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.

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.

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.

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.

Abstract: According to the World Health Organization, epilepsy affects more than 50 million people in the world, and specifically, 80% of them live in developing countries. Therefore, epilepsy has become among the major public issue for many governments and deserves to be engaged. Epilepsy is characterized by uncontrollable seizures in the subject due to a sudden abnormal functionality of the brain. Recurrence of epilepsy attacks change people’s lives and interferes with their daily activities. Although epilepsy has no cure, it could be mitigated with an appropriated diagnosis and medication. Usually, epilepsy diagnosis is based on the analysis of an electroencephalogram (EEG) of the patient. However, the process of searching for seizure patterns in a multichannel EEG recording is a visual demanding and time consuming task, even for experienced neurologists. Despite the recent progress in automatic recognition of epilepsy, the multichannel nature of EEG recordings still challenges current methods. In this work, a new method to detect epilepsy in multichannel EEG recordings is proposed. First, the method uses convolutions to perform channel fusion, and next, a self-attention network extracts temporal features to classify between interictal and ictal epilepsy states. The method was validated in the public CHB-MIT dataset using the k-fold cross-validation and achieved 99.74% of specificity and 99.15% of sensitivity, surpassing current approaches.