Abstract: We describe an equivalence of categories between the category of mixed Hodge structures and a category of equivariant vector bundles on a toric model of the complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalizes the notion of R-split mixed Hodge structure and give calculations for the first group of cohomology of possibly non smooth or non-complete curves of genus 0 and 1. Finally, we describe some extension groups of mixed Hodge structures in terms of equivariant extensions of coherent sheaves. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Abstract: A common way to model multi-class classification problems is by means of Error-Correcting Output Codes (ECOC). Given a multi-class problem, the ECOC technique designs a codeword for each class, where each position of the code identifies the membership of the class for a given binary problem.A classification decision is obtained by assigning the label of the class with the closest code. In this paper, we overview the state-of-the-art on ECOC designs and test them in real applications. Results on different multi-class data sets show the benefits of using the ensemble of classifiers when categorizing objects in images.

Abstract: One of the most widely used assumptions in supervised learning is that data is independent and identically distributed. This assumption does not hold true in many real cases. Sequential learning is the discipline of machine learning that deals with dependent data such that neighboring examples exhibit some kind of relationship. In the literature, there are different approaches that try to capture and exploit this correlation, by means of different methodologies. In this paper we focus on meta-learning strategies and, in particular, the stacked sequential learning approach. The main contribution of this work is two-fold: first, we generalize the stacked sequential learning. This generalization reflects the key role of neighboring interactions modeling. Second, we propose an effective and efficient way of capturing and exploiting sequential correlations that takes into account long-range interactions by means of a multi-scale pyramidal decomposition of the predicted labels. Additionally, this new method subsumes the standard stacked sequential learning approach. We tested the proposed method on two different classification tasks: text lines classification in a FAQ data set and image classification. Results on these tasks clearly show that our approach outperforms the standard stacked sequential learning. Moreover, we show that the proposed method allows to control the trade-off between the detail and the desired range of the interactions.

Abstract: Deep understanding of myocardial structure of the heart would unravel crucial knowledge for clinical and medical procedures. Although the muscular architecture of the heart has been debated by countless researchers, the controversy is still alive. Diffusion Tensor MRI, DT-MRI, is a unique imaging technique for computational validation of the muscular structure of the heart. By the complex arrangement of myocites, existing techniques can not provide comprehensive descriptions of the global muscular architecture. In this paper we introduce a multiresolution reconstruction technique based on DT-MRI streamlining for simplified global myocardial model generation. Our reconstructions can restore the most complex myocardial structures and indicate a global helical organization

Abstract: Object recoloring is one of the most popular photo-editing tasks. The problem of object recoloring is highly under-constrained, and existing recoloring methods limit their application to objects lit by a white illuminant. Application of these methods to real-world scenes lit by colored illuminants, multiple illuminants, or interreflections, results in unrealistic recoloring of objects. In this paper, we focus on the recoloring of single-colored objects presegmented from their background. The single-color constraint allows us to fit a more comprehensive physical model to the object. We demonstrate that this permits us to perform realistic recoloring of objects lit by non-white illuminants, and multiple illuminants. Moreover, the model allows for more realistic handling of illuminant alteration of the scene. Recoloring results captured by uncalibrated cameras demonstrate that the proposed framework obtains realistic recoloring for complex natural images. Furthermore we use the model to transfer color between objects and show that the results are more realistic than existing color transfer methods.

Abstract: The classification of large number of object categories is a challenging trend in the Pattern Recognition field. In the literature, this is often addressed using an ensemble of classifiers . In this scope, the Error-Correcting Output Codes framework has demonstrated to be a powerful tool for combining classifiers. However, most of the state-of-the-art ECOC approaches use a linear or exponential number of classifiers, making the discrimination of a large number of classes unfeasible. In this paper, we explore and propose a compact design of ECOC in terms of the number of classifiers. Evolutionary computation is used for tuning the parameters of the classifiers and looking for the best compact ECOC code configuration. The results over several public UCI data sets and different multi-class Computer Vision problems show that the proposed methodology obtains comparable (even better) results than the state-of-the-art ECOC methodologies with far less number of dichotomizers.

Abstract: In this paper we present a computer vision system for daytime vehicle detection and localization, an essential step in the development of several types of advanced driver assistance systems. It has a reduced processing time and high accuracy thanks to the combination of vehicle detection with lane-markings estimation and temporal tracking of both vehicles and lane markings. Concerning vehicle detection, our main contribution is a frame scanning process that inspects images according to the geometry of image formation, and with an Adaboost-based detector that is robust to the variability in the different vehicle types (car, van, truck) and lighting conditions. In addition, we propose a new method to estimate the most likely three-dimensional locations of vehicles on the road ahead. With regards to the lane-markings estimation component, we have two main contributions. First, we employ a different image feature to the other commonly used edges: we use ridges, which are better suited to this problem. Second, we adapt RANSAC, a generic robust estimation method, to fit a parametric model of a pair of lane markings to the image features. We qualitatively assess our vehicle detection system in sequences captured on several road types and under very different lighting conditions. The processed videos are available on a web page associated with this paper. A quantitative evaluation of the system has shown quite accurate results (a low number of false positives and negatives) at a reasonable computation time.

Abstract: Human detection is a key component in fields such as advanced driving assistance and video surveillance. However, even detecting non-occluded standing humans remains a challenge of intensive research. Finding good features to build human models for further detection is probably one of the most important issues to face. Currently, shape, texture and motion features have deserve extensive attention in the literature. However, color-based features, which are important in other domains (e.g., image categorization), have received much less attention. In fact, the use of RGB color space has become a kind of choice by default. The focus has been put in developing first and second order features on top of RGB space (e.g., HOG and co-occurrence matrices, resp.). In this paper we evaluate the opponent colors (OPP) space as a biologically inspired alternative for human detection. In particular, by feeding OPP space in the baseline framework of Dalal et al. for human detection (based on RGB, HOG and linear SVM), we will obtain better detection performance than by using RGB space. This is a relevant result since, up to the best of our knowledge, OPP space has not been previously used for human detection. This suggests that in the future it could be worth to compute co-occurrence matrices, self-similarity features, etc., also on top of OPP space, i.e., as we have done with HOG in this paper.