Abstract: Non-linear dimensionality reduction techniques are affected by two critical aspects: (i) the design of the adjacency graphs, and (ii) the embedding of new test data-the out-of-sample problem. For the first aspect, the proposed solutions, in general, were heuristically driven. For the second aspect, the difficulty resides in finding an accurate mapping that transfers unseen data samples into an existing manifold. Past works addressing these two aspects were heavily parametric in the sense that the optimal performance is only achieved for a suitable parameter choice that should be known in advance. In this paper, we demonstrate that the sparse representation theory not only serves for automatic graph construction as shown in recent works, but also represents an accurate alternative for out-of-sample embedding. Considering for a case study the Laplacian Eigenmaps, we applied our method to the face recognition problem. To evaluate the effectiveness of the proposed out-of-sample embedding, experiments are conducted using the K-nearest neighbor (KNN) and Kernel Support Vector Machines (KSVM) classifiers on six public face datasets. The experimental results show that the proposed model is able to achieve high categorization effectiveness as well as high consistency with non-linear embeddings/manifolds obtained in batch modes.

Abstract: A novel technique for rank estimation in 3D multibody motion segmentation is proposed. It is based on the study of the frequency spectra of moving rigid objects and does not use or assume a prior knowledge of the objects contained in the scene (i.e. number of objects and motion). The significance of rank estimation on multibody motion segmentation results is shown by using two motion segmentation algorithms over both synthetic and real data.

Abstract: In two previous experiments [Parraga et al, 2009 J. of Im. Sci. and Tech 53(3) 031106; Benavente et al,2009 Perception 38 ECVP Supplement, 36] the boundaries of basic colour categories were measured.
In the first experiment, samples were presented in isolation (ie on a dark background) and boundaries were measured using a yes/no paradigm. In the second, subjects adjusted the chromaticity of a sample presented on a random Mondrian background to find the boundary between pairs of adjacent colours.
Results from these experiments showed significant dierences but it was not possible to conclude whether this discrepancy was due to the absence/presence of a colourful background or to the dierences in the paradigms used. In this work, we settle this question by repeating the first experiment (ie samples presented on a dark background) using the second paradigm. A comparison of results shows that
although boundary locations are very similar, boundaries measured in context are significantly dierent(more diuse) than those measured in isolation (confirmed by a Student’s t-test analysis on the subject’s answers statistical distributions). In addition, we completed the mapping of colour name space by measuring the boundaries between chromatic colours and the achromatic centre. With these results we
completed our parametric fuzzy-sets model of colour naming space.

Abstract: This paper introduces a method to obtain a detailed 3D reconstruction of facial skin from a single RGB image.
To this end, we propose the exclusive use of an input image without requiring any information about the observed material nor training data to model the wrinkle properties. They are detected and characterized directly from the image via a simple and effective parametric model, determining several features such as location, orientation, width, and height. With these ingredients, we propose to minimize a photometric error to retrieve the final detailed 3D map, which is initialized by current techniques based on deep learning. In contrast with other approaches, we only require estimating a depth parameter, making our approach fast and intuitive. Extensive experimental evaluation is presented in a wide variety of synthetic and real images, including different skin properties and facial
expressions. In all cases, our method outperforms the current approaches regarding 3D reconstruction accuracy, providing striking results for both large and fine wrinkles.

Abstract: Motion perception is an amazing innate ability of the creatures on the planet. This adroitness entails a functional advantage that enables species to compete better in the wild. The motion perception ability is usually employed at different levels, allowing from the simplest interaction with the ’physis’ up to the most transcendental survival tasks. Among the five classical perception system , vision is the most widely used in the motion perception field. Millions years of evolution have led to a highly specialized visual system in humans, which is characterized by a tremendous accuracy as well as an extraordinary robustness. Although humans and an immense diversity of species can distinguish moving object with a seeming simplicity, it has proven to be a difficult and non trivial problem from a computational perspective. In the field of Computer Vision, the detection of moving objects is a challenging and fundamental research area. This can be referred to as the ’origin’ of vast and numerous vision-based research sub-areas. Nevertheless, from the bottom to the top of this hierarchical analysis, the foundations still relies on when and where motion has occurred in an image. Pixels corresponding to moving objects in image sequences can be identified by measuring changes in their values. However, a pixel’s value (representing a combination of color and brightness) could also vary due to other factors such as: variation in scene illumination, camera noise and nonlinear sensor responses among others. The challenge lies in detecting if the changes in pixels’ value are caused by a genuine object movement or not. An additional challenging aspect in motion detection is represented by moving cast shadows. The paradox arises because a moving object and its cast shadow share similar motion patterns. However, a moving cast shadow is not a moving object. In fact, a shadow represents a photometric illumination effect caused by the relative position of the object with respect to the light sources. Shadow detection methods are mainly divided in two domains depending on the application field. One normally consists of static images where shadows are casted by static objects, whereas the second one is referred to image sequences where shadows are casted by moving objects. For the first case, shadows can provide additional geometric and semantic cues about shape and position of its casting object as well as the localization of the light source. Although the previous information can be extracted from static images as well as video sequences, the main focus in the second area is usually change detection, scene matching or surveillance. In this context, a shadow can severely affect with the analysis and interpretation of the scene. The work done in the thesis is focused on the second case, thus it addresses the problem of detection and removal of moving cast shadows in video sequences in order to enhance the detection of moving object.