Finding the collineation between two projective reconstructions

Abstract

The problem of finding the collineation between two 3D projective reconstructions has been proved to be useful for a variety of tasks such as calibration of a stereo rig and 3D affine and/or Euclidean reconstruction. Moreover, such a collineation may well be viewed as a point transfer method between two image pairs with applications to visually guided robot control. Despite this potential, methods for properly estimating such a projective transformation have received little attention in the past. In this paper we describe linear, nonlinear, and robust methods for estimating this transformation. We test the numerical stability of these methods with respect to image noise, to the number of matched points, and as a function of the number of outliers. Finally, we devise a specialized technique for the case where 3D Euclidean coordinates are provided for a number of control points.