Efficient view point selection for silhouettes of convex polyhedra

AbstractSilhouettes of polyhedra are an important primitive in application areas such as machine vision and computer graphics. In this paper, we study how to select view points of convex polyhedra such that the silhouette satisfies certain properties. Specifically, we give algorithms to find all projections of a convex polyhedron such that a given set of edges, faces and/or vertices appear on the silhouette.We present an algorithm to solve this problem in O(k2) time for k edges. For orthogonal projections, we give an improved algorithm that is fully adaptive in the number l of connected components formed by the edges, and has a time complexity of O(klogk+kl). We then generalize this algorithm to edges and/or faces appearing on the silhouette

3D regularized B-spline surface reconstruction from occluding contours of a sequence of images

The three dimensional surface reconstruction of a non polyhedral object is a difficult problem in computer vision . In this paper, a new method for reconstructing three dimensional surface from the recovered motion of occluding contours is presented through calibrated image sequences . We use the uniform bicubic Bspline surface patches to give a parametric representation of an object surface . Finally, the problem of three dimensional B-spline surface patches reconstruction is equivalent to find their control points by solving a nonlinear system . Two numerical methods are outlined : Levenberg-Marquardt, Quasi-Newton . To avoid the classic camera calibration that needs a calibration pattern, we propose a direct nonlinear method of the autocalibration of a camera using the stable points in the scene. Our approach can be applied in the case where the camera is calibrated, the object is smooth, specifically, that its surface is at least C2. Results for reconstruction based on synthetic and real data are presented .La reconstruction de surfaces tridimensionnelles d'un objet non polyédrique est un problème difficile de la vision par ordinateur. Dans cet article, une nouvelle approche est presentée pour la reconstruction des surfaces tridimensionnelles à partir de l'observation du mouvement des contours occultants dans une séquence d'images calibrées. La surface de cet objet est modélisée par des surfaces B-splines uniformes et bicubiques. Nous ramenons le problème de la reconstruction des surfaces au problème de résolution d'un système d'équations non linéaires déterminant leurs points de contrôle. Deux méthodes numériques de résolution du problème sont utilisées: Levenberg-Marquardt et Quasi-Newton. Pour éviter le calibrage classique nécessitant une mire, nous avons utilisé des points stables de la scène pour autocalibrer la caméra. L'approche proposée s'applique dans le cas d'un mouvement d'une caméra calibrée avec des surfaces C2. Des résultats expérimentaux sur des données simulées et réelles sont présentés

Viewpoint From Occluding Contour

In this paper we present the geometry and the algorithms for organizing a viewercentered representation of the occluding contour of polyhedra. The contour is computed from a polyhedral boundary model as it would appear under orthographic projection into the image plane from every viewpoint on the view sphere. Using this representation, we show how to derive constraints on regions in viewpoint space from the relationship between detected image features and our precomputed contour model. Such constraints are based on both qualitative (viewpoint extent) and quantitative (angle measurements and relative geometry) information that has been precomputed about how the contour appears in the image plane as a set of projected curves and T-junctions from self-occlusion. The results we show from an experimental system demonstrate that features of the occluding contour can be computed in a model-based framework, and and their geometry constrains the viewpoints from which a model will pro..