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

Abstract: Shape representation and registration are two important problems in computer vision and graphics. Representing the given cloud of points through an implicit function provides a higher level information describing the data. This representation can be more compact more robust to noise and outliers, hence it can be exploited in different computer vision application. In the first part of this thesis implicit shape representations, including both implicit B-spline and polynomial, are tackled. First, an approximation of a geometric distance is proposed to measure the closeness of the given cloud of points and the implicit surface. The analysis of the proposed distance shows an accurate estimation with smooth behavior. The distance by itself is used in a RANSAC based quadratic fitting method. Moreover, since the gradient information of the distance with respect to the surface parameters can be analytically computed, it is used in Levenberg-Marquadt algorithm to refine the surface parameters. In a different approach, an algebraic fitting method is used to represent an object through implicit B-splines. The outcome is a smooth flexible surface and can be represented in different levels from coarse to fine. This property has been exploited to solve the registration problem in the second part of the thesis. In the proposed registration technique the model set is replaced with an implicit representation provided in the first part; then, the point-to-point registration is converted to a point-to-model one in a higher level. This registration error can benefit from different distance estimations to speed up the registration process even without need of correspondence search. Finally, the non-rigid registration problem is tackled through a quadratic distance approximation that is based on the curvature information of the model set. This approximation is used in a free form deformation model to update its control lattice. Then it is shown how an accurate distance approximation can benefit non-rigid registration problems.

Abstract: This chapter describes a stereo-based algorithm that provides candidate image windows to a latter 2D classification stage in an on-board pedestrian detection system. The proposed algorithm, which consists of three stages, is based on the use of both stereo imaging and scene prior knowledge (i.e., pedestrians are on the ground) to reduce the candidate searching space. First, a successful road surface fitting algorithm provides estimates on the relative ground-camera pose. This stage directs the search toward the road area thus avoiding irrelevant regions like the sky. Then, three different schemes are used to scan the estimated road surface with pedestrian-sized windows: (a) uniformly distributed through the road surface (3D); (b) uniformly distributed through the image (2D); (c) not uniformly distributed but according to a quadratic function (combined 2D-3D). Finally, the set of candidate windows is reduced by analyzing their 3D content. Experimental results of the proposed algorithm, together with statistics of searching space reduction are provided.