Catálogo de publicaciones - libros

We present a novel algorithm for recovering a smooth manifold of unknown dimension and topology from a set of points known to belong to it. Numerous applications in computer vision can be naturally interpreted as instanciations of this fundamental problem. Recently, a non-iterative discrete approach, , has been introduced to solve this problem and has been applied successfully to various applications. As an alternative, we propose a of this problem in the setting and derive an algorithm which approximates its solutions. This method and tensor voting are somewhat the differential and integral form of one another. Although iterative methods are slower in general, the strength of the suggested method is that it can easily be applied when the ambient space is not Euclidean, which is important in many applications. The algorithm consists in solving a partial differential equation that performs a special anisotropic diffusion on an implicit representation of the known set of points. This results in connecting isolated neighbouring points. This approach is very simple, mathematically sound, robust and powerful since it handles in a homogeneous way manifolds of arbitrary dimension and topology, embedded in Euclidean or non-Euclidean spaces, with or without border. We shall present this approach and demonstrate both its benefits and shortcomings in two different contexts: (i) data visual analysis, (ii) skin detection in color images.

We address the problem of estimating the three-dimensional shape and radiance of a surface in space from images obtained with different focal settings. We pose the problem as an infinite-dimensional optimization and seek for the global shape of the surface by numerically solving a partial differential equation (PDE). Our method has the advantage of being global (so that regularization can be imposed explicitly), efficient (we use level set methods to solve the PDE), and geometrically correct (we do not assume a shift-invariant imaging model, and therefore are not restricted to equifocal surfaces).

We present a method to solve shape-from-shadow using shadow graphs which give a new graph-based representation for shadow constraints. It can be shown that the shadow graph alone is enough to solve the shape-from-shadow problem from a dense set of images. Shadow graphs provide a simpler and more systematic approach to represent and integrate shadow constraints from multiple images. To recover shape from a sparse set of images, we propose a method for integrated shadow and shading constraints. Previous shape-from-shadow algorithms do not consider shading constraints while shape-from-shading usually assumes there is no shadow. Our method is based on collecting a set of images from a fixed viewpoint as a known light source changes its position. It first builds a shadow graph from shadow constraints from which an upper bound for each pixel can be derived if the height values of a small number of pixels are initialized properly. Finally, a constrained optimization procedure is designed to make the results from shape-from-shading consistent with the upper bounds derived from the shadow constraints. Our technique is demonstrated on both synthetic and real imagery.

Lambertian photometric stereo with uncalibrated light directions and intensities determines the surface normals only up to an invertible linear transformation. We show that if object reflectance is a sum of Lambertian and specular terms, the ambiguity reduces into a 2dof group of transformations (compositions of isotropic scaling, rotation around the viewing vector, and change in coordinate frame handedness).

Such ambiguity reduction is implied by the constraint which requires that all lights reflected around corresponding specular normals must give the same vector (the viewing direction). To employ the constraint, identification of specularities in images corresponding to four different point lights in general configuration suffices. When the consistent viewpoint constraint is combined with integrability constraint, binary convex/concave ambiguity composed with isotropic scaling results. The approach is verified experimentally.

We observe that an analogical result applies to the case of uncalibrated geometric stereo with four affine cameras in a general configuration observing specularities from a single distant point light source.

In this paper we provide a direct link between the EM algorithm and matrix factorisation methods for grouping via pairwise clustering. We commence by placing the pairwise clustering process in the setting of the EM algorithm. We represent the clustering process using two sets of variables which need to be estimated. The first of these are cluster-membership indicators. The second are revised link-weights between pairs of nodes. We work with a model of the grouping process in which both sets of variables are drawn from a Bernoulli distribution. The main contributioin in this paper is to show how the cluster-memberships may be estimated using the leading eigenvector of the revised link-weight matrices. We also establish convergence conditions for the resulting pair-wise clustering process. The method is demonstrated on the problem of multiple moving object segmentation.

Level Set Representations, the pioneering framework introduced by Osher and Sethian [] is the most common choice for the implementation of variational frameworks in Computer Vision since it is implicit, intrinsic, parameter and topology free. However, many Computer vision applications refer to entities with physical meanings that follow a shape form with a certain degree of variability. In this paper, we propose a novel energetic form to introduce shape constraints to level set representations. This formulation exploits all advantages of these representations resulting on a very elegant approach that can deal with a large number of parametric as well as continuous transformations. Furthermore, it can be combined with existing well known level set-based segmentation approaches leading to paradigms that can deal with noisy, occluded and missing or physically corrupted data. Encouraging experimental results are obtained using synthetic and real images.

We present a variational integration of nonlinear shape statistics into a Mumford—Shah based segmentation process. The nonlinear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel PCA to a stochastic framework.

The idea is to assume that the training data forms a Gaussian distribution after a nonlinear mapping to a potentially higher-dimensional feature space. Due to the strong nonlinearity, the corresponding density estimate in the original space is highly non–Gaussian. It can capture essentially arbitrary data distributions (e.g. multiple clusters, ring- or banana–shaped manifolds).

Applications of the nonlinear shape statistics in segmentation and tracking of 2D and 3D objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real—world shapes. It makes the segmentation process robust against misleading information due to noise, clutter and occlusion.

In this paper we present a novel class-based segmentation method, which is guided by a stored representation of the shape of objects within a general class (such as horse images). The approach is different from bottom-up segmentation methods that primarily use the continuity of grey-level, texture, and bounding contours. We show that the method leads to markedly improved segmentation results and can deal with significant variation in shape and varying backgrounds. We discuss the relative merits of class-specific and general image-based segmentation methods and suggest how they can be usefully combined.

This paper proposes a quasi-dense reconstruction from uncalibrated sequence. The main innovation is that all geometry is computed based on re-sampled quasi-dense correspondences rather than the standard sparse points of interest. It not only produces more accurate and robust reconstruction due to highly redundant and well spread input data, but also fills the gap of insufficiency of sparse reconstruction for visualization application. The computational engine is the quasi-dense 2-view and the quasi-dense 3-view algorithms developed in this paper. Experiments on real sequences demonstrate the superior performance of quasi-dense w.r.t. sparse reconstruction both in accuracy and robustness.

The geometry of two uncalibrated views obtained with a parabolic catadioptric device is the subject of this paper. We introduce the notion of circle space, a natural representation of line images, and the set of incidence preserving transformations on this circle space which happens to equal the Lorentz group. In this space, there is a bilinear constraint on transformed image coordinates in two parabolic catadioptric views involving what we call the catadioptric fundamental matrix. We prove that the angle between corresponding epipolar curves is preserved and that the transformed image of the absolute conic is in the kernel of that matrix, thus enabling a Euclidean reconstruction from two views. We establish the necessary and sufficient conditions for a matrix to be a catadioptric fundamental matrix.