Catálogo de publicaciones - libros

We analyze the problem of recovering the shape of a mirror surface. We generalize the results of [], where the special case of planar and spherical mirror surfaces was considered, extending that analysis to any smooth surface. A calibrated scene composed of lines passing through a point is assumed. The lines are reflected by the mirror surface onto the image plane of a calibrated camera, where the intersection and orientation of such reflections are measured. The relationship between the local geometry of the surface around the point of reflection and the measurements is analyzed. We give necessary and sufficient conditions, as well as a practical algorithm, for recovering first order local information (positions and normals) when three intersecting lines are visible. A small number of ‘ghost solutions’ may arise. Second order surface geometry may also be obtained up to one unknown parameter. Experimental results with real mirror surfaces are presented.

This paper deals with the matching of geometric shapes. Our primary contribution is the use of a simple, robust, rich and efficient way to represent shapes, the level set representations according to singed distance transforms. Based on these representations we propose a variational framework for global as well as local shape registration that can be extended to deal with structures of higher dimension. The optimization criterion is invariant to rotation, translation and scale and combines efficiently a global motion model with local pixel-wise deformations. Promising results are obtained on examples showing small and large global deformations as well as arbitrary topological changes.

This article presents an approach to the shape from shading problem which is based upon the notion of viscosity solutions to the shading partial differential equation, in effect a Hamilton-Jacobi equation. The power of this approach is twofolds: 1) it allows nonsmooth, i.e. nondifferentiable, solutions which allows to recover objects with sharp troughs and creases and 2) it provides a framework for deriving a numerical scheme for computing approximations on a discrete grid of these solutions as well as for proving its correctness, i.e. the convergence of these approximations to the solution when the grid size vanishes.

Our work extends previous work in the area in three aspects. First, it deals with the case of a general illumination in a simpler and a more general way (since they assume that the solutions are continuously differentiable) than in the work of Dupuis and Oliensis []. Second, it allows us to prove the existence and uniqueness of ”” solutions to the shading equation in a more general setting (general direction of illumination) than in the work of Rouy and Tourin [], thereby extending the applicability of shape from shading methods to more realistic scenes. Third, it allows us to produce an approximation scheme for computing approximations of the ”continuous” solution on a discrete grid as well as a proof of their convergence toward that solution.

This paper deals with the three-dimensional reconstruction of an underwater environment from multiple acoustic range views acquired by a remotely operated vehicle. The problem is made challenging by the very noisy nature of the data, the low resolution and the narrow field of view of the sensor. Our contribution is twofold: first, we introduce a statistically sound thresholding (the X84 rejection rule) to improve ICP robustness against noise and non-overlapping data. Second, we propose a new global registration technique to distribute registration errors evenly across all views. Our approach does not use data points after the first pairwise registration, for it works only on the transformations. Therefore, it is fast and occupies only a small memory. Experimental results suggest that ICP with X84 performs better than Zhang’s ICP, and that the global registration technique is effective in reducing and equalizing the error.

The multiple view geometry of static scenes is now well understood. Recently attention was turned to dynamic scenes where scene points may move while the cameras move. The triangulation of linear trajectories is now well handled. The case of quadratic trajectories also received some attention.

We present a complete generalization and address the Problem of general trajectory triangulation of moving points from non-synchronized cameras. Our method is based on a particular representation of curves (trajectories) where a curve is represented by a family of hypersurfaces in the projective space ℙ. This representation is linear, even for highly non-linear trajectories. We show how this representation allows the recovery of the trajectory of a moving point from non-synchronized sequences. We show how this representation can be converted into a more standard representation. We also show how one can extract directly from this representation the positions of the moving point at each time instant an image was made. Experiments on synthetic data and on real images demonstrate the feasibility of our approach.

In this paper we address the problem of uncalibrated structure and motion recovery from image sequences that contain dominant planes in some of the views. Traditional approaches fail when the features common to three consecutive views are all located on a plane. This happens because in the uncalibrated case there is a fundamental ambiguity in relating the structure before and after the plane. This is, however, a situation that is often hard to avoid in man-made environments. We propose a complete approach that detects the problem and defers the computation of parameters that are ambiguous in projective space (i.e. the registration between partial reconstructions only sharing a common plane and poses of cameras only seeing planar features) till after self-calibration. Also a new linear self-calibration algorithm is proposed that couples the intrinsics between multiple subsequences. The final result is a complete metric 3D reconstruction of both structure and motion for the whole sequence. Experimental results on real image sequences show that the approach yields very good results.

This paper investigates the use of an implicit prior in Bayesian model-based 3D reconstruction of architecture from image sequences. In our previous work architecture is represented as a combination of basic primitives such as windows and doors etc, each with their own prior. The contribution of this work is to provide a global prior for the spatial organization of the basic primitives. However, it is difficult to explicitly formulate the prior on spatial organization. Instead we define an implicit representation that favours global regularities prevalent in architecture (e.g. windows lie in rows etc.). Specifying exact parameter values for this prior is problematic at best, however it is demonstrated that for a broad range of values the prior provides reasonable results. The validity of the prior is tested visually by generating synthetic buildings as draws from the prior simulated using MCMC. The result is a fully Bayesian method for structure from motion in the domain of architecture.

We consider dynamic scenes consisting of moving points whose motion is constrained to happen in one of a pencil of planes. This is for example the case when rigid objects move independently, but on a common ground plane (each point moves in one of a pencil of planes parallel to the ground plane). We consider stereo pairs of the dynamic scene, taken by a moving stereo system, that allow to obtain 3D reconstructions of the scene, for different time instants. We derive matching constraints for pairs of such 3D reconstructions, especially we introduce a simple tensor, that encapsulates parts of the motion of the stereo system and parts of the scene structure. This tensor allows to partially recover the dynamic structure of the scene. Complete recovery of structure and motion can be performed in a number of ways, e.g. using the information of static points or linear trajectories. We also develop a special self-calibration method for the considered scenario.

In this paper we examine the problem of synthesizing virtual views from scene points the scene, i.e., from scene points which are imaged by the real cameras. On one hand this provides a simple way of defining the position of the virtual camera in an uncalibrated setting. On the other hand, it implies changes in viewpoint between the virtual and real cameras. Such extreme changes in viewpoint are not typical of most New-View-Synthesis (NVS) problems.

In our algorithm the virtual view is obtained by aligning and comparing all the projections of each line-of-sight emerging from the “virtual camera” center in the input views. In contrast to most previous NVS algorithms, our approach does not require prior correspondence estimation nor any explicit 3D reconstruction. It can handle any number of input images while simultaneously using the information from all of them. However, very few images are usually enough to provide reasonable synthesis quality. We show results on real images as well as synthetic images with ground-truth.