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Registration of 3D Points Using Geometric Algebra and Tensor Voting (2006)
| Citations: | 4 - 2 self |
BibTeX
@MISC{Reyes06registrationof,
author = {Leo Reyes and Gerard Medioni and Eduardo Bayro},
title = {Registration of 3D Points Using Geometric Algebra and Tensor Voting},
year = {2006}
}
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Abstract
Abstract. We address the problem of finding the correspondences of two point sets in 3D undergoing a rigid transformation. Using these correspondences the motion between the two sets can be computed to perform registration. Our approach is based on the analysis of the rigid motion equations as expressed in the Geometric Algebra framework. Through this analysis it was apparent that this problem could be cast into a problem of finding a certain 3D plane in a different space that satisfies certain geometric constraints. In order to find this plane in a robust way, the Tensor Voting methodology was used. Unlike other common algorithms for point registration (like the Iterated Closest Points algorithm), ours does not require an initialization, works equally well with small and large transformations, it cannot be trapped in “local minima ” and works even in the presence of large amounts of outliers. We also show that this algorithm is easily extended to account for multiple motions and certain non-rigid or elastic transformations. Keywords: computer vision, 3D motion estimation, tensor voting, geometric algebra
Keyphrases
geometric algebra tensor voting geometric algebra framework rigid motion equation tensor voting methodology iterated closest point algorithm common algorithm large transformation different space local minimum multiple motion point set robust way computer vision motion estimation large amount rigid transformation point registration elastic transformation certain geometric constraint
