Catálogo de publicaciones - libros

We report here on the problem of estimating a smooth planar curve γ: [0, ] → ℝ and its derivatives from an ordered sample of interpolation points γ(), γ(),...,γ(-1),γ(),...,γ(-1),γ(), where 0 = < <... < - 1 < <...< - 1 < = , and the are for 0 < < . Such situtation may appear while searching for the boundaries of planar objects or tracking the mass center of a rigid body with no times available. In this paper we assume that the distribution of coincides with . A fast algorithm, yielding based on 4-point piecewise-quadratic interpolation is analysed and tested. Our algorithm forms a substantial improvement (with respect to the speed of convergence) of piecewise 3-point quadratic Lagrange intepolation [] and []. Some related work can be found in []. Our results may be of interest in computer vision and digital image processing [], [], [], [], [] or [], computer graphics [], [], [], [], [] or [], approximation and complexity theory [], [], [], [], [] or [], and digital and computational geometry [] and [].

One of the problems that hinders the application of conventional methods for shape-from-shading to the analysis of shiny objects is the presence of local highlights. The first of these are specularities which appear at locations on the viewed object where the local surface normal is the bisector of the light source and viewing directions. Highlights also occur at the occluding limb of the object where roughness results in backscattering from microfacets which protrude above the surface. In this paper, we consider how to subtract both types of highlight from shiny surfaces in order to improve the quality of surface normal information recoverable using shape-from-shading.

Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in ( log ) time for an × × voxel grid, and computes a multiresolution approximation in ( log ) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.

We analyze walking people using a gait sequence representation that bypasses the need for frame-to-frame tracking of body parts. The gait representation maps a video sequence of silhouettes into a pair of two-dimensional spatio-temporal patterns that are near-periodic along the time axis. Mathematically, such patterns are called “frieze” patterns and associated symmetry groups “frieze groups”. With the help of a walking humanoid avatar, we explore variation in gait frieze patterns with respect to viewing angle, and find that the frieze groups of the gait patterns and their canonical tiles enable us to estimate viewing direction of human walking videos. In addition, analysis of periodic patterns allows us to determine the dynamic time warping and affine scaling that aligns two gait sequences from similar viewpoints. We also show how gait alignment can be used to perform human identification and model-based body part segmentation.

This paper presents a novel technique for medial axis noise removal. The method introduced removes the branches generated by noise on an object’s boundary without losing the fine features that are often altered or destroyed by current pruning methods. The algorithm consists of an intuitive threshold-based pruning process, followed by an automatic feature reconstruction phase that effectively recovers lost details without reintroducing noise. The result is a technique that is robust and easy to use. Tests show that the method works well on a variety of objects with significant differences in shape complexity, topology and noise characteristics.

Many approaches have been proposed to locate faces in an image. There are, however, two problems in previous facial shape models using feature points. First, the dimension of the solution space is too big since a large number of key points are needed to model a face. Second, the local features associated with the key points are assumed to be independent. Therefore, previous approaches require good initialization (which is often done manually), and may generate inaccurate localization. To automatically locate faces, we propose a novel hierarchical shape model (HSM) or multi-resolution shape models corresponding to a Gaussian pyramid of the face image. The coarsest shape model can be quickly located in the lowest resolution image. The located coarse model is then used to guide the search for a finer face model in the higher resolution image. Moreover, we devise a Global and Local (GL) distribution to learn the likelihood of the joint distribution of facial features. A novel hierarchical data-driven Markov chain Monte Carlo (HDDMCMC) approach is proposed to achieve the global optimum of face localization. Experimental results demonstrate that our algorithm produces accurate localization results quickly, bypassing the need for good initialization.

Free-form deformations (FFD) constitute an important geometric shape modification method that has been extensively investigated for computer animation and geometric modelling. In this work, we show that FFDs are also very effective to fit deformable models to the kind of noisy 3-D data that vision algorithms such as stereo tend to produce.

We advocate the use of Dirichlet Free Form Deformation (DFFD) instead of more conventional FFDs because they give us the ability to place control points at arbitrary locations rather than on a regular lattice, and thus much greater flexibility. We tested our approach on stereo data acquired from monocular video-sequences and show that it can be successfully used to reconstruct a complex object such as the whole head, including the neck and the ears, as opposed to the face only.

The instabilities of the medial axis of a shape under deformations have long been recognized as a major obstacle to its use in recognition and other applications. These instabilities, or , occur when the structure of the medial axis graph changes abruptly under deformations of shape. The recent classification of these transitions in 2D for the medial axis and for the shock graph, was a key factor both in the development of an object recognition system and an approach to perceptual organization. This paper classifies generic transitions of the 3D medial axis, by examining the order of contact of spheres with the surface, leading to an enumeration of possible transitions, which are then examined on a case by case basis. Some cases are ruled out as never occurring in any family of deformations, while others are shown to be non-generic in a one-parameter family of deformations. Finally, the remaining cases are shown to be viable by developing a specific example for each. We relate these transitions to a classification by Bogaevsky of singularities of the viscosity solutions of the Hamilton-Jacobi equation. We believe that the classification of these transitions is vital to the successful regularization of the medial axis and its use in real applications.

We present a novel method for inferring three-dimensional shape from a collection of defocused images. It is based on the observation that defocused images are the null-space of certain linear operators that depend on the three-dimensional shape of the scene as well as on the optics of the camera. Unlike most current work based on inverting the imaging model to recover the “deblurred” image and the shape of the scene, we approach the problem from a new angle by collecting a number of deblurred images, and estimating the operator that spans their left null space directly. This is done using a singular value decomposition. Since the operator depends on the depth of the scene, we repeat the procedure for a number of different depths. Once this is done, depth can be recovered in real time: the new image is projected onto each null-space, and the depth that results in the smallest residual is chosen. The most salient feature of this algorithm is its robustness: not only can one learn the operators with one camera and then use them to successfully retrieve depth from images taken with another camera, but one can even learn the operators from simulated images, and use them to retrieve depth from real images. Thus we train the system with synthetic patterns, and then use it on real data without knowledge of the optics of the camera. Another attractive feature is that the algorithm does not rely on a discretization or an approximation of the radiance of the scene (the “deblurred” image). In fact, the operator we recover is finite-dimensional, but it arises as the orthogonal projector of a semi-infinite operator that maps square-integrable radiance distributions onto images. Thus, the radiance is never approximated or represented via a finite set of filters. Instead, the rank of the operator learned from real data provides an estimate of the intrinsic dimensionality of the radiance distribution of real images. The algorithm is optimal in the sense of and can be implemented in real time.

In this paper we define a function which is defined for any polygon and which maps a given polygon into a number from the interval (0, 1]. The number can be used as an estimate of the of . The mapping has the following desirable properties:

A simple procedure for computing for a given polygon is described as well.