Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images
Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images
复制标题
有效存储通过 3D 二进制图像计算的组成良好的多面体复合体
DOI：
10.1007/s10851-017-0722-8
复制
发表时间：
2017
影响因子：
2
通讯作者：
B. Medrano
中科院分区：
文献类型：
--
作者：
Rocio Gonzalez;M. Jiménez;B. Medrano
一个三维二值图像I可以自然地用一种称为立方复形的组合代数结构表示，记为Q（I），其基本构造块是顶点、边、正方形面和立方体。在Gonzalez-Diaz等人（Discret Appl Math 183：59-77，2015）中，我们提出了一种方法来“局部修复“Q（I）以获得多面体复形P（I）（其基本构建块是顶点、边、特定多边形和多面体），同伦等价于Q（I），满足其边界表面是2D流形。此外，我们还开发了一个新的P（I）编码系统，将P（I）细胞的几何信息以三维灰度图像的形式编码，将P（I）细胞的边界面关系以一组结构元素的形式编码。在本文中，我们建立在（Gonzalez-Diaz et al. 2015）的基础上，并证明了要检索P（I）的拓扑和几何信息，每个多面体只需存储一个3D点就足够了，因此既不需要灰度图像也不需要结构元素集。从P（I）的这种“最小”编码出发，我们最后给出了计算P（I）边界曲面中2-胞腔的方法。
A 3D binary imageIcan be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted byQ(I), whose basic building blocks are vertices, edges, square faces and cubes. In Gonzalez-Diaz et al. (Discret Appl Math 183:59–77, 2015), we presented a method to “locally repair”Q(I) to obtain a polyhedral complexP(I) (whose basic building blocks are vertices, edges, specific polygons and polyhedra), homotopy equivalent toQ(I), satisfying that its boundary surface is a 2D manifold.P(I) is called awell-composed polyhedral complex over the pictureI. Besides, we developed a new codification system forP(I), encoding geometric information of the cells ofP(I) under the form of a 3D grayscale image, and the boundary face relations of the cells ofP(I) under the form of a set of structuring elements. In this paper, we build upon (Gonzalez-Diaz et al. 2015) and prove that, to retrieve topological and geometric information ofP(I), it is enough to store just one 3D point per polyhedron and hence neither grayscale image nor set of structuring elements are needed. From this “minimal” codification ofP(I), we finally present a method to compute the 2-cells in the boundary surface ofP(I).
影响因子：
1.3
作者：
D. Kozlov
通讯作者：
D. Kozlov