Šiame darbe buvo tiriama LLE algoritmo darbo kokybės priklausomybė nuo vienintelio tam įtakos turinčio parametro, tai taško kaimynų naudojamų skaičiavimams skaičiaus k. Taip pat buvo tiriamas keturių topologijos išlaikymo įverčių: Spirmano koeficiento, liekamosios dispersijos, DS paklaidos ir Prokrusto analizės tinkamumas LLE algoritmo darbo rezultatų kokybės įvertinimui, ir galimybė panaudojant juos parinkti geriausias taško kaimynų naudojamų skaičiavimuose skaičiaus k reikšmes, ar reikšmių intervalus. Tyrimai atlikti naudojant MATLAB 7.1programinę terpę. / The paper Application of LLE algorithm for visualization of multidimensional data deals with locally linear embedding (LLE) algorithm's quality of work dependence on number of nearest neighbors k used in calculations. In it four topology preservation measures: Spearman coefficient, residual variance, MDS errors and Procrustes analysis have also been tested. Their suitability for the algorithm’s quality of work assessment, and the possibility of using them to select the best number or ranges of values of nearest neighbors k used in calculations. Investigations were carried out using MATLAB 7.1 software.

Des études cliniques sur les nouveau-nés prématurés montrent qu'une large proportion des grands prématurés (moins de 32 semaines d’aménorrhée) présentera des troubles cognitifs, moteurs ou comportementaux. Un objectif clinique est donc d’approfondir les études du développement cérébral et de détecter les anomalies chez les patients néonataux. Parmi les modalités d'imagerie, l'IRM peut fournir une information 3D morphologique, non-invasive, non ionisante et avec une résolution spatiale de l'ordre du millimètre, propriétés qui sont bien adaptées à cette problématique. En outre, la segmentation de ces images permet de fournir des informations quantitatives de l'anatomie, comme le volume ou la forme. Il existe de nombreuses méthodes pour l'IRM chez l'adulte. Néanmoins, la plupart d'entre elles ne peuvent pas s'appliquer directement chez le nouveau-né, où la maturation des tissus cérébraux induit des modifications de contraste dans l'image (dues, par exemple, à la non-myélinisation de la substance blanche). De plus, des détériorations visuelles, telles que les effets de volume partiels, se produisent par l'effet conjugué de la résolution des images et de la finesse des structures (par exemple, le cortex). Cette thèse se focalise sur la segmentation de la surface corticale des nouveau-nés en utilisant des images IRM, avec une précision satisfaisante pour des applications subséquentes (comme la génération de maillages surfaciques). Dans cette thèse, nous nous sommes intéressés dans un premier temps aux approches par atlas ou multi-atlas. Cette famille de méthodes est connue pour son efficacité en termes de segmentation cérébrale grâce à des a priori spatiaux intégrés au modèle, qui permettent de guider la segmentation. Néanmoins, le cortex étant une structure très fine, des erreurs topologiques peuvent se produire. Afin de résoudre ce problème, une étape de correction topologique multi échelle est mise en oeuvre. Les résultats montrent le potentiel de ces deux types d'approches pour l’analyse des données considérées. / Clinical studies for preterm infants (less than 32 weeks of gestation) emphasize the fact that an important part of the very or extreme preterm infants will present cognitive, motor or behavioral disorders. The clinical aim is to improve brain development studies and be able to detect and predict abnormalities in neonatal subjects. Among the medical imaging, MRI can provide non-invasive non-ionizing morphological 3D images with a spatial resolution of the order of a millimeter, properties that are well adapted to this issue. In addition, the segmentation of these images provides quantitative anatomical information, such as volume or shape. There are many existing methods for adult MRI that successfully segment brain subparts. However, these methods cannot be directly applied to the newborn, where the maturation of brain tissue modifies the contrasts in the image (for example, the non-myelination of the white matter). Moreover, factors related to the resolution together with structural fineness, especially in the cortex, induce partial volume effects in tissue boundaries. This thesis focuses on the segmentation of the cortical surface in neonatal infants using MR images, with satisfactory accuracy for further applications (such as the generation of surface meshes). In this thesis, we first focused on the so-called atlas or multi-atlas approaches. This family of methods is known for its effectiveness in brain segmentation, thanks to spatial priors that can be embedded in the model for guiding the segmentation. However, since the neonatal cortex is very thin, there are often discontinuities or wrong connections. In order to tackle this issue, a topological correction step is proposed to fill gaps and separate erroneous connections. The results emphasize the potential of these two types of approaches for this purpose.

The research described in this thesis was motivated by the need of a robust model capable of representing 3D data obtained with 3D sensors, which are inherently noisy. In addition, time constraints have to be considered as these sensors are capable of providing a 3D data stream in real time. This thesis proposed the use of Self-Organizing Maps (SOMs) as a 3D representation model. In particular, we proposed the use of the Growing Neural Gas (GNG) network, which has been successfully used for clustering, pattern recognition and topology representation of multi-dimensional data. Until now, Self-Organizing Maps have been primarily computed offline and their application in 3D data has mainly focused on free noise models, without considering time constraints. It is proposed a hardware implementation leveraging the computing power of modern GPUs, which takes advantage of a new paradigm coined as General-Purpose Computing on Graphics Processing Units (GPGPU). The proposed methods were applied to different problem and applications in the area of computer vision such as the recognition and localization of objects, visual surveillance or 3D reconstruction.

Nowadays, new computers generation provides a high performance that enables to build computationally expensive computer vision applications applied to mobile robotics. Building a map of the environment is a common task of a robot and is an essential part to allow the robots to move through these environments. Traditionally, mobile robots used a combination of several sensors from different technologies. Lasers, sonars and contact sensors have been typically used in any mobile robotic architecture, however color cameras are an important sensor due to we want the robots to use the same information that humans to sense and move through the different environments. Color cameras are cheap and flexible but a lot of work need to be done to give robots enough visual understanding of the scenes. Computer vision algorithms are computational complex problems but nowadays robots have access to different and powerful architectures that can be used for mobile robotics purposes. The advent of low-cost RGB-D sensors like Microsoft Kinect which provide 3D colored point clouds at high frame rates made the computer vision even more relevant in the mobile robotics field. The combination of visual and 3D data allows the systems to use both computer vision and 3D processing and therefore to be aware of more details of the surrounding environment. The research described in this thesis was motivated by the need of scene mapping. Being aware of the surrounding environment is a key feature in many mobile robotics applications from simple robotic navigation to complex surveillance applications. In addition, the acquisition of a 3D model of the scenes is useful in many areas as video games scene modeling where well-known places are reconstructed and added to game systems or advertising where once you get the 3D model of one room the system can add furniture pieces using augmented reality techniques. In this thesis we perform an experimental study of the state-of-the-art registration methods to find which one fits better to our scene mapping purposes. Different methods are tested and analyzed on different scene distributions of visual and geometry appearance. In addition, this thesis proposes two methods for 3d data compression and representation of 3D maps. Our 3D representation proposal is based on the use of Growing Neural Gas (GNG) method. This Self-Organizing Maps (SOMs) has been successfully used for clustering, pattern recognition and topology representation of various kind of data. Until now, Self-Organizing Maps have been primarily computed offline and their application in 3D data has mainly focused on free noise models without considering time constraints. Self-organising neural models have the ability to provide a good representation of the input space. In particular, the Growing Neural Gas (GNG) is a suitable model because of its flexibility, rapid adaptation and excellent quality of representation. However, this type of learning is time consuming, specially for high-dimensional input data. Since real applications often work under time constraints, it is necessary to adapt the learning process in order to complete it in a predefined time. This thesis proposes a hardware implementation leveraging the computing power of modern GPUs which takes advantage of a new paradigm coined as General-Purpose Computing on Graphics Processing Units (GPGPU). Our proposed geometrical 3D compression method seeks to reduce the 3D information using plane detection as basic structure to compress the data. This is due to our target environments are man-made and therefore there are a lot of points that belong to a plane surface. Our proposed method is able to get good compression results in those man-made scenarios. The detected and compressed planes can be also used in other applications as surface reconstruction or plane-based registration algorithms. Finally, we have also demonstrated the goodness of the GPU technologies getting a high performance implementation of a CAD/CAM common technique called Virtual Digitizing.

We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface from a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. This latter contribution receives significant focus in this thesis as it is crucial to obtain the desired unfolding effect derived from the first energy functional and flow. Without it, the resulting topology changes render the unconstrained evolution uninteresting for the purpose of cortical visualization, exploration, and inspection. The third is a method that dramatically improves the computational speed of the 3D topology-preservation approach by creating a tree structure of the triangulated surface and using a recursion technique.