Motion Recovery by Integrating over the Joint Image Manifold

Recovery of epipolar geometry is a fundamental problem in computer vision. The introduction of the “joint image manifold” (JIM) allows to treat the recovery of camera motion and epipolar geometry as the problem of fitting a manifold to the data measured in a stereo pair. The manifold has a singularity and boundary, therefore special care must be taken when fitting it. Four fitting methods are discussed—direct, algebraic, geometric, and the integrated maximum likelihood (IML) based method. The first three methods are the exact analogues of three common methods for recovering epipolar geometry. The more recently introduced IML method seeks the manifold which has the highest “support,” in the sense that the largest measure of its points are close to the data. While computationally more intensive than the other methods, its results are better in some scenarios. Both simulations and experiments suggest that the advantages of IML manifold fitting carry over to the task of recovering epipolar geometry, especially when the extent of the data and/or the motion are small.