Finding the Collineation between Two Projective Reconstructions

The problem of nding the collineation between two 3-D projective reconstructions has been proved to be useful for a variety of tasks such as calibration of a stereo rig and 3-D a ne 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. In spite of this potential, methods for properly estimating such a projective transformation have received little attention in the past. In this paper we describe linear, non-linear and robust methods for estimating this transformation. We test the numerical stability of these methods with respect to image noise and to the number of matched points. Finally we brie y describe three applications: stereo image transfer, Euclidean reconstruction, and self calibration of a stereoscopic camera pair. Key-words: projective reconstruction, 3-D projective transformation, image transfer, projective to Euclidean mapping