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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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Debora Gil, & Petia Radeva. (2004). Shape Restoration via a Regularized Curvature Flow. Journal of Mathematical Imaging and Vision, 21(3), 205–223.
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.
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Oriol Pujol, & Petia Radeva. (2004). Texture Segmentation by Statistical Deformable Models. IJIG - International Journal of Image and Graphics, 433–452.
Abstract: Deformable models have received much popularity due to their ability to include high-level knowledge on the application domain into low-level image processing. Still, most proposed active contour models do not sufficiently profit from the application information and they are too generalized, leading to non-optimal final results of segmentation, tracking or 3D reconstruction processes. In this paper we propose a new deformable model defined in a statistical framework to segment objects of natural scenes. We perform a supervised learning of local appearance of the textured objects and construct a feature space using a set of co-occurrence matrix measures. Linear Discriminant Analysis allows us to obtain an optimal reduced feature space where a mixture model is applied to construct a likelihood map. Instead of using a heuristic potential field, our active model is deformed on a regularized version of the likelihood map in order to segment objects characterized by the same texture pattern. Different tests on synthetic images, natural scene and medical images show the advantages of our statistic deformable model.
Keywords: Texture segmentation, parametric active contours, statistic snakes
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Oriol Rodriguez-Leon, Josefina Mauri, Eduard Fernandez-Nofrerias, Antonio Tovar, Vicente del Valle, Aura Hernandez-Sabate, et al. (2004). Utilización de la Estructura de los Campos Vectoriales para la Detección de la Adventicia en Imágenes de Ecografía Intracoronaria. Revista Internacional de Enfermedades Cardiovasculares Revista Española de Cardiología, 57(2), 100.
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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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