CSAIL Event Calendar: Previous Series
Projective Visual Hulls
Speaker: Jean Ponce , University of Illinois at Urbana-Champaign
I will present in this talk an image-based algorithm for computing the visual hull of a smooth surface from a finite number of weakly calibrated perspective views. This algorithm exploits the essentially projective structure of the visual hull to compute a combinatorial description of its boundary without any knowledge of the cameras' (Euclidean) positions and intrinsic parameters. After setting up the problem, I will discuss (informally) its theoretical grounding in oriented projective geometry and differential projective geometry. The latter field is largely untapped by the computer vision community but offers the right framework for relating smooth curves and surfaces to their perspective images. As an example, I will consider the famous theorem of Koenderink that states that convex (resp. concave) portions of the apparent contour of a smooth surface are the projections of elliptic (resp. hyperbolic) points of this surface, and I will show that this theorem is really projective in nature, that is, it can be proven without appealing to Euclidean concepts such as curvature. After these rather theoretical considerations, I will turn to the presentation of the visual hull algorithm, and present results from a preliminary implementation.