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Type: Conference paper
Title: Conformal surface alignment with optimal Möbius search
Other Titles: Conformal surface alignment with optimal Mobius search
Author: Le, H.
Chin, T.
Suter, D.
Citation: Proceedings / CVPR, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2016, vol.2016-December, pp.2507-2516
Publisher: IEEE
Issue Date: 2016
Series/Report no.: IEEE Conference on Computer Vision and Pattern Recognition
ISBN: 9781467388511
ISSN: 1063-6919
Conference Name: 2016 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPR 2016) (26 Jun 2016 - 1 Jul 2016 : Las Vegas, NV)
Statement of
Huu Le, Tat-Jun Chin and David Suter
Abstract: Deformations of surfaces with the same intrinsic shape can often be described accurately by a conformal model. A major focus of computational conformal geometry is the estimation of the conformal mapping that aligns a given pair of object surfaces. The uniformization theorem enables this task to be acccomplished in a canonical 2D domain, wherein the surfaces can be aligned using a Möbius transformation. Current algorithms for estimating Möbius transformations, however, often cannot provide satisfactory alignment or are computationally too costly. This paper introduces a novel globally optimal algorithm for estimating Möbius transformations to align surfaces that are topological discs. Unlike previous methods, the proposed algorithm deterministically calculates the best transformation, without requiring good initializations. Further, our algorithm is also much faster than previous techniques in practice. We demonstrate the efficacy of our algorithm on data commonly used in computational conformal geometry.
Keywords: Shape, three-dimensional displays, partitioning algorithms, iterative closest point algorithm, two dimensional displays, geometry, conformal mapping
Rights: © 2016 IEEE
DOI: 10.1109/CVPR.2016.275
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