Debora Gil. (2004). Geometric Differential Operators for Shape Modelling (Jordi Saludes i Closa, & Petia Radeva, Eds.). Ph.D. thesis, Ediciones Graficas Rey, Barcelona (Spain).
Abstract: Medical imaging feeds research in many computer vision and image processing fields: image filtering, segmentation, shape recovery, registration, retrieval and pattern matching. Because of their low contrast changes and large variety of artifacts and noise, medical imaging processing techniques relying on an analysis of the geometry of image level sets rather than on intensity values result in more robust treatment. From the starting point of treatment of intravascular images, this PhD thesis ad- dresses the design of differential image operators based on geometric principles for a robust shape modelling and restoration. Among all fields applying shape recovery, we approach filtering and segmentation of image objects. For a successful use in real images, the segmentation process should go through three stages: noise removing, shape modelling and shape recovery. This PhD addresses all three topics, but for the sake of algorithms as automated as possible, techniques for image processing will be designed to satisfy three main principles: a) convergence of the iterative schemes to non-trivial states avoiding image degeneration to a constant image and representing smooth models of the originals; b) smooth asymptotic behav- ior ensuring stabilization of the iterative process; c) fixed parameter values ensuring equal (domain free) performance of the algorithms whatever initial images/shapes. Our geometric approach to the generic equations that model the different processes approached enables defining techniques satisfying all the former requirements. First, we introduce a new curvature-based geometric flow for image filtering achieving a good compromise between noise removing and resemblance to original images. Sec- ond, we describe a new family of diffusion operators that restrict their scope to image level curves and serve to restore smooth closed models from unconnected sets of points. Finally, we design a regularization of snake (distance) maps that ensures its smooth convergence towards any closed shape. Experiments show that performance of the techniques proposed overpasses that of state-of-the-art algorithms.
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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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Debora Gil, & Petia Radeva. (2004). Inhibition of False Landmarks. In J. V. et al (Ed.), Recent Advances in Artificial Intelligence Research and Development (pp. 233–244). Barcelona (Spain): IOS Press.
Abstract: We argue that a corner detector should be based on the degree of continuity of the tangent vector to the image level sets, work on the image domain and need no assumptions on neither the image local structure nor the particular geometry of the corner/junction. An operator measuring the degree of differentiability of the projection matrix on the image gradient fulfills the above requirements. Its high sensitivity to changes in vector directions makes it suitable for landmark location in real images prone to need smoothing to reduce the impact of noise. Because using smoothing kernels leads to corner misplacement, we suggest an alternative fake response remover based on the receptive field inhibition of spurious details. The combination of both orientation discontinuity detection and noise inhibition produce our Inhibition Orientation Energy (IOE) landmark locator.
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E. Barakova, Maya Dimitrova, T. Lorents, & Petia Radeva. (2004). The Web as an “Autobiographical Agent”.
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Ernest Valveny, & Philippe Dosch. (2004). Performance Evaluation of Symbol Recognition. In A. D.(E.) S. Marinai (Ed.), Document Analysis Systems (Vol. 3163, 354–365).
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Ernest Valveny, & Philippe Dosch. (2004). Symbol Recognition Contest: A Synthesis.
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Fernando Vilariño, Debora Gil, & Petia Radeva. (2004). A Novel FLDA Formulation for Numerical Stability Analysis. In P. R. and I. A. J. Vitrià (Ed.), Recent Advances in Artificial Intelligence Research and Development (Vol. 113, pp. 77–84). IOS Press.
Abstract: Fisher Linear Discriminant Analysis (FLDA) is one of the most popular techniques used in classification applying dimensional reduction. The numerical scheme involves the inversion of the within-class scatter matrix, which makes FLDA potentially ill-conditioned when it becomes singular. In this paper we present a novel explicit formulation of FLDA in terms of the eccentricity ratio and eigenvector orientations of the within-class scatter matrix. An analysis of this function will characterize those situations where FLDA response is not reliable because of numerical instability. This can solve common situations of poor classification performance in computer vision.
Keywords: Supervised Learning; Linear Discriminant Analysis; Numerical Stability; Computer Vision
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Francesc Tous, Maria Vanrell, & Ramon Baldrich. (2004). Exploring Colour Constancy Solutions..
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Gemma Sanchez, Ernest Valveny, Josep Llados, Joan Mas, & N. Lozano. (2004). A platform to extract knowledge from graphic documents. Application to an architectural sketch understanding scenario.
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Gemma Sanchez, & Josep Llados. (2004). Syntactic models to represent perceptually regular repetitive patterns in graphic documents.
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Georg Langs, Petia Radeva, David Rotger, & Francesc Carreras. (2004). Explorative Building of 3D Vessel Tree Models.
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Georg Langs, Petia Radeva, David Rotger, & Francesc Carreras. (2004). Building and Registering Parameterized 3D Models of Vessel Trees for Visualization during Intervention.
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Jaume Amores, N. Sebe, Petia Radeva, Theo Gevers, & A. Smeulders. (2004). Boosting Contextual Information in Content-based Image Retrieval.
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Jaume Amores, & Petia Radeva. (2004). Registration and retrieval of medical images. Application to IVUS.
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