Approximation of Non Projective Mapping and Their Efficient Application for a Geometrically Based 3d Point Determination Using Multiple Views

In this paper an unusual taxonomy for optical mappings is introduced based on their geometric characteristics: 1. type of projection center (single viewpoint, non single viewpoint) and 2. type of transformation (projective, non projective). Under this background we survey the multi media geometry (refraction resulting from different optical media). Strict physical models of non projective mappings can be very complex in dependency on their geometric nature. Therefor different methods for reducing the complexity exist. This paper describes a method of ascertaining a virtual camera to approximate non projective mappings by a projective model and their application for a 3D point determination using multiple views with non projective multi media geometry. As will be seen, the approximation can be used without loosing the quality of the strict model significantly. For the matching process we introduce a new algorithm for multiple views based on geometric constrains alone which uses all images simultaneously.