A Canonic Framework for Sequences of Images: The Uncalibrated Case

This paper deals with the problem of analysing sequences of images taken by uncalibrated cameras. It is assumed that the correspondences between the points in the different images are known. This paper introduces a new framework for this problem. The situation of two cameras is described by the reduced fundamental matrix. Another new concept, the reduced fundamental tensor, describes the situation of three images. In the first case we get bilinear constraints on the image coordinates and in the second we get trilinear constraints. Furthermore it is shown that the trilinear constraints in general can be expressed by the bilinear and that constraints for four or more images always can be expressed by three images constraints. Finally a new canonic form for the camera matrices are given which has a lot of similarities with the calibrated case. From this description it is also possible to calculate the camera movement.