Shape Analysis of Elastic Curves in Euclidean Spaces
Shape Analysis of Elastic Curves in Euclidean Spaces
复制标题
DOI：
10.1109/tpami.2010.184
复制
发表时间：
2011-07-01
影响因子：
23.6
通讯作者：
Jermyn, Ian H.
中科院分区：
文献类型：
--
作者：
Srivastava, Anuj;Klassen, Eric;Jermyn, Ian H.
在弹性度量下，给出了欧氏空间曲线形状的平方根速度表示。在这种SRV表示中，弹性度量简化为L-2度量，重新参数化群通过等距作用，单位长度曲线的空间成为单位球面。闭曲线的形状空间是单位球面、模旋转和重参数化群（的子流形）的商空间，我们使用路径拉直方法在该空间中找到测地线。这些测地线和测地线距离提供了一个框架，用于最佳匹配，变形和比较形状。这些想法被证明使用：1）研究蛋白质结构的圆柱螺旋的形状分析，2）识别人脸的面部曲线的形状分析，3）用于捕获平面闭合曲线形状的包裹概率分布，以及4）用于从新姿势预测形状的变形的并行传输。
This paper introduces a square-root velocity (SRV) representation for analyzing shapes of curves in euclidean spaces under an elastic metric. In this SRV representation, the elastic metric simplifies to the L-2 metric, the reparameterization group acts by isometries, and the space of unit length curves becomes the unit sphere. The shape space of closed curves is the quotient space of (a submanifold of) the unit sphere, modulo rotation, and reparameterization groups, and we find geodesics in that space using a path straightening approach. These geodesics and geodesic distances provide a framework for optimally matching, deforming, and comparing shapes. These ideas are demonstrated using: 1) shape analysis of cylindrical helices for studying protein structure, 2) shape analysis of facial curves for recognizing faces, 3) a wrapped probability distribution for capturing shapes of planar closed curves, and 4) parallel transport of deformations for predicting shapes from novel poses.