Tracking geometrical descriptors on 3-D deformable surfaces: application to the left-ventricular surface of the heart

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Abstract
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.

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