Scene reconstruction based on constraints: Details on the equation system decomposition

Abstract

We present a new approach to 3D scene modeling based on geometrical constraints. Contrary to most of the existing methods, we obtain 3D scene models that respect the given constraints exactly. Our tool can describe a large variety of linear and non-linear constraints in a flexible way. Our approach is based on a dictionary of so-called r-methods, based on theorems in geometry, which can solve a subset of geometrical constraints in a very efficient way. Two fast and complete graph-based algorithms are proposed to find a reduced parameterization of a scene, and to decompose the equation system in a sequence of r-methods. © Springer-Verlag 2003.