Abstract: Distortion of Left Ventricle (LV) external anatomy is related to some dysfunctions, such as hypertrophy. The architecture of myocardial fibers determines LV electromechanical activation patterns as well as mechanics. Thus, their joined modelling would allow the design of specific interventions (such as peacemaker implantation and LV remodelling) and therapies (such as resynchronization). On one hand, accurate modelling of external anatomy requires either a dense sampling or a continuous infinite dimensional approach, which requires non-Euclidean statistics. On the other hand, computation of fiber models requires statistics on Riemannian spaces. Most approaches compute separate statistical models for external anatomy and fibers architecture. In this work we propose a general mathematical framework based on differential geometry concepts for computing a statistical model including, both, external and fiber anatomy. Our framework provides a continuous approach to external anatomy supporting standard statistics. We also provide a straightforward formula for the computation of the Riemannian fiber statistics. We have applied our methodology to the computation of complete anatomical atlas of canine hearts from diffusion tensor studies. The orientation of fibers over the average external geometry agrees with the segmental description of orientations reported in the literature.

Abstract: International conference on Cardiac electrophysiological simulation challenge
In this paper, we show that canonical (shape-based) geometries can be endowed to cardiac structures using tubular coordinates defined over their medial axis. We give an analytic formulation of these geometries by means of B-Splines. Since B-Splines present vector space structure PCA can be applied to their control points and statistical models relating boundaries and the interior of the anatomical structures can be derived. We demonstrate the applicability in two cardiac structures, the 3D Left Ventricular volume, and the 2D Left-Right ventricle set in 2D Short Axis view.

Abstract: Smoothing of biomedical images should preserve gray-level transitions between adjacent tissues, while restoring contours consistent with anatomical structures. Anisotropic diffusion operators are based on image appearance discontinuities (either local or contextual) and might fail at weak inter-tissue transitions. Meanwhile, the output of block-wise and morphological operations is prone to present a block structure due to the shape and size of the considered pixel neighborhood. In this contribution, we use differential geometry concepts to define a diffusion operator that restricts to image consistent level-sets. In this manner, the final state is a non-uniform intensity image presenting homogeneous inter-tissue transitions along anatomical structures, while smoothing intra-structure texture. Experiments on different types of medical images (magnetic resonance, computerized tomography) illustrate its benefit on a further process (such as segmentation) of images.

Abstract: There is a large range of image processing applications that act on an input sequence of image frames that are continuously received. Throughput is a key performance measure to be optimized when execu- ting them. In this paper we propose a new task replication methodology for optimizing throughput for an image processing application in the field of medicine. The results show that by applying the proposed methodo- logy we are able to achieve the desired throughput in all cases, in such a way that the input frames can be processed at any given rate.