Han Xiao, Xu Chenyang, Prince Jerry L
CMS Software, Elekta Inc., St. Louis, MO 63043.
Int J Comput Vis. 2009 Aug 1;84(1):63-79. doi: 10.1007/s11263-009-0231-3.
Geometric deformable models based on the level set method have become very popular in the last decade. To overcome an inherent limitation in accuracy while maintaining computational efficiency, adaptive grid techniques using local grid refinement have been developed for use with these models. This strategy, however, requires a very complex data structure, yields large numbers of contour points, and is inconsistent with the implementation of topology-preserving geometric deformable models (TGDMs). In this paper, we investigate the use of an alternative adaptive grid technique called the moving grid method with geometric deformable models. In addition to the development of a consistent moving grid geometric deformable model framework, our main contributions include the introduction of a new grid nondegeneracy constraint, the design of a new grid adaptation criterion, and the development of novel numerical methods and an efficient implementation scheme. The overall method is simpler to implement than using grid refinement, requiring no large, complex, hierarchical data structures. It also offers an extra benefit of automatically reducing the number of contour vertices in the final results. After presenting the algorithm, we demonstrate its performance using both simulated and real images.
在过去十年中，基于水平集方法的几何可变形模型变得非常流行。为了在保持计算效率的同时克服精度方面的固有局限性，已经开发了使用局部网格细化的自适应网格技术来与这些模型一起使用。然而，这种策略需要非常复杂的数据结构，会产生大量的轮廓点，并且与拓扑保持几何可变形模型（TGDM）的实现不一致。在本文中，我们研究了一种称为移动网格方法的替代自适应网格技术与几何可变形模型的结合使用。除了开发一个一致的移动网格几何可变形模型框架外，我们的主要贡献还包括引入了一个新的网格非退化约束、设计了一个新的网格自适应准则，以及开发了新颖的数值方法和高效的实现方案。总体方法比使用网格细化更易于实现，不需要大型、复杂的层次数据结构。它还具有自动减少最终结果中轮廓顶点数量的额外优点。在介绍了算法之后，我们使用模拟图像和真实图像展示了它的性能。
