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: A system to recognize hand drawn architectural drawings in a CAD environment has been deve- loped. In this paper we focus on its high level interpretation module. To interpret a floor plan, the system must identify several building elements, whose description is stored in a library of pat- terns, as well as their spatial relationships. We propose a structural approach based on subgraph isomorphism techniques to obtain a high-level interpretation of the document. The vectorized input document and the patterns to be recognized are represented by attributed graphs. Discrete relaxation techniques (AC4 algorithm) have been applied to develop the matching algorithm. The process has been divided in three steps: node labeling, local consistency and global consistency verification. The hand drawn creation causes disturbed line drawings with several accuracy errors, which must be taken into account. Here we have identified them and the AC4 algorithm has been adapted to manage them.

Abstract: Cardiovascular Diseases, specially those affecting the Left Ventricle (LV), are the leading cause of death in developed countries with approximately a 30% of all global deaths. In order to address this public health concern, physicians focus on diagnosis and therapy planning. On one hand, early and accurate detection of Regional Wall Motion Abnormalities (RWMA) significantly contributes to a quick diagnosis and prevents the patient to reach more severe stages. On the other hand, a thouroughly knowledge of the normal gross anatomy of the LV, as well as, the distribution of its muscular fibers is crucial for designing specific interventions and therapies (such as pacemaker implanction). Statistical models obtained from the analysis of different imaging modalities allow the computation of the normal ranges of variation within a given population. Normality models are a valuable tool for the definition of objective criterions quantifying the degree of (anomalous) deviation of the LV function and anatomy for a given subject. The creation of statistical models involve addressing three main issues: extraction of data from images, definition of a common domain for comparison of data across patients and designing appropriate statistical analysis schemes. In this PhD thesis we present generic image processing tools for the creation of statistical models of the LV anatomy and function. On one hand, we use differential geometry concepts to define a computational framework (the Normalized Parametric Domain, NPD) suitable for the comparison and fusion of several clinical scores obtained over the LV. On the other hand, we present a variational approach (the Harmonic Phase Flow, HPF) for the estimation of myocardial motion that provides dense and continuous vector fields without overestimating motion at injured areas. These tools are used for the creation of statistical models. Regarding anatomy, we obtain an atlas jointly modelling, both, LV gross anatomy and fiber architecture. Regarding function, we compute normality patterns of scores characterizing the (global and local) LV function and explore, for the first time, the configuration of local scores better suited for RWMA detection.

Abstract: Bronchoscopy allows to examine the patient airways for detection of lesions and sampling of tissues without surgery. A main drawback in lung cancer diagnosis is the diculty to check whether the exploration is following the correct path to the nodule that has to be biopsied. The most extended guidance uses uoroscopy which implies repeated radiation of clinical sta and patients. Alternatives such as virtual bronchoscopy or electromagnetic navigation are very expensive and not completely robust to blood, mocus or deformations as to be extensively used. We propose a method that extracts and tracks stable lumen regions at dierent levels of the bronchial tree. The tracked regions are stored in a tree that encodes the anatomical structure of the scene which can be useful to retrieve the path to the lesion that the clinician should follow to do the biopsy. We present a multi-expert validation of our anatomical landmark extraction in 3 intra-operative ultrathin explorations.

Abstract: Any image filtering operator designed for automatic shape restoration should satisfy robustness (whatever the nature and degree of noise is) as well as non-trivial smooth asymptotic behavior. Moreover, a stopping criterion should be determined by characteristics of the evolved image rather than dependent on the number of iterations. Among the several PDE based techniques, curvature flows appear to be highly reliable for strongly noisy images compared to image diffusion processes.
In the present paper, we introduce a regularized curvature flow (RCF) that admits non-trivial steady states. It is based on a measure of the local curve smoothness that takes into account regularity of the curve curvature and serves as stopping term in the mean curvature flow. We prove that this measure decreases over the orbits of RCF, which endows the method with a natural stop criterion in terms of the magnitude of this measure. Further, in its discrete version it produces steady states consisting of piece-wise regular curves. Numerical experiments made on synthetic shapes corrupted with different kinds of noise show the abilities and limitations of each of the current geometric flows and the benefits of RCF. Finally, we present results on real images that illustrate the usefulness of the present approach in practical applications.