This paper focuses on the issue of translating the relative variation of one shape with respect to another in a template centered representation. The context is the theory of Diffeomorphic Pattern Matching which provides a representation of the space of shapes of objects, including images and point sets, as an infinite dimensional Riemannian manifold which is acted upon by groups of diffeomorphisms. We discuss two main options for achieving our goal; the first one is the parallel translation, based on the Riemannian metric; the second one, based on the group action, is the coadjoint transport. These methods are illustrated with 3D experiments.

中文翻译：

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微分同胚群中关系结构的传输。

本文重点讨论在以模板为中心的表示中转换一种形状相对于另一种形状的相对变化的问题。上下文是微分同胚模式匹配理论，该理论提供了对象形状空间的表示，包括图像和点集，作为由微分同胚群作用的无限维黎曼流形。我们讨论实现目标的两种主要选择；第一个是平行平移，基于黎曼度量；第二个，基于群作用，是协同运输。这些方法通过 3D 实验进行了说明。