Combination of Polyaffine Transformations and Supervised Learning for the Automatic Diagnosis of LV Infarct

International audienceIn this article, we present an application of the polyaffine transformations to classify a population of hearts with myocardial infarction. Polyaffine transformations aim at representing motion by the combination of a limited number of affine transformations defined locally on a regional division of the space. We show that these transformations not only serve as a first (non-learnt) dimension reduction, but also allow to interpret each of the parameters and relate them to known clinical parameters. Then, we use standard supervised learning algorithms on these parameters to classify the population between infarcted and non-infarcted subjects. The method is applied on the STACOM statistical shape modeling labeled data consisting of 200 cases, comprising the same number of healthy subjects and patients with infarct. We train classifiers using different standard machine learning algorithms. Finally, we validate our method with 10-fold cross-validation and get more than 95% of correct classification on yet-unseen data. The method is promising and ready to be tested on the remaining 200 test cases of the challenge

Statistical shape modeling of the left ventricle: myocardial infarct classification challenge

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

Statistical analysis of organs' shapes and deformations: the Riemannian and the affine settings in computational anatomy

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and medicine that aims at analyzing and modeling the biological variability of organs' shapes at the population level. Shapes are equivalence classes of images, surfaces or deformations of a template under rigid body (or more general) transformations. Thus, they belong to non-linear manifolds. In order to deal with multiple samples in non-linear spaces, a consistent statistical framework on Riemannian manifolds has been designed over the last decade. We detail in this chapter the extension of this framework to Lie groups endowed with the affine symmetric connection, a more invariant (and thus more consistent) but non-metric structure on transformation groups. This theory provides strong theoretical bases for the use of one-parameter subgroups and diffeomorphisms parametrized by stationary velocity fields (SVF), for which efficient image registration methods like log-Demons have been developed with a great success from the practical point of view. One can further reduce the complexity with locally affine transformations , leading to parametric diffeomorphisms of low dimension encoding the major shape variability. We illustrate the methodology with the modeling of the evolution of the brain with Alzheimer's disease and the analysis of the cardiac motion from MRI sequences of images

Incorporation of a deformation prior in image reconstruction

International audienceThis article presents a method to incorporate a deformation prior in image reconstruction via the formalism of deformation modules. The framework of deformation modules allows to build diffeomorphic deformations that satisfy a given structure. The idea is to register a template image against the indirectly observed data via a modular deformation, incorporating this way the deformation prior in the reconstruction method. We show that this is a well-defined regularization method (proving existence, stability and convergence) and present numerical examples of reconstruction from 2-D tomographic simulations and partially-observed images

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy