationally attractive but produces suboptimal solutions, whereas SA is asymptotically optimal but converges very slowly. In this paper, we introduce a new class of hybrid algorithms which combines the theoretical advantages of SA with the practical advantages of deterministic continuation. We call this class of algorithms stochastic continuation (SC). In a nutshell, SC is a variation of SA in which both the energy function and the communication mechanism are allowed to be time-dependent. We first prove that SC inherits the convergence properties of generalized SA under weak assumptions. Then, we show that SC can be successfully applied to optimization issues raised by the Bayesian approach to signal reconstruction. The considered class of energy functions arises in maximum a posteriori estimation with a Markov random field prior. The associated minimization task is NP-hard and beyond the scope of popular methods such as loopy belief propagation, tree-reweighted message passing, and graph cuts and its extensions. We perform numerical experiments in the context of three-dimensional reconstruction from a very limited number of projections; our results show that SC can substantially outperform both deterministic continuation and SA.

A new neural network-based approach is proposed to estimate motion hierarchy in image sequences taking into consideration motion discontinuities. The network consists in an input layer, an intermediate layer and an output layer. In order to estimate the most likely displacement at each pixel, we have transposed the block matching approach into the neural network approach and add mechanisms to detect motion discontinuities. Information redundancy allows for parallel processing in view of real-time complex motion estimation tasks. Preliminary tests on synthetic and real images are very promising.

We consider a recent parametric level-set segmentation approach where the implicit interface is the zero level of a continuous function expanded onto compactly supported radial basis functions, defined by their centers, coefficients and supports. We propose to introduce prior knowledge of the shape to be recovered by placing the centers quasi-uniformly over an uncertainty area.

Compared with other medical imaging modalities, ultrasound imaging has its own advantages. The three-dimensional (3-D) ultrasound stereo visualization technique has a broad promising future for its ability superior to traditional two-dimensional (2-D) ultrasound image, and it helps to understand the complex structures of tissues as well as to measure tissular volumes. However, it is often difficult to interpret the 3-D structure from acoustic data because of the speckle noise. To solve this problem, we propose a new enhancement algorithm which is based on calculating nonstationary degree of ultrasound data to improve the image quality. We observe data within a finite length window and then map them to an N-dimensional space where every point represents the observed data. According to the data features, we divide this space into two parts: the stationary subspace constituted by the stationary points, which represent a line in the space, and the nonstationary subspace is formed by the points out of the line. Then the nonstationary degree of a set of observed data is defined as the distance from the correspondent point to the stationary line. Thus, we can enhance the image since the nonstationary degree is larger on tissular border where features vary rapidly. Finally, the application of the proposed algorithm to real data of the liver of a rabbit is described. The results are shown by means of 3-D ultrasound stereo visualization, and the results demonstrate a significant improvement compared with the original image.

We address the problem of reconstructing a piecewise constant 3-D object from a few noisy 2-D line-integral projections. More generally, the theory developed here readily applies to the recovery of an ideal n-D signal (n > or =1) from indirect measurements corrupted by noise. Stabilization of this ill-conditioned inverse problem is achieved with the Potts prior model, which leads to a challenging optimization task. To overcome this difficulty, we introduce a new class of hybrid algorithms that combines simulated annealing with deterministic continuation. We call this class of algorithms stochastic continuation (SC). We first prove that, under mild assumptions, SC inherits the finite-time convergence properties of generalized simulated annealing. Then, we show that SC can be successfully applied to our reconstruction problem. In addition, we look into the concave distortion acceleration method introduced for standard simulated annealing and we derive an explicit formula for choosing the free parameter of the cost function. Numerical experiments using both synthetic data and real radiographic testing data show that SC outperforms standard simulated annealing.

We present a vascular segmentation and quantification method based on the right generalized cylinder state model (RGC-sm). The RGC-sm model includes a curvilinear axis associated to a stack of contours. The axis is described by a state vector (local curvature, torsion and rotation). The contours are described by a Fourier series decomposition. The challenge is to automatically adjust this model to 3D vascular data (segmentation). By fitting the synthetic model to the actual medical data, it is possible to get the state model parameters and quantification measures. We present quantitative results on a set of calibrated phantoms and qualitative results on clinical datasets (carotid 3D-CTA and aortic 3D-MRA).

A new approach for correcting bias field in magnetic resonance (MR) images is proposed using the mathematical model of singularity function analysis (SFA), which represents a discrete signal or its spectrum as a weighted sum of singularity functions. Through this model, an MR image's low spatial frequency components corrupted by a smoothly varying bias field are first removed, and then reconstructed from its higher spatial frequency components not polluted by bias field. The thus reconstructed image is then used to estimate bias field for final image correction. The approach does not rely on the assumption that anatomical information in MR images occurs at higher spatial frequencies than bias field. The performance of this approach is evaluated using both simulated and real clinical MR images.

Medical data represent tremendous amount of data for which automatic analysis is increasingly needed. Grids are very promising to face today's challenging health issues such as epidemiological studies through large image data sets. However, the sensitive nature of medical data makes it difficult to widely distribute medical applications over computational grids. In this paper, we review fundamental medical data manipulation requirements and we propose a distributed data management architecture that addresses the medical data security and high performance constraints. A prototype is currently being developed inside our laboratories to demonstrate the architecture capability to face realistic distributed medical data manipulation situations.

The availability of digital imagers inside hospitals and their ever growing inspection capabilities have established digital medical images as a key component of many pathologies diagnosis, follow-up and treatment. To face the growing image analysis requirements, automated medical image processing algorithms have been developed over the two past decades. In parallel, medical image databases have been set up in health centers. Some attempts have been made to cross data coming from different origins for studies involving large databases. Grid technologies appear to be a promising tool to face the raising challenges of computational medicine. They offer wide area access to distributed databases in a secured environment and they bring the computational power needed to complete some large scale statistical studies involving image processing. In this paper, we review grid-related requirements of medical application that we illustrate through two real examples.

The dominant methodology for image restoration is to stabilize the problem by including a roughness penalty in addition to faithfulness to the data. Among various choices, concave stabilizers stand out for their boundary detection capabilities, but the resulting cost function to be minimized is generally multimodal. Although simulated annealing is theoretically optimal to take up this challenge, standard stochastic algorithms suffer from two drawbacks: i) practical convergence difficulties are encountered with second-order prior models and ii) it remains computationally demanding to favor the formation of smooth contour lines by taking the discontinuity field explicitly into account. This work shows that both weaknesses can be overcome in a multiresolution framework by means of the 2-D discrete wavelet transform (DWT). We first propose to improve convergence toward global minima by single-site updating on the wavelet domain. For this purpose, a new restricted DWT space is introduced and a theoretically sound updating mechanism is constructed on this subspace. Next, we suggest to incorporate the smoothness of the discontinuity field via an additional penalty term defined on the high frequency subbands. The resulting increase in complexity is small and the approach requires the specification of a unique extra parameter for which an explicit selection formula is derived.

In this paper, the current status of cardiac image registration methods is reviewed. The combination of information from multiple cardiac image modalities, such as magnetic resonance imaging, computed tomography, positron emission tomography, single-photon emission computed tomography, and ultrasound, is of increasing interest in the medical community for physiologic understanding and diagnostic purposes. Registration of cardiac images is a more complex problem than brain image registration because the heart is a nonrigid moving organ inside a moving body. Moreover, as compared to the registration of brain images, the heart exhibits much fewer accurate anatomical landmarks. In a clinical context, physicians often mentally integrate image information from different modalities. Automatic registration, based on computer programs, might, however, offer better accuracy and repeatability and save time.

The new MPEG-4 standard will provide superior services for the user, as it introduces the video objects concept. However, there is no generic segmentation technique able to provide the segmentation maps for such a coding system. We propose a novel mesh-based video segmentation and objects tracking algorithm with both robust motion estimation and modeling of motion discontinuities. In addition, occlusions and uncovered regions are well managed. This allows the mesh deformation without the need to process remeshing in motion occlusion regions. The spatial properties of each frame are considered to make the mesh edges fit the image contents and a temporal smoothness constraint is also implemented. The proposed algorithm is able to segment multiple objects at the same time. Some experimental results are shown.

We propose a novel deformable model to assess the deformation of a textured object in an image sequence by simultaneously tracking edge and intensity information. The proposed model is defined as an elastic region with snake-like rigidity constraints at its boundaries. By regularizing the displacement estimation with an elasticity-based constraint, this model is able to assess physically realistic deformations inside a region. By incorporating rigidity constraint at its boundaries, it can also accurately track edges. The numerical implementation of the model is performed using the finite element method. The good behavior of the proposed model is illustrated on synthetic images which simulates the heart contraction in tagged magnetic resonance imaging (MRI). The contour tracking abilities of the model are also illustrated on standard MR images.

We propose a new subdivision scheme derived from the regular 1:4 face split, allowing analysis of irregularly subdivided triangular meshes by the wavelet transforms. Some experimental results on real medical meshes prove the efficiency of this approach in multiresolution schemes. In addition we show the effectiveness of the proposed algorithm for lossless compression.

Typically, the linear image restoration problem is an ill-conditioned, underdetermined inverse problem. Here, stabilization is achieved via the introduction of a first-order smoothness constraint which allows the preservation of edges and leads to the minimization of a nonconvex functional. In order to carry through this optimization task, we use stochastic relaxation with annealing. We prefer the Metropolis dynamics to the popular, but computationally much more expensive, Gibbs sampler. Still, Metropolis-type annealing algorithms are also widely reported to exhibit a low convergence rate. Their finite-time behavior is outlined and we investigate some inexpensive acceleration techniques that do not alter their theoretical convergence properties; namely, restriction of the state space to a locally bounded image space and increasing concave transform of the cost functional. Successful experiments about space-variant restoration of simulated synthetic aperture imaging data illustrate the performance of the resulting class of algorithms and show significant benefits in terms of convergence speed.

A method has been developed to reconstruct three-dimensional (3-D) surfaces from two-dimensional (2-D) projection data. It is used to produce individualized boundary element models, consisting of thorax and lung surfaces, for electro- and magnetocardiographic inverse problems. Two orthogonal projections are utilized. A geometrical prior model, built using segmented magnetic resonance images, is deformed according to profiles segmented from projection images. In our method, virtual X-ray images of the prior model are first constructed by simulating real X-ray imaging. The 2-D profiles of the model are segmented from the projections and elastically matched with the profiles segmented from patient data. The displacement vectors produced by the elastic 2-D matching are back projected onto the 3-D surface of the prior model. Finally, the model is deformed, using the back-projected vectors. Two different deformation methods are proposed. The accuracy of the method is validated by a simulation. The average reconstruction error of a thorax and lungs was 1.22 voxels, corresponding to about 5 mm.

We consider the coding of a quadrangular mesh structure generated by a multiresolution deformable quadtree algorithm. Such a structure has been found efficient for region based video coding, but few works deal with the coding of the mesh structure. We propose to use the rules of the mesh generation to significantly reduce the number of bits required for the coding of the nodes position defining the mesh structure. This reduction induces an improvement of either the image quality or either the global bit rate.

We address the linear image restoration problem in the case of a spatially varying blur. Most of the time, the recovery of the original image from its degraded measurements is an ill-conditioned, underdetermined inverse problem. Here, stabilization is achieved via concave potential functions and minimization is carried out using Metropolis-type simulated annealing. Still, the ordinary approach can be subject to some convergence difficulties and it remains an ambitious challenge to take into account the mutual dependence between neighboring discontinuities. We first propose to improve convergence towards global minima through single-site updating in the discrete wavelet transform (DWT) space. For this purpose, a suitable restricted DWT space is introduced and it turns out that the resulting class of algorithms shows less sensitivity to the choice of the hyperparameters. Next, we show that the smoothness of the discontinuity field can be incorporated implicitly in a multiresolution framework by means of a simple penalty term defined on the high frequency channels.

The synthetic aperture image formation process can be formulated as a space-variant 2D convolution. The recovery of the original reflection density is an ill-posed inverse problem which is both underdetermined and ill-conditioned. Its stabilization is achieved via concave stabilizers that are well adapted to the preservation of discontinuities. This leads to the minimization of a non-convex functional, a task which is successfully carried out using a Metropolis-type annealing algorithm. For improved performance, we investigate some inexpensive acceleration techniques which do not alter the theoretical convergence results; their efficiency is demonstrated through restorations from simulated data.

Medical imaging is a powerful mean to access dynamic function of 3D deformable organs of the body. Due to the flow of incoming data, multiresolution methods on parallel computers is the only way to achieve complex processings in reasonable time. We present an active pyramid to model dynamic volumes. This pyramid is built on the first volume of a sequence and contains a binary model of the objects of interest. Previous knowledge is introduced within this binary model. The structure of the pyramid is rigid, but its main interest is that its components are deformed to fit the data using energetical constraints. A multiresolution algorithm based on self-organizing maps is then applied to deform the model through time. This algorithm matches the different levels of the pyramid in a coarse to fine approach. The output of the matching process is the field of deformation, modeling the transformations. This pyramid is applied to real data in the result section. The rigid structure of the pyramid is suitable for massively parallel architectures.

Motion and deformation analysis of the myocardium are of utmost interest in cardiac imaging. Part of the, research is devoted to the estimation of the heart function by analysis of the shape changes of the left-ventricular endocardial surface. However, most clinically used shape-based approaches are often two-dimensional (2-D) and based on the analysis of the shape at only two cardiac instants. Three-dimensional (3-D) approaches generally make restrictive hypothesis about the actual endocardium motion to be able to recover a point-to-point correspondence between two surfaces. The present work is a first step toward the automatic spatio-temporal analysis and recognition of deformable surfaces. A curvature-based and easily interpretable description of the surfaces is derived. Based on this description, shape dynamics is first globally estimated through the temporal shape spectra. Second, a regional curvature-based tracking approach is proposed assuming a smooth deformation. It combines geometrical and spatial information in order to analyze a specific endocardial region. These methods are applied both on true 3-D X-ray data and on simulated normal and abnormal left ventricles. The results are coherent and easily interpretable. Shape dynamics estimations and comparisons between deformable object sequences are now possible through these techniques. This promising framework is a suitable tool for a complete regional description of deformable surfaces.

In medical imaging, 3D boundary extraction is a preliminary requisite for a coherent shape analysis of an organ. Deformable objects, like the heart cavities, are often hard to detect because of the artefacts caused by the motion. The authors present a 3D deformable surface model based on a parameterized representation combined with a random process of deformation. The solution is searched for by the minimization of an energy function through simulated annealing. The authors also discuss the introduction of a priori shape information about the object. The boundary extraction algorithm is applied to 3D CT data of a dog's heart.