Estudio y desarrollo de un preproceso basado en la difusión no lineal para la segmentación en imágenes

En esta Tesis Doctoral se aborda la utilización de filtros de difusión no lineal para obtener imágenes constantes a trozos como paso previo al proceso de segmentación. En una primera parte se propone un formulación intrínseca para la ecuación de difusión no lineal que proporcione las condiciones de diseño necesarias sobre los filtros de difusión. A partir del marco teórico propuesto, se proporciona una nueva familia de difusividades; éstas son obtenidas a partir de técnicas de difusión no lineal relacionadas con los procesos de difusión regresivos. El objetivo es descomponer la imagen en regiones cerradas que sean homogéneas en sus niveles de grises sin contornos difusos. Asimismo, se prueba que la función de difusividad propuesta satisface las condiciones de un correcto planteamiento semi-discreto. Esto muestra que mediante el esquema semi-implícito habitualmente utilizado, realmente se hace un proceso de difusión no lineal directa, en lugar de difusión inversa, conectando con proceso de preservación de bordes. Bajo estas condiciones establecidas, se plantea un criterio de parada para el proceso de difusión, para obtener imágenes constantes a trozos con un bajo coste computacional. Una vez aplicado todo el proceso al caso unidimensional, se extienden los resultados teóricos, al caso de imágenes en 2D y 3D. Para el caso en 3D, se detalla el esquema numérico para el problema evolutivo no lineal, con condiciones de contorno Neumann homogéneas. Finalmente, se prueba el filtro propuesto para imágenes reales en 2D y 3D y se ilustran los resultados de la difusividad propuesta como método para obtener imágenes constantes a trozos. En el caso de imágenes 3D, se aborda la problemática del proceso previo a la segmentación del hígado, mediante imágenes reales provenientes de Tomografías Axiales Computarizadas (TAC). En ese caso, se obtienen resultados sobre la estimación de los parámetros de la función de difusividad propuesta. This Ph.D. Thesis deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. I have first shown an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, I have proposed a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. It has also proved that the proposed filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edgepreserving process. Under the conditions established for the diffusivity and using a stopping criterion I for the diffusion time, I have obtained piecewise constant images with a low computational effort. The whole process in the one-dimensional case is extended to the case where 2D and 3D theoretical results are applied to real images. For 3D, develops in detail the numerical scheme for nonlinear evolutionary problem with homogeneous Neumann boundary conditions. Finally, I have tested the proposed filter with real images for 2D and 3D and I have illustrated the effects of the proposed diffusivity function as a method to get piecewise constant images. For 3D I have developed a preprocess for liver segmentation with real images from CT (Computerized Tomography). In this case, I have obtained results on the estimation of the parameters of the given diffusivity function.

Optimal Multiresolution 3D Level-Set Method for Liver Segmentation incorporating Local Curvature Constraints

Advanced liver surgery requires a precise pre-operative planning, where liver segmentation and remnant liver volume are key elements to avoid post-operative liver failure. In that context, level-set algorithms have achieved better results than others, especially with altered liver parenchyma or in cases with previous surgery. In order to improve functional liver parenchyma volume measurements, in this work we propose two strategies to enhance previous level-set algorithms: an optimal multi-resolution strategy with fine details correction and adaptive curvature, as well as an additional semiautomatic step imposing local curvature constraints. Results show more accurate segmentations, especially in elongated structures, detecting internal lesions and avoiding leakages to close structures

Coronary Artery Tracking in 3D Cardiac CT Images Using Local Morphological Reconstruction Operators

Automatic segmentation and tracking of the coronary artery tree from Cardiac Multislice-CT images is an important goal to improve the diagnosis and treatment of coronary artery disease. This paper presents a semi-automatic algorithm (one input point per vessel) based on morphological grayscale local reconstructions in 3D images devoted to the extraction of the coronary artery tree. The algorithm has been evaluated in the framework of the Coronary Artery Tracking Challenge 2008 [1], obtaining consistent results in overlapping measurements (a mean of 70% of the vessel well tracked). Poor results in accuracy measurements suggest that future work should refine the centerline extraction. The algorithm can be efficiently implemented and its general strategy can be easily extrapolated to a completely automated centerline extraction or to a user interactive vessel extraction

Efficient local unfolding with ancestor stacks

The most successful unfolding rules used nowadays in the partial evaluation of logic programs are based on well quasi orders (wqo) applied over (covering) ancestors, i.e., a subsequence of the atoms selected during a derivation. Ancestor (sub)sequences are used to increase the specialization power of unfolding while still guaranteeing termination and also to reduce the number of atoms for which the wqo has to be checked. Unfortunately, maintaining the structure of the ancestor relation during unfolding introduces significant overhead. We propose an efficient, practical local unfolding rule based on the notion of covering ancestors which can be used in combination with a wqo and allows a stack-based implementation without losing any opportunities for specialization. Using our technique, certain non-leftmost unfoldings are allowed as long as local unfolding is performed, i.e., we cover depth-first strategies. To deal with practical programs, we propose assertion-based techniques which allow our approach to treat programs that include (Prolog) built-ins and external predicates in a very extensible manner, for the case of leftmost unfolding. Finally, we report on our mplementation of these techniques embedded in a practical partial evaluator, which shows that our techniques, in addition to dealing with practical programs, are also significantly more efficient in time and somewhat more efficient in memory than traditional tree-based implementations. To appear in Theory and Practice of Logic Programming (TPLP).