Reconciling distance functions and level sets
Reconciling distance functions and level sets
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DOI：
10.1006/jvci.1999.0439
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发表时间：
2000-06-01
影响因子：
2.6
通讯作者：
Faugeras, O
中科院分区：
文献类型：
--
作者：
Gomes, J;Faugeras, O
利用隐式表示法模拟偏微分方程驱动的闭曲面演化。在大多数应用中，隐式表示的自然选择是闭合曲面的带符号距离函数。Osher和Sethian提出用Hamilton-Jacobi方程来演化距离函数。不幸的是，这个方程的解不是距离函数。因此，水平集方法在实际应用中遇到了这样的问题：我们什么时候必须重新初始化距离函数？如何重新初始化距离函数？这揭示了理论和实现之间的分歧。本文提出了一种替代使用的Hamilton-Jacobi方程，消除了这一矛盾：在我们的方法中，隐式表示始终保持距离函数的建设，并实现不不同于理论了。这是通过引入一个新的方程来实现的。除了理论上的优点外，该方法还具有几个实际的优点，我们在三个应用中证明了这一点：（i）使用两个耦合表面（X. Zeng等人，in Proceedings of the International Conference on Computer Vision and Pattern Recognition，June 1998），（ii）3D表面的欧几里德骨架的层次结构的构建，（iii）通过立体（O. Faugeras和R. Keriven，《计算机科学讲义》，第1252卷，第1252页。272-283）。(C)北京大学出版社.
This paper is concerned with the simulation of the partial differential equation driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian have proposed to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately the solution to this equation is not a distance function. As a consequence, the practical application of the level set method is plagued with such questions as When do we have to reinitialize the distance function? How do we reinitialize the distance function?, which reveal a disagreement between the theory and its implementation. This paper proposes an alternative to the use of Hamilton-Jacobi equations which eliminates this contradiction: in our method the implicit representation always remains a distance function by construction, and the implementation does not differ from the theory anymore. This is achieved through the introduction of a new equation. Besides its theoretical advantages, the proposed method also has several practical advantages which we demonstrate in three applications: (i) the segmentation of the human cortex surfaces from MRI images using two coupled surfaces (X. Zeng, et al., in Proceedings of the International Conference on Computer Vision and Pattern Recognition, June 1998), (ii) the construction of a hierarchy of Euclidean skeletons of a 3D surface, (iii) the reconstruction of the surface of 3D objects through stereo (O. Faugeras and R. Keriven, Lecture Notes in Computer Science, Vol. 1252, pp. 272-283). (C) 2000 Academic Press.