This work addresses the problem of non-rigid registration of 3D scans, which is at the core of shape modeling techniques. Firstly, we propose a new kernel based on geodesic distances for the Gaussian Process Morphable Models (GPMMs) framework. The use of geodesic distances into the kernel makes it more adapted to the topological and geometric characteristics of the surface and leads to more realistic deformations around holes and curved areas. Since the kernel possesses hyperparameters we have optimized them for the task of face registration on the FaceWarehouse dataset. We show that the Geodesic squared exponential kernel performs significantly better than state of the art kernels for the task of face registration on all the 20 expressions of the FaceWarehouse dataset. Secondly, we propose a modification of the loss function used in the non-rigid ICP registration algorithm, that allows to weight the correspondences according to the confidence given to them. As a use case, we show that we can make the registration more robust to outliers in the 3D scans, such as non-skin parts.

Statistical shape modeling is a powerful tool for visualizing and quantifying geometric and functional patterns of the heart. After myocardial infarction (MI), the left ventricle typically remodels in response to physiological challenges. Several methods have been proposed in the literature to describe statistical shape changes. Which method best characterizes left ventricular remodeling after MI is an open research question. A better descriptor of remodeling is expected to provide a more accurate evaluation of disease status in MI patients. We therefore designed a challenge to test shape characterization in MI given a set of three-dimensional left ventricular surface points. The training set comprised 100 MI patients, and 100 asymptomatic volunteers (AV). The challenge was initiated in 2015 at the Statistical Atlases and Computational Models of the Heart workshop, in conjunction with the MICCAI conference. The training set with labels was provided to participants, who were asked to submit the likelihood of MI from a different (validation) set of 200 cases (100 AV and 100 MI). Sensitivity, specificity, accuracy and area under the receiver operating characteristic curve were used as the outcome measures. The goals of this challenge were to (1) establish a common dataset for evaluating statistical shape modeling algorithms in MI, and (2) test whether statistical shape modeling provides additional information characterizing MI patients over standard clinical measures. Eleven groups with a wide variety of classification and feature extraction approaches participated in this challenge. All methods achieved excellent classification results with accuracy ranges from 0.83 to 0.98. The areas under the receiver operating characteristic curves were all above 0.90. Four methods showed significantly higher performance than standard clinical measures. The dataset and software for evaluation are available from the Cardiac Atlas Project website1.

Delineation of the left ventricular cavity, myocardium, and right ventricle from cardiac magnetic resonance images (multi-slice 2-D cine MRI) is a common clinical task to establish diagnosis. The automation of the corresponding tasks has thus been the subject of intense research over the past decades. In this paper, we introduce the "Automatic Cardiac Diagnosis Challenge" dataset (ACDC), the largest publicly available and fully annotated dataset for the purpose of cardiac MRI (CMR) assessment. The dataset contains data from 150 multi-equipments CMRI recordings with reference measurements and classification from two medical experts. The overarching objective of this paper is to measure how far state-of-the-art deep learning methods can go at assessing CMRI, i.e., segmenting the myocardium and the two ventricles as well as classifying pathologies. In the wake of the 2017 MICCAI-ACDC challenge, we report results from deep learning methods provided by nine research groups for the segmentation task and four groups for the classification task. Results show that the best methods faithfully reproduce the expert analysis, leading to a mean value of 0.97 correlation score for the automatic extraction of clinical indices and an accuracy of 0.96 for automatic diagnosis. These results clearly open the door to highly accurate and fully automatic analysis of cardiac CMRI. We also identify scenarios for which deep learning methods are still failing. Both the dataset and detailed results are publicly available online, while the platform will remain open for new submissions.

In this article, we study the consistency of the template estimation with the Fréchet mean in quotient spaces. The Fréchet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images, etc. We demonstrate the asymptotic bias of template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter $\sigma$ describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it if needed; they are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected, which reveals the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

Computer models of the heart are of increasing interest for clinical applications due to their discriminative and predictive abilities. However a single 3D simulation can be computationally expensive and long, which can make some practical applications such as the personalisation phase, or a sensitivity analysis of mechanical parameters over the simulated behaviour quite slow. In this manuscript we present a multiscale 0D/3D model which allows us to have a reliable (and extremely fast) approximation of the behaviour of the 3D model under a few simplifying assumptions. We first detail the two different models, then explain the coupling of the two models to get fast 0D approximation of 3D simulations. Finally we demonstrated how the multiscale model can speed-up an efficient optimization algorithm, which enables a fast personalisation of the 3D simulations by leveraging on the advantages of each scale. 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.

In this paper, we propose a novel approach to study cardiac motion in 4D image sequences. Whereas traditional approaches rely on the registration of the whole sequence with respect to the first frame usually corresponding to the end-diastole (ED) image, we define a more generic basis using the barycentric subspace spanned by a number of references images of the sequence. These subspaces are implicitly defined as the locus of points which are weighted Karcher means of \(k+1\) references images. We build such subspace on the cardiac motion images, to get a Barycentric Template that is no longer defined by a single image but parametrized by coefficients: the barycentric coordinates. We first show that the barycentric coordinates - the coefficients of the projection of the motion during a cardiac sequence - define a meaningful signature for group-wise analysis of dynamics and can efficiently separate two populations. Then, we use the barycentric template as a prior for regularization in cardiac motion tracking, efficiently reducing the error of tracking between end-systole and end-diastole by almost 40 % as well as the error of the evaluation of the ejection fraction. Finally, to best exploit the fact that multiple reference images allow to reduce the registration displacement, we derived a symmetric and transitive registration that can be used both for frame-to-frame and frame-to-reference registration and further improves the accuracy of the registration. 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.

Given that heart disease can cause abnormal motion dynamics over the cardiac cycle, understanding and quantifying cardiac motion can provide insight for clinicians to aid with diagnosis, therapy planning, and determining prognosis. The goal of this paper is to extract population-specific motion patterns from 3D displacements in order to identify the mean motion in a population, and to describe pathology-specific motion patterns in terms of the spatial and temporal components. Since there are common motion patterns observed in patients with the same condition, extracting these can lead towards a better understanding of the disease. Quantifying cardiac motion at a population level is not a simple task since images can vary widely in terms of image quality, size, resolution, and pose. To overcome this, we analyze the parameters obtained from a cardiac-specific Polyaffine motion-tracking algorithm, which are aligned both spatially and temporally to a common reference space. Once all parameters are aligned, different subjects can be compared and analyzed in the space of Polyaffine transformations by projecting the transformations to a reduced order subspace in which dominant motion patterns in each population can be extracted. Using tensor decomposition, the spatial and temporal aspects can be decoupled in order to study the components individually. The proposed method was validated on healthy volunteers and Tetralogy of Fallot patients according to known spatial and temporal behavior for each population. A key advantage of this method is the ability to regenerate motion sequences from the models, which can be visualized in terms of the full motion.

Given the observed abnormal motion dynamics of patients with heart conditions, quantifying cardiac motion in both normal and pathological cases can provide useful insights for therapy planning. In order to be able to analyse the motion over multiple subjects in a robust manner, it is desirable to represent the motion by a low number of parameters. We propose a reduced order cardiac motion model, reduced in space through a polyaffine model, and reduced in time by statistical model order reduction. The method is applied to a data-set of synthetic cases with known ground truth to validate the accuracy of the left ventricular motion tracking, and to validate a patient-specific reduced-order motion model. Population-based statistics are computed on a set of 15 healthy volunteers to obtain separate spatial and temporal bases. Results demonstrate that the reduced model can efficiently detect abnormal motion patterns and even allowed to retrospectively reveal abnormal unnoticed motion within the control subjects.

To achieve sparse parametrizations that allow intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the large deformation diffeomorphic metric mapping (LDDMM) registration framework. While the zeroth-order moments previously used in LDDMM only describe local displacement, the first-order momenta that are proposed here represent a basis that allows local description of affine transformations and subsequent compact description of nontranslational movement in a globally nonrigid deformation. The resulting representation contains directly interpretable information from both mathematical and modeling perspectives. We develop the mathematical construction of the registration framework with higher-order momenta, we show the implications for sparse image registration and deformation description, and we provide examples of how the parametrization enables registration with a very low number of parameters. The capacity and interpretability of the parametrization using higher-order momenta lead to natural modeling of articulated movement, and the method promises to be useful for quantifying ventricle expansion and progressing atrophy during Alzheimer's disease.

In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented , where the deformation was regularized by penalizing deviations from a zero rate of strain. In , the terms regularizing the deformation included the covariance of the deformation matrices (Σ) and the vector fields (q) . Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies.

Cardiac remodelling plays a crucial role in heart diseases. Analyzing how the heart grows and remodels over time can provide precious insights into pathological mechanisms, eventually resulting in quantitative metrics for disease evaluation and therapy planning. This study aims to quantify the regional impacts of valve regurgitation and heart growth upon the end-diastolic right ventricle (RV) in patients with tetralogy of Fallot, a severe congenital heart defect. The ultimate goal is to determine, among clinical variables, predictors for the RV shape from which a statistical model that predicts RV remodelling is built. Our approach relies on a forward model based on currents and a diffeomorphic surface registration algorithm to estimate an unbiased template. Local effects of RV regurgitation upon the RV shape were assessed with Principal Component Analysis (PCA) and cross-sectional multivariate design. A generative 3-D model of RV growth was then estimated using partial least squares (PLS) and canonical correlation analysis (CCA). Applied on a retrospective population of 49 patients, cross-effects between growth and pathology could be identified. Qualitatively, the statistical findings were found realistic by cardiologists. 10-fold cross-validation demonstrated a promising generalization and stability of the growth model. Compared to PCA regression, PLS was more compact, more precise and provided better predictions.

In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative that ignores the reorientation in the gradient computation. We show that the exact gradient leads to significantly better registration at the cost of computation time. Independently of the choice of Euclidean or Log-Euclidean interpolation and sum of squared differences dissimilarity measure, the exact gradient achieves better alignment over an entire spectrum of deformation penalties. Alignment quality is assessed with a battery of metrics including tensor overlap, fractional anisotropy, inverse consistency and closeness to synthetic warps. The improvements persist even when a different reorientation scheme, preservation of principal directions, is used to apply the final deformations.

Production grids are complex and highly variable systems whose behavior is not well understood and difficult to anticipate. The goal of this study is to estimate the impact of the variability of those infrastructures on the performance of workflow-based applications. A probabilistic model of workflows execution time is proposed and evaluated. Results show that the variability of the EGEE grid infrastructure impacts the execution time of a particular medical image analysis application by a factor 2. The model gives interesting insights on the grid behavior for different application parallelization modes.

The impact of lossy compression has often been discussed in the medical area. In this study, an evaluation of the impact of lossy compression on the performance of rigid registration algorithms for medical images is proposed. The robustness, repeatability and accuracy of these algorithms is estimated through a statistical procedure for each compression ratio. Results are obtained thanks to a grid technology handling the computation cost of the method. Experiments reveal that the impact of compression is quite negligible below a significant compression ratio if the registration algorithm has a good multi-scale handling. Beyond this threshold, feature-based methods are highly penalized.

This paper introduces a method to analyze the variability of the spine shape and of the spine shape deformations using articulated shape models. The spine shape was expressed as a vector of relative poses between local coordinate systems of neighboring vertebrae. Spine shape deformations were then modeled by a vector of rigid transformations that transforms one spine shape into another. Because rigid transformations do not naturally belong to a vector space, conventional mean and covariance could not be applied. The Fréchet mean and a generalized covariance were used instead. The spine shapes of a group of 295 scoliotic patients were quantitatively analyzed as well as the spine shape deformations associated with the Cotrel-Dubousset corrective surgery (33 patients), the Boston brace (39 patients), and the scoliosis progression without treatment (26 patients). The variability of intervertebral poses was found to be inhomogeneous (lumbar vertebrae were more variable than the thoracic ones) and anisotropic (with maximal rotational variability around the coronal axis and maximal translational variability along the axial direction). Finally, brace and surgery were found to have a significant effect on the Fréchet mean and on the generalized covariance in specific spine regions where treatments modified the spine shape.

This paper presents a method to optimize the timeout value of computing jobs. It relies on a model of the job execution time that considers the job management system latency through a random variable. It also takes into account a proportion of outliers to model either reliable clusters or production grids characterized by faults causing jobs loss. Job management systems are first studied considering classical distributions. Different behaviors are exhibited, depending on the weight of the tail of the distribution and on the amount of outliers. Experimental results are then shown based on the latency distribution and outlier ratios measured on the EGEE grid infrastructure1. Those results show that using the optimal timeout value provided by our method reduces the impact of outliers and leads to a 1.36 speed-up even for reliable systems without outliers.

Diffusion tensor magnetic resonance imaging (DT-MRI or DTI) is an imaging modality that is gaining importance in clinical applications. However, in a clinical environment, data have to be acquired rapidly, often at the expense of the image quality. This often results in DTI datasets that are not suitable for complex postprocessing like fiber tracking. We propose a new variational framework to improve the estimation of DT-MRI in this clinical context. Most of the existing estimation methods rely on a log-Gaussian noise (Gaussian noise on the image logarithms), or a Gaussian noise, that do not reflect the Rician nature of the noise in MR images with a low signal-to-noise ratio (SNR). With these methods, the Rician noise induces a shrinking effect: the tensor volume is underestimated when other noise models are used for the estimation. In this paper, we propose a maximum likelihood strategy that fully exploits the assumption of a Rician noise. To further reduce the influence of the noise, we optimally exploit the spatial correlation by coupling the estimation with an anisotropic prior previously proposed on the spatial regularity of the tensor field itself, which results in a maximum a posteriori estimation. Optimizing such a nonlinear criterion requires adapted tools for tensor computing. We show that Riemannian metrics for tensors, and more specifically the log-Euclidean metrics, are a good candidate and that this criterion can be efficiently optimized. Experiments on synthetic data show that our method correctly handles the shrinking effect even with very low SNR, and that the positive definiteness of tensors is always ensured. Results on real clinical data demonstrate the truthfulness of the proposed approach and show promising improvements of fiber tracking in the brain and the spinal cord.

We propose a unified computational framework to build a statistical atlas of the cardiac fiber architecture from diffusion tensor magnetic resonance images (DT-MRIs). We apply this framework to a small database of nine ex vivo canine hearts. An average cardiac fiber architecture and a measure of its variability are computed using most recent advances in diffusion tensor statistics. This statistical analysis confirms the already established good stability of the fiber orientations and a higher variability of the laminar sheet orientations within a given species. The statistical comparison between the canine atlas and a standard human cardiac DT-MRI shows a better stability of the fiber orientations than their laminar sheet orientations between the two species. The proposed computational framework can be applied to larger databases of cardiac DT-MRIs from various species to better establish intraspecies and interspecies statistics on the anatomical structure of cardiac fibers. This information will be useful to guide the adjustment of average fiber models onto specific patients from in vivo anatomical imaging modalities.

Grids technologies enable the deployment of complex data-intensive scientific applications. Nonspecific scientific codes may benefit from grid computing capabilities by (i) assembling codes in workflows (code parallelism) and (ii) processing large amounts of data (data parallelism). We designed MOTEUR, a service-based workflow manager, to describe data-intensive scientific applications in a compact framework and to efficiently process the resulting computations by transparently exploiting different parallelism levels. Theoretical performances are analyzed and results are shown based on a real application to medical image databases processing

Production grids have a potential for parallel execution of a very large number of tasks but also introduce a high overhead that significantly impacts the execution of short tasks. In this work, we present a strategy to optimize the partitioning of jobs on a grid infrastructure. This method takes into account the variability and the difficulty to model a multi-user large-scale environment used for production. It is based on probabilistic estimations of the grid overhead. We first study analytically modeled environments and then we show results on a real grid infrastructure. We demonstrate that this method leads to a significant time speed-up and to a substantial saving of the number of submitted tasks with respect to a blind maximal partitioning strategy.

Medical image analysis plays a crucial role in the diagnosis, planning, control, and follow-up of therapy. To be combined efficiently with medical robotics, medical image analysis can be supported by the development of specific computational models of the human body operating at various levels. We describe a hierarchy of these computational models, including the geometrical, physical, and physiological levels, and illustrate their potential use in a number of advanced medical applications including image-guided robot-assisted and simulated medical interventions. We conclude with scientific perspectives.

Data intensive medical image processing applications can easily benefit from grid capabilities. However, the setting up of complex medical experiments is not straight forward on current grid infrastructures. To ease such experiments we are developing a generic and grid-enabled workflow framework, relying on current standards. We show results on a concrete application to medical image registration assessment. We discuss the limitations induced by current standards and tools and how they were overcome for deploying the application.

Digital medical image processing is a promising application area for grids. Given the volume of data, the sensitivity of medical information, and the joint complexity of medical datasets and computations expected in clinical practice, the challenge is to fill the gap between the grid middleware and the requirements of clinical applications. The research project AGIR (Grid Analysis of Radiological Data) presented in this paper addresses this challenge through a combined approach: on one hand, leveraging the grid middleware through core grid medical services which target the requirements of medical data processing applications; on the other hand, grid-enabling a panel of applications ranging from algorithmic research to clinical applications.

Radio-frequency ablation is a difficult operative task that requires a precise needle positioning in the centre of the pathology. This article presents an augmented reality system for hepatic therapy guidance that superimposes in real-time 3D reconstructions (from CT acquisition) and a virtual model of the needle on external views of a patient. The superimposition of reconstructed models is performed with a 3D/2D registration based on radio-opaque markers stuck on to the patient's skin. The characteristics of the problem (accuracy, robustness and time processing) led us to develop automatic procedures to extract and match the markers and to track the needle in real time. Experimental studies confirmed that our algorithms are robust and reliable. Preliminary experiments conducted on a human abdomen phantom showed that our system is highly accurate (needle positioning error within 3 mm) and enables the surgeon to reach a target in less than 1 minute on average. Our next step will be to perform an in vivo evaluation. Copyright © 2005 John Wiley & Sons, Ltd.

Medical image processing led to a major improvement of patient care: the 3D modeling of patients from their CT-scan or MRI provides an improved surgical planning and simulation allows to train the surgical gesture before carrying it out. These two preoperative steps can be used intra-operatively with the development of augmented reality (AR). In this paper, we present the tools we developed to provide our first prototypal AR guiding system for abdominal surgery.

Multi-subject non-rigid registration algorithms using dense deformation fields often encounter cases where the transformation to be estimated has a large spatial variability. In these cases, linear stationary regularization methods are not sufficient. In this paper, we present an algorithm that uses a priori information about the nature of imaged objects in order to adapt the regularization of the deformations. We also present a robustness improvement that gives higher weight to those points in images that contain more information. Finally, a fast parallel implementation using networked personal computers is presented. In order to improve the usability of the parallel software by a clinical user, we have implemented it as a grid service that can be controlled by a graphics workstation embedded in the clinical environment. Results on inter-subject pairs of images show that our method can take into account the large variability of most brain structures. The registration time for images of size 256 x 256 x 124 is 5 min on 15 standard PCs. A comparison of our non-stationary visco-elastic smoothing versus solely elastic or fluid regularizations shows that our algorithm converges faster towards a more optimal solution in terms of accuracy and transformation regularity.

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We present a new image-based technique to rigidly register intraoperative three-dimensional ultrasound (US) with preoperative magnetic resonance (MR) images. Automatic registration is achieved by maximization of a similarity measure which generalizes the correlation ratio, and whose novelty is to incorporate multivariate information from the MR data (intensity and gradient). In addition, the similarity measure is built upon a robust intensity-based distance measure, which makes it possible to handle a variety of US artifacts. A cross-validation study has been carried out using a number of phantom and clinical data. This indicates that the method is quite robust and that the worst registration errors are of the order of the MR image resolution.

MOTIVATION: Most biological actions of proteins depend on some typical parts of their three-dimensional structure, called 3D motifs. It is desirable to find automatically common geometric substructures between proteins to discover similarities in new structures or to model precisely a particular motif. Most algorithms for structural comparison of proteins deal with large (fold) similarities. Here, we focus on small but precise similarities. RESULTS: We propose a new 3D substructure matching algorithm based on geometric hashing techniques. The key feature of the method is the introduction of a 3D reference frame attached to each residue. This allows us to reduce drastically the complexity of the recognition. Our experimental results confirm the validity of the approach and allow us to find smaller similarities than previous methods. AVAILABILITY: The program uses commercial libraries and thus cannot be completely freely distributed. It can be found at ftp://www.inria.fr in the directory epidaure/Outgoing/xpennec/Prospect, but it requires a key to be run, available by request to [email protected] CONTACT: [email protected]; [email protected]

It is often necessary to handle randomness and geometry in computer vision, for instance to match and fuse together noisy geometric features such as points, lines or 3D frames, or to estimate a geometric transformation from a set of matched features. However, the proper handling of these geometric features is far more difficult than for points, and a number of paradoxes can arise. We analyse in this article three basic problems: (1) what is a uniform random distribution of features, (2) how to define a distance between features, and (3) what is the "mean feature" of a number of feature measurements, and we propose generic methods to solve them.

We propose a new method to estimate a rigid transform from a set of 3-D matched points or matched frames, and we concentrate on the analysis of the uncertainty of the estimated transform. The theoretical contributions are an intrinsic model of noise for transformations based on composition rather than addition, a unified formalism for the estimation of both the rigid transform and its covariance matrix for points or frames correspondences, and also a statistical validation method to verify the error estimation, which applies even when no "ground truth" is available. The practical contribution is the validation of our transform estimation method in the case of 3-D medical images, which shows that a precision of the registration, far below the size of a voxel, can be achieved.>