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: Image registration has been for many years the gold standard method to bring two images into correspondence. It has been used extensively in the eld of medical imaging in order to put images of dierent patients into a common overlapping spatial position. However, medical image registration is a slow, iterative optimization process, where many variables and prone to fall into the pit traps local minima.
A coordinate system parameterizing the interior of organs is a powerful tool for a systematic localization of injured tissue. If the same coordinate values are assigned to specic anatomical sites, parameterizations ensure integration of data across different medical image modalities. Harmonic mappings have been used to produce parametric meshes over the surface of anatomical shapes, given their ability to set values at specic locations through boundary conditions. However, most of the existing implementations in medical imaging restrict to either anatomical surfaces, or the depth coordinate with boundary conditions is given at discrete sites of limited geometric diversity.
The medial surface of the shape can be used to provide a continuous basis for the denition of a depth coordinate. However, given that dierent methods for generation of medial surfaces generate dierent manifolds, not all of them are equally suited to be the basis of radial coordinate for a parameterization. It would be desirable that the medial surface will be smooth, and robust to surface shape noise, with low number of spurious branches or surfaces.
In this thesis we present methods for computation of smooth medial manifolds and apply them to the generation of for anatomical volumetric parameterization that extends current harmonic parameterizations to the interior anatomy using information provided by the volume medial surface. This reference system sets a solid base for creating anatomical models of the anatomical shapes, and allows comparing several patients in a common framework of reference.

Abstract: For millennia, the study of the couple brain-mind has fascinated the humanity in order to understand the complex nature of cognitive states. A cognitive state is the state of the mind at a specific time and involves cognition activities to acquire and process information for making a decision, solving a problem, or achieving a goal.
While normal cognitive states assist in the successful accomplishment of tasks; on the contrary, abnormal states of the mind can lead to task failures due to a reduced cognition capability. In this thesis, we focus on the assessment of cognitive states by means of the analysis of ElectroEncephaloGrams (EEG) signals using deep learning methods. EEG records the electrical activity of the brain using a set of electrodes placed on the scalp that output a set of spatiotemporal signals that are expected to be correlated to a specific mental process.
From the point of view of artificial intelligence, any method for the assessment of cognitive states using EEG signals as input should face several challenges. On the one hand, one should determine which is the most suitable approach for the optimal combination of the multiple signals recorded by EEG electrodes. On the other hand, one should have a protocol for the collection of good quality unambiguous annotated data, and an experimental design for the assessment of the generalization and transfer of models. In order to tackle them, first, we propose several convolutional neural architectures to perform data fusion of the signals recorded by EEG electrodes, at raw signal and feature levels. Four channel fusion methods, easy to incorporate into any neural network architecture, are proposed and assessed. Second, we present a method to create an unambiguous dataset for the prediction of cognitive mental workload using serious games and an Airbus-320 flight simulator. Third, we present a validation protocol that takes into account the levels of generalization of models based on the source and amount of test data.
Finally, the approaches for the assessment of cognitive states are applied to two use cases of high social impact: the assessment of mental workload for personalized support systems in the cockpit and the detection of epileptic seizures. The results obtained from the first use case show the feasibility of task transfer of models trained to detect workload in serious games to real flight scenarios. The results from the second use case show the generalization capability of our EEG channel fusion methods at k-fold cross-validation, patient-specific, and population levels.

Abstract: Tagged magnetic resonance is a very usefull and unique tool that provides a complete local and global knowledge of the left ventricle (LV) motion. In this article we introduce a method capable of tracking and segmenting the LV. Spectral methods are applied in order to obtain the so called HARP images which encode information about movement and are the base for LV point-tracking. For segmentation we use Active Shapes (ASM) that model LV shape variation in order to overcome possible local misplacements of the boundary. We finally show experiments on both synthetic and real data which appear to be very promising.

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.