Elastic shape matching of parameterized surfaces using square root normal fields

Jermyn, Ian H.; Kurtek, Sebastian; Klassen, Eric; Srivastava, Anuj

Abstract

In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape deformations that are being quantified. Second, this metric is invariant under the action of the reparameterization group. We also introduce a novel representation of surfaces termed square root normal fields or SRNFs. This representation is convenient for shape analysis because, under this representation, a reduced version of the general elastic metric becomes the simple \ensuremathL2\ensuremathL2 metric. Thus, this transformation greatly simplifies the implementation of our framework. We validate our approach using multiple shape analysis examples for quadrilateral and spherical surfaces. We also compare the current results with those of Kurtek et al. [1]. We show that the proposed method results in more natural shape matchings, and furthermore, has some theoretical advantages over previous methods.

Citation

Jermyn, I. H., Kurtek, S., Klassen, E., & Srivastava, A. (2012, October). Elastic shape matching of parameterized surfaces using square root normal fields. Presented at 12th European Conference on Computer Vision (ECCV), Florence, Italy

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 12th European Conference on Computer Vision (ECCV)
• Start Date: Oct 7, 2012
• End Date: Oct 13, 2012
• Publication Date: Oct 13, 2012
• Deposit Date: Jul 27, 2015
• Publicly Available Date: Mar 30, 2016
• Print ISSN: 0302-9743
• Volume: 7576
• Pages: 804-817
• Series Title: Lecture notes in computer science
• Series ISSN: 0302-9743,1611-3349
• Book Title: Computer vision - ECCV 2012 : 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012. Proceedings. Part V.
• ISBN: 9783642337147
• DOI: https://doi.org/10.1007/978-3-642-33715-4_58
• Public URL: https://durham-repository.worktribe.com/output/1152262