Abstract: Medial representations are powerful tools for describing and parameterizing the volumetric shape of anatomical structures. Existing methods show excellent results when applied to 2D objects, but their quality drops across dimensions. This paper contributes to the computation of medial manifolds in two aspects. First, we provide a standard scheme for the computation of medial manifolds that avoid degenerated medial axis segments; second, we introduce an energy based method which performs independently of the dimension. We evaluate quantitatively the performance of our method with respect to existing approaches, by applying them to synthetic shapes of known medial geometry. Finally, we show results on shape representation of multiple abdominal organs, exploring the use of medial manifolds for the representation of multi-organ relations.

Abstract: Fisher Linear Discriminant Analysis (FLDA) is one of the most popular techniques used in classification applying dimensional reduction. The numerical scheme involves the inversion of the within-class scatter matrix, which makes FLDA potentially ill-conditioned when it becomes singular. In this paper we present a novel explicit formulation of FLDA in terms of the eccentricity ratio and eigenvector orientations of the within-class scatter matrix. An analysis of this function will characterize those situations where FLDA response is not reliable because of numerical instability. This can solve common situations of poor classification performance in computer vision.

Abstract: Medial representations are a widely used technique in abdominal organ shape representation and parametrization. Those methods require good medial manifolds as a starting point. Any medial
surface used to parametrize a volume should be simple enough to allow an easy manipulation and complete enough to allow an accurate reconstruction of the volume. Obtaining good quality medial
surfaces is still a problem with current iterative thinning methods. This forces the usage of generic, pre-calculated medial templates that are adapted to the final shape at the cost of a drop in volume reconstruction.
This paper describes an operator for generation of medial structures that generates clean and complete manifolds well suited for their further use in medial representations of abdominal organ volumes. While being simpler than thinning surfaces, experiments show its high performance in volume reconstruction and preservation of medial surface main branching topology.

Abstract: In order to provide more intuitive and easily interpretable representations of complex shapes/organs, medial manifolds should reach a compromise between simplicity in geometry and capability for restoring the anatomy/shape of the organ/volume. Existing morphological methods show excellent results when applied to 2D objects, but their quality drops across dimensions.
This paper contributes to the computation of medial manifolds in two aspects. First, we provide a standard scheme for the computation of medial manifolds that avoids degenerated medial axis segments. Second, we introduce a continuous operator for accurate and efficient computation of medial structures of arbitrary dimension. We evaluate quantitatively the performance of our method with respect to existing approaches, by applying them to syn- thetic shapes of known medial geometry. We also show its higher performance for medical imaging applications in terms of simplicity of medial structures and capability for reconstructing the anatomical volume.

Abstract: This paper presents a patient-sensitive simulation strategy capable of using the most efficient way the high-performance computational resources. The proposed strategy directly involves three different players: Computational Mechanics Scientists (CMS), Image Processing Scientists and Cardiologists, each one mastering its own expertise area within the project. This paper describes the general integrative scheme but focusing on the CMS side presents a massively parallel implementation of computational electrophysiology applied to cardiac tissue simulation. The paper covers different angles of the computational problem: equations, numerical issues, the algorithm and parallel implementation. The proposed methodology is illustrated with numerical simulations testing all the different possibilities, ranging from small domains up to very large ones. A key issue is the almost ideal scalability not only for large and complex problems but also for medium-size meshes. The explicit formulation is particularly well suited for solving this highly transient problems, with very short time-scale.