Abstract: This paper deals with the recognition of symbols and struc- tural textures in architectural plans using string matching techniques. A plan is represented by an attributed graph whose nodes represent characteristic points and whose edges represent segments. Symbols and textures can be seen as a set of regions, i.e. closed loops in the graph, with a particular arrangement. The search for a symbol involves a graph matching between the regions of a model graph and the regions of the graph representing the document. Discriminating a texture means a clus- tering of neighbouring regions of this graph. Both procedures involve a similarity measure between graph regions. A string codification is used to represent the sequence of outlining edges of a region. Thus, the simila- rity between two regions is defined in terms of the string edit distance between their boundary strings. The use of string matching allows the recognition method to work also under presence of distortion.

Abstract: In this work, we present a fully automated method for tissue deformation estimation in tagged magnetic resonance images (TMRI). Gabor filter banks, tuned independently for each left ventricle level, provide optimally filtered complex images which phase remains constant along the cardiac cycle. This fact can be thought as the brightness constancy condition required by classical optical flow (OF) methods. Pairs of these filtered sequences, together with a variational formulation are used in a second step to obtain dense continuous deformation maps that we call Harmonic Phase Flow. This method has been used to determine reference values of ventricular torsion (VT) in a set of 8 healthy volunteers. The results encourage the use of VT as a useful parameter for ventricular function assessment in clinical routine.

Abstract: Computation of functional regional scores requires proper identification of LV contours. On one hand, manual segmentation is robust, but it is time consuming and requires high expertise. On the other hand, the tag pattern in TMR sequences is a problem for automatic segmentation of LV boundaries. We propose a segmentation method based on a predictorcorrector (Active Contours – Shape Models) scheme. Special stress is put in the definition of the AC external forces. First, we introduce a semantic description of the LV that discriminates myocardial tissue by using texture and motion descriptors. Second, in order to ensure convergence regardless of the initial contour, the external energy is decoupled according to the orientation of the edges in the image potential. We have validated the model in terms of error in segmented contours and accuracy of regional clinical scores.

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: 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.