Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

Pattern Recognition

A wealth of advanced pattern recognition algorithms are emerging from the interdiscipline between technologies of effective visual features and the human-brain cognition process. Effective visual features are made possible through the rapid developments in appropriate sensor equipments, novel filter designs, and viable information processing architectures. While the understanding of human-brain cognition process broadens the way in which the computer can perform pattern recognition tasks. The present book is intended to collect representative researches around the globe focusing on low-level vision, filter design, features and image descriptors, data mining and analysis, and biologically inspired algorithms. The 27 chapters coved in this book disclose recent advances and new ideas in promoting the techniques, technology and applications of pattern recognition

Tensor Representations for Object Classification and Detection

A key problem in object recognition is finding a suitable object representation. For historical and computational reasons, vector descriptions that encode particular statistical properties of the data have been broadly applied. However, employing tensor representation can describe the interactions of multiple factors inherent to image formation. One of the most convenient uses for tensors is to represent complex objects in order to build a discriminative description. Thus thesis has several main contributions, focusing on visual data detection (e.g. of heads or pedestrians) and classification (e.g. of head or human body orientation) in still images and on machine learning techniques to analyse tensor data. These applications are among the most studied in computer vision and are typically formulated as binary or multi-class classification problems. The applicative context of this thesis is the video surveillance, where classification and detection tasks can be very hard, due to the scarce resolution and the noise characterising sensor data. Therefore, the main goal in that context is to design algorithms that can characterise different objects of interest, especially when immersed in a cluttered background and captured at low resolution. In the different amount of machine learning approaches, the ensemble-of-classifiers demonstrated to reach excellent classification accuracy, good generalisation ability, and robustness of noisy data. For these reasons, some approaches in that class have been adopted as basic machine classification frameworks to build robust classifiers and detectors. Moreover, also kernel machines has been exploited for classification purposes, since they represent a natural learning framework for tensors

Robust signatures for 3D face registration and recognition

PhDBiometric authentication through face recognition has been an active area of research for the last few decades, motivated by its application-driven demand. The popularity of face recognition, compared to other biometric methods, is largely due to its minimum requirement of subject co-operation, relative ease of data capture and similarity to the natural way humans distinguish each other. 3D face recognition has recently received particular interest since three-dimensional face scans eliminate or reduce important limitations of 2D face images, such as illumination changes and pose variations. In fact, three-dimensional face scans are usually captured by scanners through the use of a constant structured-light source, making them invariant to environmental changes in illumination. Moreover, a single 3D scan also captures the entire face structure and allows for accurate pose normalisation. However, one of the biggest challenges that still remain in three-dimensional face scans is the sensitivity to large local deformations due to, for example, facial expressions. Due to the nature of the data, deformations bring about large changes in the 3D geometry of the scan. In addition to this, 3D scans are also characterised by noise and artefacts such as spikes and holes, which are uncommon with 2D images and requires a pre-processing stage that is speci c to the scanner used to capture the data. The aim of this thesis is to devise a face signature that is compact in size and overcomes the above mentioned limitations. We investigate the use of facial regions and landmarks towards a robust and compact face signature, and we study, implement and validate a region-based and a landmark-based face signature. Combinations of regions and landmarks are evaluated for their robustness to pose and expressions, while the matching scheme is evaluated for its robustness to noise and data artefacts

Catégorisation par mesures de dissimilitude et caractérisation d'images en multi échelle

Dans cette thèse, on introduit la métrique "Coefficient de forme" pour la classement des données de dissimilitudes. Cette approche est inspirée par l'analyse discriminante géométrique et on a défini des règles de décision pour imiter le comportement du classifieur linéaire et quadratique. Le nombre de paramètres est limité (deux par classe). On a également étendu et amélioré cette démarche avantageuse et rapide pour apprendre uniquement à partir des représentations de dissimilitudes en utilisant l'efficacité du classificateur des Machines à Vecteurs de Support. Comme contexte applicatif pour la classification par dissimilitudes, on utilise la recherche d'images à l'aide d'une représentation des images en multi échelle en utilisant la "Pyramide Réduite Différentielle". Une application pour la description de visages est développée. Des résultats de classification à partir du coefficient de forme et utilisant une version adaptée des Machines à Vecteurs de Support, sur des bases de données issues des applications du monde réel sont présentés et comparés avec d'autres méthodes de classement basées sur des dissimilitudes. Il en ressort une forte robustesse de la méthode proposée avec des perfommances supérieures ou égales aux algorithmes de l'état de l'art.The dissimilarity representation is an alternative for the use of features in the recognition of real world objects like images, spectra and time-signal. Instead of an absolute characterization of objects by a set of features, the expert or the system is asked to define a measure that estimates the dissimilarity between pairs of objects. Such a measure may also be defined for structural representations such as strings and graphs. The dissimilarity representation is potentially able to bridge structural and statistical pattern recognition. In this thesis we introduce a new fast Mahalanobis-like metric the Shape Coefficient for classification of dissimilarity data. Our approach is inspired by the Geometrical Discriminant Analysis and we have defined decision rules to mimic the behavior of the linear and quadratic classifier. The number of parameters is limited (two per class). We also expand and ameliorate this advantageous and rapid adaptive approach to learn only from dissimilarity representations by using the effectiveness of the Support Vector Machines classifier for real-world classification tasks. Several methods for incorporating dissimilarity representations are presented, investigated and compared to the Shape Coefficient in this thesis: Pekalska and Duin prototype dissimilarity based classifiers; Haasdonk's kernel based SVM classifier; KNN classifier. Numerical experiments on artificial and real data show interesting behavior compared to Support Vector Machines and to KNN classifier: (a) lower or equivalent error rate, (b) equivalent CPU time, (c) more robustness with sparse dissimilarity data. The experimental results on real world dissimilarity databases show that the Shape Coefficient can be an alternative approach to these known methods and can be as effective as them in terms of accuracy for classification.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Trends in Mathematical Imaging and Surface Processing

Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments

3D object reconstruction using computer vision : reconstruction and characterization applications for external human anatomical structures

Tese de doutoramento. Engenharia Informática. Faculdade de Engenharia. Universidade do Porto. 201