Fundamental Problems in Computer Vision
Projektive Geometrie, Kameramodelle und Mehrbildgeometrieprobleme
The term "Computer Vision" comprises all laws and techniques of image formation by cameras and the subsequent processing of the acquired data by computers, with the goal of infering 3D information, recognition, description and understanding of the observed scene. In the present project we consider in particular the subarea of vision that explores, describes and applies the geometric laws that relate different views of a 3D scene. This facet of vision has seen in the nineties and till this day heavy research efforts with partly impressive results.
From the theoretical point of view, the users of images with a three-dimensional content have been provided with a unified mathematical framework in which the problems can be clearly stated and analysed, avoiding to a great extent the need for dealing with special cases. This has been achieved by employing projective geometry and modelling the cameras as projective, geometric engines. In addition, using algebraic projective geometry to describe the underlying relations has turned many properties and techniques around projection, from the conservation of the cross ratio (already known to ancient Greeks) up to sophisticated 3D reconstruction techniques, to simple applications of Linear Algebra concepts. The central mathematical entities that have arisen in the course of developing the theory have been the so called multiview tensors that appear as blocks of coefficients connecting and relating the contents of the different images with each other.
The present project is concerned with all kinds of problems that emerge around the extraction of projective, affine and Euclidean information from the multiview tensors as well as with the extension of the whole framework from static to dynamic scenes.