Datar Manasi, Gur Yaniv, Paniagua Beatriz, Styner Martin, Whitaker Ross
Scientific Computing and Imaging Institute, University of Utah, USA.
Med Image Comput Comput Assist Interv. 2011;14(Pt 2):368-75. doi: 10.1007/978-3-642-23629-7_45.
An ensemble of biological shapes can be represented and analyzed with a dense set of point correspondences. In previous work, optimal point placement was determined by optimizing an information theoretic criterion that depends on relative spatial locations on different shapes combined with pairwise Euclidean distances between nearby points on the same shape. These choices have prevented such methods from effectively characterizing shapes with complex geometry such as thin or highly curved features. This paper extends previous methods for automatic shape correspondence by taking into account the underlying geometry of individual shapes. This is done by replacing the Euclidean distance for intrashape pairwise particle interactions by the geodesic distance. A novel set of numerical techniques for fast distance computations on curved surfaces is used to extract these distances. In addition, we introduce an intershape penalty term that incorporates surface normal information to achieve better particle correspondences near sharp features. Finally, we demonstrate this new method on synthetic and biological datasets.
一组生物形状可以通过密集的点对应集来表示和分析。在先前的工作中，最佳点放置是通过优化一个信息论标准来确定的，该标准依赖于不同形状上的相对空间位置以及同一形状上相邻点之间的成对欧几里得距离。这些选择使得此类方法无法有效地表征具有复杂几何形状的形状，如细薄或高度弯曲的特征。本文通过考虑单个形状的基础几何结构，扩展了先前用于自动形状对应的方法。这是通过用测地距离替换形状内成对粒子相互作用的欧几里得距离来实现的。一组用于曲面上快速距离计算的新颖数值技术被用于提取这些距离。此外，我们引入了一个形状间惩罚项，该项纳入了表面法线信息，以在尖锐特征附近实现更好的粒子对应。最后，我们在合成数据集和生物数据集上演示了这种新方法。
