Radon-based structure from motion without correspondences
Makadia, A.; Geyer, C.; Sastry, S.; Daniilidis, K.
Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on
Volume 1, Issue , 20-25 June 2005 Page(s): 796 - 803 vol. 1
Digital Object Identifier 10.1109/CVPR.2005.285
Summary: We present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. We assume a similarity function defined on the cross-product 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 resulting resolution in the motion space depends on the bandwidth we keep from the spherical transform. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions. The algorithm has been tested in sequences of real omnidirectional images and it outperforms correspondence-based structure from motion.
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