Radon-Based Structure from Motion without Correspondences

We present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. We assume a similarity function defined on the crossproduct of two images which assigns a weight to all feature pairs. This similarity function is integrated over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to filtering the similarity function with a Dirac function embedding the epipolar constraint. The result of this convolution is a function of the five unknown motion parameters with maxima at the positions of compatible rigid motions. The breakthrough is in the realization that the Radon transform is a filtering operator: If we assume that images are defined on spheres and the epipolar constraint is a group action of two rotations on two spheres, then the Radon transform is a convolution/correlation integral. We propose a new algorithm to compute this integral from the spherical harmonics of the similarity and Dirac functions. The...

• Type: Conference
• Year: 2005
• Where: CVPR
• Authors: Ameesh Makadia, Christopher Geyer, Shankar Sastry, Kostas Daniilidis
• Keywords: Computer Vision, CVPR 2005, Dirac Function, Epipolar Constraint, Radon Transform, Similarity Function, Spherical Transform