Volume 25, 2019
|Number of page(s)||24|
|Published online||27 November 2019|
A relaxed approach for curve matching with elastic metrics
Florida State University,
2 Brunel University London, London, UK.
3 Johns Hopkins University, Baltimore, MD, USA.
* Corresponding author: firstname.lastname@example.org
Accepted: 23 September 2018
In this paper, we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the family of H2-metrics with constant coefficients and scale-invariant H2-metrics on both open and closed immersed curves. These families include as particular cases the class of first-order elastic metrics. An essential difference with prior approaches is the way that boundary constraints are dealt with. By leveraging varifold-based similarity metrics we propose a relaxed variational formulation for the matching problem that avoids the necessity of optimizing over the reparametrization group. Furthermore, we show that we can also quotient out finite-dimensional similarity groups such as translation, rotation and scaling groups. The different properties and advantages are illustrated through numerical examples in which we also provide a comparison with related diffeomorphic methods used in shape registration.
Mathematics Subject Classification: 68Q25 / 68R10 / 68U05
Key words: Shape analysis / curve matching / intrinsic metrics / varifolds
© EDP Sciences, SMAI 2019
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