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Javier Bernal and Jim Lawrence develop a method for comparing the shapes of surfaces in three-dimensional space. They formulate partial elastic registration through rotations and a restricted family of reparametrizations, using dynamic programming to search for a useful alignment.
The mathematical development introduces homeomorphisms, surface area, shape functions and elastic shape distance before describing the computational procedure. A separate treatment of rigid alignment supplies the rotation matrix used alongside the reparametrization step.
Examples show how the method performs on selected surfaces and how its result can provide an initial solution for a broader optimization. The complete November 2023 technical note preserves the equations, diagrams, implementation results and references.
Javier Bernal and Jim Lawrence. NIST,2023. https://doi.org/10.6028/NIST.TN.2274. Courtesy of the National Institute of Standards and Technology. Original notices and credits retained.