A Bayesian method for triangulation and its application to finding corresponding points

The problems of finding corresponding points from multiple perspective projection images, and estimating the 3-D points from which these points have arisen, are addressed. The problem of finding corresponding points is formulated as a hypothesis verification problem. Given a set of 2-D points, one from each of N perspective projection images, under the hypothesis that the points are projections of the same 3-D point, the coordinates of the 3-D point are estimated. The triangulation problem-the problem of estimating the coordinates of a 3-D point, given its projections in N perspective projection images-is posed as a Bayesian estimation problem, taking into account the uncertainties in the observed image points and the camera parameters. Based on the Bayesian estimate of the triangulated point, a statistical test is derived for verifying the hypothesis that the given set of image points is in correspondence. For finding N-tuples of corresponding points from N perspective projection images, this test can be used on each N-tuple of points to verify the hypothesis that that N-tuple of points is in correspondence, selecting those N-tuples that pass the hypothesis test. Experiments are described for characterizing the distance of the 3-D point estimated by the Bayesian triangulation from the true 3-D point, and characterizing the misdetection and false alarm rates of this method of finding corresponding points.