Oriented projective geometry for computer vision

Abstract

We present an extension of the usual projective geometric framework for computer vision which can nicely take into account an information that was previously not used, i.e. the fact that the pixels in an image correspond to points which lie in front of the camera. This framework, called the oriented projective geometry, retains all the advantages of the unoriented projective geometry, namely its simplicity for expressing the viewing geometry of a system of cameras, while extending its adequation to model realistic situations. We discuss the mathematical and practical issues raised by this new framework for a number of computer vision algorithms. We present different experiments where this new tool clearly helps.