Abstract
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel framework, which has several potential advantages over previous works. First, our variational formulation allows us to minimize over reparametrizations without discretizing the reparametrization group. Second, the objective function and gradient are easy to implement and efficient to evaluate numerically. Third, the initial and target surface may have different samplings and even different topologies. Fourth, texture can be incorporated as additional information in the matching term similarly to the fshape framework. We demonstrate the usefulness of this approach with several numerical examples of curves and surfaces.
P. Harms is supported by the Freiburg Institute of Advanced Studies in the form of a Junior Fellowship. N. Charon is supported by NSF grant no 1819131.
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Computer Vision Group at LEMS at Brown University: Database of 99 binary shapes. https://vision.lems.brown.edu/content/available-software-and-databases.
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Bauer, M., Charon, N., Harms, P. (2019). Inexact Elastic Shape Matching in the Square Root Normal Field Framework. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science(), vol 11712. Springer, Cham. https://doi.org/10.1007/978-3-030-26980-7_2
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