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Elastic shape matching of parameterized surfaces using square root normal fields.

Jermyn, Ian H. and Kurtek, Sebastian and Klassen, Eric and Srivastava, Anuj (2012) 'Elastic shape matching of parameterized surfaces using square root normal fields.', in Computer vision - ECCV 2012 : 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012. Proceedings. Part V. Berlin, Heidelberg: Springer, pp. 804-817. Lecture notes in computer science., 7576


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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:30 March 2016
Date of first online publication:October 2012
Date first made open access:No date available

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