On Analyzing Symmetry of Objects using Elastic Deformations
On Analyzing Symmetry of Objects using Elastic Deformations
复制标题
利用弹性变形分析物体的对称性
DOI：
10.5220/0001797201940200
复制
发表时间：
2009
影响因子：
23.6
通讯作者：
S. Kurtek
中科院分区：
文献类型：
--
作者：
C. Samir;Anuj Srivastava;M. Daoudi;S. Kurtek
我们介绍了一种利用物体边界的弹性变形来分析二维和三维物体对称性的框架。基本思想是定义弹性形状的空间，并使用黎曼结构计算对象与其反射之间的最短(测地线)路径。弹性匹配基于曲线的最优(非线性)重新参数化，与以前使用的线性配准相比，提供了更好的跨形状的点配准。方向对齐的一个关键步骤，类似于寻找对称平面，是作为搜索最短测地线路径来执行的。该框架是完全自动的，并提供：不对称度量、最接近的对称形状、使对象对称的最佳变形以及给定对象的对称平面。
We introduce a framework for analyzing symmetry of 2D and 3D objects using elastic deformations of their boundaries. The basic idea is to define spaces of elastic shapes and to compute shortest (geodesic) paths between the objects and their reflections using a Riemannian structure. Elastic matching, based on optimal (nonlinear) re-parameterizations of curves, provides a better registration of points across shapes, as compared to the previously-used linear registrations. A crucial step of orientation alignment, akin to finding planes of symmetry, is performed as a search for shortest geodesic paths. This framework is fully automatic and provides: a measure of asymmetry, the nearest symmetric shape, the optimal deformation to make an object symmetric, and the plane of symmetry for a given object.