Registration of 3D Points Using Geometric Algebra and Tensor Voting

13 years 4 months ago

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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 an...

Leo Reyes, Gérard G. Medioni, Eduardo Bayro

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