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Debora Gil, David Roche, Agnes Borras, & Jesus Giraldo. (2015). "Terminating Evolutionary Algorithms at their Steady State " . Computational Optimization and Applications, 61(2), 489–515.
Abstract: Assessing the reliability of termination conditions for evolutionary algorithms (EAs) is of prime importance. An erroneous or weak stop criterion can negatively affect both the computational effort and the final result. We introduce a statistical framework for assessing whether a termination condition is able to stop an EA at its steady state, so that its results can not be improved anymore. We use a regression model in order to determine the requirements ensuring that a measure derived from EA evolving population is related to the distance to the optimum in decision variable space. Our framework is analyzed across 24 benchmark test functions and two standard termination criteria based on function fitness value in objective function space and EA population decision variable space distribution for the differential evolution (DE) paradigm. Results validate our framework as a powerful tool for determining the capability of a measure for terminating EA and the results also identify the decision variable space distribution as the best-suited for accurately terminating DE in real-world applications.
Keywords: Evolutionary algorithms; Termination condition; Steady state; Differential evolution
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Patricia Marquez, Debora Gil, & Aura Hernandez-Sabate. (2013). "Evaluation of the Capabilities of Confidence Measures for Assessing Optical Flow Quality " In ICCV Workshop on Computer Vision in Vehicle Technology: From Earth to Mars (pp. 624–631).
Abstract: Assessing Optical Flow (OF) quality is essential for its further use in reliable decision support systems. The absence of ground truth in such situations leads to the computation of OF Confidence Measures (CM) obtained from either input or output data. A fair comparison across the capabilities of the different CM for bounding OF error is required in order to choose the best OF-CM pair for discarding points where OF computation is not reliable. This paper presents a statistical probabilistic framework for assessing the quality of a given CM. Our quality measure is given in terms of the percentage of pixels whose OF error bound can not be determined by CM values. We also provide statistical tools for the computation of CM values that ensures a given accuracy of the flow field.
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David Roche. (2015)." A Statistical Framework for Terminating Evolutionary Algorithms at their Steady State" (Debora Gil, & Jesus Giraldo, Eds.). Ph.D. thesis, Ediciones Graficas Rey, .
Abstract: As any iterative technique, it is a necessary condition a stop criterion for terminating Evolutionary Algorithms (EA). In the case of optimization methods, the algorithm should stop at the time it has reached a steady state so it can not improve results anymore. Assessing the reliability of termination conditions for EAs is of prime importance. A wrong or weak stop criterion can negatively aect both the computational eort and the nal result.
In this Thesis, we introduce a statistical framework for assessing whether a termination condition is able to stop EA at its steady state. In one hand a numeric approximation to steady states to detect the point in which EA population has lost its diversity has been presented for EA termination. This approximation has been applied to dierent EA paradigms based on diversity and a selection of functions covering the properties most relevant for EA convergence. Experiments show that our condition works regardless of the search space dimension and function landscape and Dierential Evolution (DE) arises as the best paradigm. On the other hand, we use a regression model in order to determine the requirements ensuring that a measure derived from EA evolving population is related to the distance to the optimum in xspace.
Our theoretical framework is analyzed across several benchmark test functions
and two standard termination criteria based on function improvement in f-space and EA population x-space distribution for the DE paradigm. Results validate our statistical framework as a powerful tool for determining the capability of a measure for terminating EA and select the x-space distribution as the best-suited for accurately stopping DE in real-world applications.
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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. (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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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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David Rotger, Misael Rosales, Jaume Garcia, Oriol Pujol, Josefina Mauri, & Petia Radeva. (2003). "Active Vessel: A New Multimedia Workstation for Intravascular Ultrasound and Angiography Fusion " . Computers in Cardiology, 30, 65–68.
Abstract: AcriveVessel is a new multimedia workstation which enables the visualization, acquisition and handling of both image modalities, on- and ofline. It enables DICOM v3.0 decompression and browsing, video acquisition,repmduction and storage for IntraVascular UltraSound (IVUS) and angiograms with their corresponding ECG,automatic catheter segmentation in angiography images (using fast marching algorithm). BSpline models definition for vessel layers on IVUS images sequence and an extensively validated tool to fuse information. This approach defines the correspondence of every IVUS image with its correspondent point in the angiogram and viceversa. The 3 0 reconstruction of the NUS catheterhessel enables real distance measurements as well as threedimensional visualization showing vessel tortuosity in the space.
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Ernest Valveny, & Enric Marti. (2001). "Learning of structural descriptions of graphic symbols using deformable template matching " In Proc. Sixth Int Document Analysis and Recognition Conf (pp. 455–459).
Abstract: Accurate symbol recognition in graphic documents needs an accurate representation of the symbols to be recognized. If structural approaches are used for recognition, symbols have to be described in terms of their shape, using structural relationships among extracted features. Unlike statistical pattern recognition, in structural methods, symbols are usually manually defined from expertise knowledge, and not automatically infered from sample images. In this work we explain one approach to learn from examples a representative structural description of a symbol, thus providing better information about shape variability. The description of a symbol is based on a probabilistic model. It consists of a set of lines described by the mean and the variance of line parameters, respectively providing information about the model of the symbol, and its shape variability. The representation of each image in the sample set as a set of lines is achieved using deformable template matching.
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Patricia Marquez. (2010). "Conditions Ensuring Accuracy of Local Optical Flow Schemes " (Vol. 157). Master's thesis, , Bellaterra 08193, Barcelona, Spain.
Abstract: Accurate computation of optical flow is a key-point in many image processing fields. Detection of anomalous and unpredicted agents (such as pedestrians, bikers or cars) in urban scenes or pathology discrimination in medical imaging sequences, to mention just a two. The above kinds sequences present two main difficulties for standard optical flow techniques. On one hand, variability in acquisition conditions (illuminance, medical imaging modality, ...) force an alterantive representation for images fulfilling the britghtness constancy constrain. On the hand, current variational schemes produce oversmoothed fields unable to properly model discontinuous behaviours such as collisions or functionless pathological areas. This master project explores the abilities and limitations of local and global optical flow approaches. The master student will put especial emphasis in the theoretical grounds behind in order to design a variational framework combining the theoretical advantages of the considered techniques. In particular an optical flow based on Gabor phase tracking (developed in the group for medical imaging) will be generalized to urban scenes.
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