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Radon-Based Structure from Motion without Correspondences

11 years 3 months ago
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...
Ameesh Makadia, Christopher Geyer, Shankar Sastry,
Added 12 Oct 2009
Updated 29 Oct 2009
Type Conference
Year 2005
Where CVPR
Authors Ameesh Makadia, Christopher Geyer, Shankar Sastry, Kostas Daniilidis
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