Abstract: In order to provide more intuitive and easily interpretable representations of complex shapes/organs, medial manifolds should reach a compromise between simplicity in geometry and capability for restoring the anatomy/shape of the organ/volume. Existing morphological methods show excellent results when applied to 2D objects, but their quality drops across dimensions.
This paper contributes to the computation of medial manifolds in two aspects. First, we provide a standard scheme for the computation of medial manifolds that avoids degenerated medial axis segments. Second, we introduce a continuous operator for accurate and efficient computation of medial structures of arbitrary dimension. We evaluate quantitatively the performance of our method with respect to existing approaches, by applying them to syn- thetic shapes of known medial geometry. We also show its higher performance for medical imaging applications in terms of simplicity of medial structures and capability for reconstructing the anatomical volume.

Abstract: Impairment of left ventricular contractility due to cardiovascular diseases is reflected in left ventricle (LV) motion patterns. An abnormal change of torsion or long axis shortening LV values can help with the diagnosis and follow-up of LV dysfunction. Tagged Magnetic Resonance (TMR) is a widely spread medical imaging modality that allows estimation of the myocardial tissue local deformation. In this work, we introduce a novel variational framework for extracting the left ventricle dynamics from TMR sequences. A bi-dimensional representation space of TMR images given by Gabor filter banks is defined. Tracking of the phases of the Gabor response is combined using a variational framework which regularizes the deformation field just at areas where the Gabor amplitude drops, while restoring the underlying motion otherwise. The clinical applicability of the proposed method is illustrated by extracting normality models of the ventricular torsion from 19 healthy subjects.

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: Hand-drawn symbols can take many different and distorted shapes from their ideal representation. Then, very flexible methods are needed to be able to handle unconstrained drawings. We propose here to extend our previous work in hand-drawn symbol recognition based on a Bayesian framework and deformable template matching. This approach gets flexibility enough to fit distorted shapes in the drawing while keeping fidelity to the ideal shape of the symbol. In this work, we define the similarity measure between an image and a symbol based on the distance from every pixel in the image to the lines in the symbol. Matching is carried out using an implementation of the EM algorithm. Thus, we can improve recognition rates and computation time with respect to our previous formulation based on a simulated annealing algorithm.

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.