Correspondence-free Structure from Motion

13 years 4 months ago

Download www.cis.upenn.edu

We present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this ﬁve dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a ﬁltering operator: If we assume that the similarity and Dirac functions are deﬁned on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical Fourier transform of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the comple...

Ameesh Makadia, Christopher Geyer, Kostas Daniilid

Real-time Traffic