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Debora Gil, & Petia Radeva. (2005). Extending anisotropic operators to recover smooth shapes. Computer Vision and Image Understanding, 99(1), 110–125.
Abstract: Anisotropic differential operators are widely used in image enhancement processes. Recently, their property of smoothly extending functions to the whole image domain has begun to be exploited. Strong ellipticity of differential operators is a requirement that ensures existence of a unique solution. This condition is too restrictive for operators designed to extend image level sets: their own functionality implies that they should restrict to some vector field. The diffusion tensor that defines the diffusion operator links anisotropic processes with Riemmanian manifolds. In this context, degeneracy implies restricting diffusion to the varieties generated by the vector fields of positive eigenvalues, provided that an integrability condition is satisfied. We will use that any smooth vector field fulfills this integrability requirement to design line connection algorithms for contour completion. As application we present a segmenting strategy that assures convergent snakes whatever the geometry of the object to be modelled is.
Keywords: Contour completion; Functional extension; Differential operators; Riemmanian manifolds; Snake segmentation
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Oriol Pujol, Debora Gil, & Petia Radeva. (2005). Fundamentals of Stop and Go active models. Image and Vision Computing, 23(8), 681–691.
Abstract: An efficient snake formulation should conform to the idea of picking the smoothest curve among all the shapes approximating an object of interest. In current geodesic snakes, the regularizing curvature also affects the convergence stage, hindering the latter at concave regions. In the present work, we make use of characteristic functions to define a novel geodesic formulation that decouples regularity and convergence. This term decoupling endows the snake with higher adaptability to non-convex shapes. Convergence is ensured by splitting the definition of the external force into an attractive vector field and a repulsive one. In our paper, we propose to use likelihood maps as approximation of characteristic functions of object appearance. The better efficiency and accuracy of our decoupled scheme are illustrated in the particular case of feature space-based segmentation.
Keywords: Deformable models; Geodesic snakes; Region-based segmentation
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Oriol Rodriguez-Leon.A.Carol, H.Tizon, Eduard Fernandez-Nofrerias, Josefina Mauri, Vicente del Valle, Debora Gil, et al. (2005). Model estadístic-determinístic per la segmentació de l adventicia en imatges d ecografía intracoronaria. Rev Societat Catalana Cardiologia, 5, 41.
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Debora Gil, & Petia Radeva. (2004). A Regularized Curvature Flow Designed for a Selective Shape Restoration. IEEE Transactions on Image Processing, 13, 1444–1458.
Abstract: Among all filtering techniques, those based exclu- sively on image level sets (geometric flows) have proven to be the less sensitive to the nature of noise and the most contrast preserving. A common feature to existent curvature flows is that they penalize high curvature, regardless of the curve regularity. This constitutes a major drawback since curvature extreme values are standard descriptors of the contour geometry. We argue that an operator designed with shape recovery purposes should include a term penalizing irregularity in the curvature rather than its magnitude. To this purpose, we present a novel geometric flow that includes a function that measures the degree of local irregularity present in the curve. A main advantage is that it achieves non-trivial steady states representing a smooth model of level curves in a noisy image. Performance of our approach is compared to classical filtering techniques in terms of quality in the restored image/shape and asymptotic behavior. We empirically prove that our approach is the technique that achieves the best compromise between image quality and evolution stabilization.
Keywords: Geometric flows, nonlinear filtering, shape recovery.
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Oriol Rodriguez-Leon, Josefina Mauri, Eduard Fernandez-Nofrerias, Antonio Tovar, Vicente del Valle, Aura Hernandez-Sabate, et al. (2004). Utilizacion de la estructura de los campos vectoriales para la deteccion de la Adventicia en imagenes de Ecografia Intracoronaria. REC - Revista Española de Cardiología, 100.
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