期刊
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
卷 25, 期 -, 页码 -出版社
EDP SCIENCES S A
DOI: 10.1051/cocv/2018053
关键词
Shape analysis; curve matching; intrinsic metrics; varifolds
资金
- National Science Foundation [1819131]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1819131] Funding Source: National Science Foundation
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 H-2-metrics with constant coefficients and scale-invariant H-2-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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据