Siemens Corporate Research, Inc., Princeton, NJ 08540, USA.
IEEE Trans Image Process. 2010 May;19(5):1191-200. doi: 10.1109/TIP.2009.2039372. Epub 2009 Dec 28.
We propose a method for 3-D shape recognition based on inexact subgraph isomorphisms, by extracting topological and geometric properties of a shape in the form of a shape model, referred to as topo-geometric shape model (TGSM). In a nutshell, TGSM captures topological information through a rigid transformation invariant skeletal graph that is constructed in a Morse theoretic framework with distance function as the Morse function. Geometric information is then retained by analyzing the geometric profile as viewed through the distance function. Modeling the geometric profile through elastic yields a weighted skeletal representation, which leads to a complete shape signature. Shape recognition is carried out through inexact subgraph isomorphisms by determining a sequence of graph edit operations on model graphs to establish subgraph isomorphisms with a test graph. Test graph is recognized as a shape that yields the largest subgraph isomorphism with minimal cost of edit operations. In this paper, we propose various cost assignments for graph edit operations for error correction that takes into account any shape variations arising from noise and measurement errors.
我们提出了一种基于非精确子图同构的 3D 形状识别方法，通过以形状模型的形式提取形状的拓扑和几何属性，称为拓扑-几何形状模型（TGSM）。简而言之，TGSM 通过刚性变换不变的骨架图来捕获拓扑信息，该骨架图是在距离函数作为 Morse 函数的 Morse 理论框架中构建的。然后，通过分析通过距离函数查看的几何轮廓来保留几何信息。通过弹性建模对几何轮廓进行建模，得到加权骨架表示，从而得到完整的形状签名。通过确定模型图上的一系列图编辑操作来执行与测试图的非精确子图同构，从而通过确定模型图上的一系列图编辑操作来执行形状识别。通过最小化编辑操作的代价来建立子图同构。在本文中，我们提出了用于图编辑操作的各种代价分配，以进行纠错，该分配考虑了由于噪声和测量误差而引起的任何形状变化。
