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: Deep understanding of myocardial structure linking morphology and function of the heart would unravel crucial knowledge for medical and surgical clinical procedures and studies. Several conceptual models of myocardial fiber organization have been proposed but the lack of an automatic and objective methodology prevented an agreement. We sought to deepen in this knowledge through advanced computer graphic representations of the myocardial fiber architecture by diffusion tensor magnetic resonance imaging (DT-MRI).
We performed automatic tractography reconstruction of unsegmented DT-MRI canine heart datasets coming from the public database of the Johns Hopkins University. Full scale tractographies have been build with 200 seeds and are composed by streamlines computed on the vectorial field of primary eigenvectors given at the diffusion tensor volumes. Also, we introduced a novel multi-scale visualization technique in order to obtain a simplified tractography. This methodology allowed to keep the main geometric features of the fiber tracts, making easier to decipher the main properties of the architectural organization of the heart.
On the analysis of the output from our tractographic representations we found exact correlation with low-level details of myocardial architecture, but also with the more abstract conceptualization of a continuous helical ventricular myocardial fiber array.
Objective analysis of myocardial architecture by an automated method, including the entire myocardium and using several 3D levels of complexity, reveals a continuous helical myocardial fiber arrangement of both right and left ventricles, supporting the anatomical model of the helical ventricular myocardial band described by Torrent-Guasp.

Abstract: Empirical and mechanistic models differ in their approaches to the analysis of pharmacological effect. Whereas the parameters of the former are not physical constants those of the latter embody the nature, often complex, of biology. Empirical models are exclusively used for curve fitting, merely to characterize the shape of the E/[A] curves. Mechanistic models, on the contrary, enable the examination of mechanistic hypotheses by parameter simulation. Regretfully, the many parameters that mechanistic models may include can represent a great difficulty for curve fitting, representing, thus, a challenge for computational method development. In the present study some empirical and mechanistic models are shown and the connections, which may appear in a number of cases between them, are analyzed from the curves they yield. It may be concluded that systematic and careful curve shape analysis can be extremely useful for the understanding of receptor function, ligand classification and drug discovery, thus providing a common language for the communication between pharmacologists and medicinal chemists.

Abstract: he objective of this work is to show the importance of a good line segmentation to obtain better results in the segmentation of words of historical documents. We have used the approach developed by Manmatha and Rothfeder [1] to segment words in old handwritten documents. In their work the lines of the documents are extracted using projections. In this work, we have developed an approach to segment lines more efficiently. The new line segmentation algorithm tackles with skewed, touching and noisy lines, so it is significantly improves word segmentation. Experiments using Spanish documents from the Marriages Database of the Barcelona Cathedral show that this approach reduces the error rate by more than 20%

Abstract: The release of challenging datasets with a vast number of images, requires the development of efficient image representations and algorithms which are able to manipulate these large-scale datasets efficiently. Nowadays the Bag-of-Words (BoW) is the most successful approach in the context of object and scene classification tasks. However, its main drawback is the absence of the important spatial information. Spatial pyramids (SP) have been successfully applied to incorporate spatial information into BoW-based image representation. Observing the remarkable performance of spatial pyramids, their growing number of applications to a broad range of vision problems, and finally its geometry inclusion, a question can be asked what are the limits of spatial pyramids. Within the SP framework, the optimal way for obtaining an image spatial representation, which is able to cope with it’s most foremost shortcomings, concretely, it’s high dimensionality and the rigidity of the resulting image representation, still remains an active research domain. In summary, the main concern of this thesis is to search for the limits of spatial pyramids and try to figure out solutions for them.

Abstract: Pattern recognition is the task that aims at distinguishing objects among different classes. When such a task wants to be solved in an automatic way a crucial step is how to formally represent such patterns to the computer. Based on the different representational formalisms, we may distinguish between statistical and structural pattern recognition. The former describes objects as a set of measurements arranged in the form of what is called a feature vector. The latter assumes that relations between parts of the underlying objects need to be explicitly represented and thus it uses relational structures such as graphs for encoding their inherent information. Vector spaces are a very flexible mathematical structure that has allowed to come up with several efficient ways for the analysis of patterns under the form of feature vectors. Nevertheless, such a representation cannot explicitly cope with binary relations between parts of the objects and it is restricted to measure the exact same number of features for each pattern under study regardless of their complexity. Graph-based representations present the contrary situation. They can easily adapt to the inherent complexity of the patterns but introduce a problem of high computational complexity, hindering the design of efficient tools to process and analyse patterns.
Solving this paradox is the main goal of this thesis. The ideal situation for solving pattern recognition problems would be to represent the patterns using relational structures such as graphs, and to be able to use the wealthy repository of data processing tools from the statistical pattern recognition domain. An elegant solution to this problem is to transform the graph domain into a vector domain where any processing algorithm can be applied. In other words, by mapping each graph to a point in a vector space we automatically get access to the rich set of algorithms from the statistical domain to be applied in the graph domain. Such methodology is called graph embedding.
In this thesis we propose to associate feature vectors to graphs in a simple and very efficient way by just putting attention on the labelling information that graphs store. In particular, we count frequencies of node labels and of edges between labels. Although their locality, these features are able to robustly represent structurally global properties of graphs, when considered together in the form of a vector. We initially deal with the case of discrete attributed graphs, where features are easy to compute. The continuous case is tackled as a natural generalization of the discrete one, where rather than counting node and edge labelling instances, we count statistics of some representatives of them. We encounter how the proposed vectorial representations of graphs suffer from high dimensionality and correlation among components and we face these problems by feature selection algorithms. We also explore how the diversity of different embedding representations can be exploited in order to boost the performance of base classifiers in a multiple classifier systems framework. An extensive experimental evaluation finally shows how the methodology we propose can be efficiently computed and compete with other graph matching and embedding methodologies.

Abstract: Feature matching is a fundamental problem in Computer Vision, having multiple applications such as tracking, image classification and retrieval, shape recognition and stereo fusion. In numerous domains, it is useful to represent the local structure of the matching features to increase the matching accuracy or to make the correspondence invariant to certain transformations (affine, homography, etc. . . ). However, encoding this knowledge requires complicating the model by establishing high-order relationships between the model elements, and therefore increasing the complexity of the optimization problem.
The importance of many-to-many matching is sometimes dismissed in the literature. Most methods are restricted to perform one-to-one matching, and are usually validated on synthetic, or non-realistic datasets. In a real challenging environment, with scale, pose and illumination variations of the object of interest, as well as the presence of occlusions, clutter, and noisy observations, many-to-many matching is necessary to achieve satisfactory results. As a consequence, finding the most likely many-to-many correspondence often involves a challenging combinatorial optimization process.
In this work, we design and demonstrate matching algorithms that compute many-to-many correspondences, applied to several challenging problems. Our goal is to make use of high-order representations to improve the expressive power of the matching, at the same time that we make feasible the process of inference or optimization of such models. We effectively use graphical models as our preferred representation because they provide an elegant probabilistic framework to tackle structured prediction problems.
We introduce a matching-based tracking algorithm which performs matching between frames of a video sequence in order to solve the difficult problem of headlight tracking at night-time. We also generalise this algorithm to solve the problem of data association applied to various tracking scenarios. We demonstrate the effectiveness of such approach in real video sequences and we show that our tracking algorithm can be used to improve the accuracy of a headlight classification system.
In the second part of this work, we move from single (point) matching to dense (region) matching and we introduce a new hierarchical image representation. We make use of such model to develop a high-order many-to-many matching between pairs of images. We show that the use of high-order models in comparison to simpler models improves not only the accuracy of the results, but also the convergence speed of the inference algorithm.
Finally, we keep exploiting the idea of region matching to design a fully unsupervised image co-segmentation algorithm that is able to perform competitively with state-of-the-art supervised methods. Our method also overcomes the typical drawbacks of some of the past works, such as avoiding the necessity of variate appearances on the image backgrounds. The region matching in this case is applied to effectively exploit inter-image information. We also extend this work to perform co-segmentation of videos, being the first time that such problem is addressed, as a way to perform video object segmentation