Elastic Shape Registration of Surfaces in 3D Space with Gradient Descent and Dynamic Programming

Published

July 31, 2024

Author(s)

Javier Bernal, James F. Lawrence

Abstract

Algorithms based on gradient descent for computing the elastic shape registration of two simple surfaces in 3−dimensional space and therefore the elastic shape distance between them have been proposed by Kurtek, Jermyn, et al., and more recently by Riseth. Their al- gorithms are designed to minimize a distance function between the surfaces by rotating and reparametrizing one of the surfaces, the min- imization for reparametrizing based on a gradient descent approach that may terminate at a local solution. On the other hand, Bernal and Lawrence have proposed a similar algorithm, the minimization for reparametrizing based on dynamic programming thus producing a partial not necessarily optimal elastic shape registration of the sur- faces. Accordingly, Bernal and Lawrence have proposed to use the rotation and reparametrization computed with their algorithm as the initial solution to any algorithm based on a gradient descent approach for reparametrizing. Here we present results from doing exactly that. We also describe and justify the gradient descent approach that is used for reparametrizing one of the surfaces.

Citation

Technical Note (NIST TN) -

NIST Pub Series

Technical Note (NIST TN)

Pub Type

NIST Pubs

Keywords

dynamic programming, elastic shape distance, diffeomorphism, gradient descent, reparametrization, shape analysis

Citation

Bernal, J. and Lawrence, J. (2024), Elastic Shape Registration of Surfaces in 3D Space with Gradient Descent and Dynamic Programming, Technical Note (NIST TN), National Institute of Standards and Technology, Gaithersburg, MD (Accessed September 26, 2024)