Koehl Patrice
Department of Computer Science and Genome Center, University of California, Davis, CA 95616, USA
J R Soc Interface. 2017 May;14(130). doi: 10.1098/rsif.2017.0031.
In this paper, we propose a new method for computing a distance between two shapes embedded in three-dimensional space. Instead of comparing directly the geometric properties of the two shapes, we measure the cost of deforming one of the two shapes into the other. The deformation is computed as the geodesic between the two shapes in the space of shapes. The geodesic is found as a minimizer of the Onsager-Machlup action, based on an elastic energy for shapes that we define. Its length is set to be the integral of the action along that path; it defines an intrinsic quasi-metric on the space of shapes. We illustrate applications of our method to geometric morphometrics using three datasets representing bones and teeth of primates. Experiments on these datasets show that the variational quasi-metric we have introduced performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.
在本文中，我们提出了一种计算三维空间中两个嵌入形状之间距离的新方法。我们不是直接比较两个形状的几何属性，而是测量将两个形状中的一个变形为另一个的代价。变形被计算为形状空间中两个形状之间的测地线。基于我们定义的形状弹性能量，测地线被找到作为昂萨格 - 马赫卢普作用量的极小值。其长度被设定为沿该路径的作用量积分；它在形状空间上定义了一种内在的拟度量。我们使用三个代表灵长类动物骨骼和牙齿的数据集来说明我们的方法在几何形态计量学中的应用。对这些数据集的实验表明，我们引入的变分拟度量在形状识别和识别进化模式方面都表现得非常出色，成功率与专家观察者获得的成功率相似，在某些情况下甚至更好。
