Abstract: Due to its complex geometry, the basal ring is often omitted when putting different heart geometries into correspondence. In this paper, we present the first results on a new mapping of the left ventricle basal rings onto a normalized coordinate system using a fold-over free approach to the solution to the Laplacian. To guarantee correspondences between different basal rings, we imposed some internal constrained positions at anatomical landmarks in the normalized coordinate system. To prevent internal fold-overs, constraints are handled by cutting the volume into regions defined by anatomical features and mapping each piece of the volume separately. Initial results presented in this paper indicate that our method is able to handle internal constrains without introducing fold-overs and thus guarantees one-to-one mappings between different basal ring geometries.

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: Dagstuhl Workshop

Abstract: A hatched area is characterized by a set of parallel straight lines placed at regular intervals. In this paper, a Hough-based schema is introduced to recognize hatched areas in technical documents from attributed graph structures representing the document once it has been vectorized. Defining a Hough-based transform from a graph instead of the raster image allows to drastically reduce the processing time and, second, to obtain more reliable results because straight lines have already been detected in the vectorization step. A second advantage of the proposed method is that no assumptions must be made a priori about the slope and frequency of hatching patterns, but they are computed in run time for each hatched area.

Abstract: This paper presents a system to understand hand drawn architectural drawings in a CAD environment. The procedure is to identify in a floor plan the building elements, stored in a library of patterns, and their spatial relationships. The vectorized input document and the patterns to recognize are represented by attributed graphs. To recognize the patterns as such, we apply a structural approach based on subgraph isomorphism techniques. In spite of their value, graph matching techniques do not recognize adequately those building elements characterized by hatching patterns, i.e. walls. Here we focus on the recognition of hatching patterns and develop a straight line Hough transform based method in order to detect the regions filled in with parallel straight fines. This allows not only to recognize filling patterns, but it actually reduces the computational load associated with the subgraph isomorphism computation. The result is that the document can be redrawn by editing all the patterns recognized