Visual Hull from Imprecise Polyhedral Scene

Abstract

Abstract-We present a framework to compute the visual hull of a polyhedral scene, in which the vertices of the polyhedra are given with some imprecision. Two kinds of visual event surfaces, namely VE and EEE surfaces are modelled under the geometric framework to derive their counterpart object, namely partial VE and partial EEE surfaces, which contain the exact information of all possible visual event surfaces given the imprecision in the input. Correspondingly, a new definition of visual number is proposed to label the cells of Euclidean space partitioned by partial VE and partial EEE surfaces. The overall algorithm maintains the same computational complexity as the classical method and generates a partial visual hull which converges to the classical visual hull as the input converges to an exact value.

Concurrency Relations between Digital Planes

“…Thus D(U, V ) is the topological closure of the set defined by (1). In general a domain is a convex polyhedron.…”

“…We will allow special kinds of domains. A domain will be a planar segment (or polygon) in R 3 if we require that the plane that separates two point sets also has to pass through a given point p 1 . Similarly, a domain will be a line segment if the separating plane has to pass through two points, and trivially, a domain is a single point if we require that the separating plane has to pass through three given points.…”

“…Part of this work is motivated by the renewed interest in visual hulls [1]. Although known for some time [2,3], multi-camera systems now provide means to acquire detailed visual hulls in real time.…”