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Javier Bernal and Jim Lawrence study how to compare the shapes of two surfaces in three-dimensional space. Their approach seeks a registration that accounts for differences in parameterization while measuring an elastic distance between the surfaces.
The report develops the mathematical formulation and describes computational methods that combine gradient descent with dynamic programming. Numerical examples illustrate how the methods behave when applied to pairs of surfaces. The complete technical study retains its derivations, algorithmic descriptions, diagrams, results and references.
Javier Bernal and Jim Lawrence (2024). Elastic Shape Registration of Surfaces in 3D Space with Gradient Descent and Dynamic Programming. National Institute of Standards and Technology, https://doi.org/10.6028/NIST.TN.2310. Republished courtesy of the National Institute of Standards and Technology.