Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences Through Reflections
We describe a new algorithm to reconstruct a rigid body motion from point correspondences. The algorithm works by constructing a series of reflections which align the points with their correspondences one by one. This is naturally and efficiently implemented in the conformal model of geometric algebra, where the resulting transformation is represented by a versor. As a direct result of this algorithm, we also present a very compact and fast formula to compute a quaternion from two vector correspondences, a surprisingly elementary result which appears to be new.
KeywordsSingular Value Decomposition Rigid Body Motion Null Vector Orthogonal Transformation Geometric Algebra
We acknowledge the support of NWO in the DASIS project (Discovery of Articulated Structures in Image Sequences) for funding this work. We are indebted to Richard Clawson who discovered and fixed the singularity in quaternion (4.5). For a more detailed description of the singularity, please refer to his write-up .
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