Generation of Three Dimensional Structuring Elements Over 3x3x3 Rectangular Grid
Generation of Three Dimensional Structuring Elements Over 3x3x3 Rectangular Grid
复制标题
在 3x3x3 矩形网格上生成三维结构元素
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
E. Rajan
中科院分区：
文献类型：
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作者：
G. R. Chandra;G. Sathya;E. Rajan
三维结构元素在三维医学图像等三维体图像处理中起着至关重要的作用。这些结构元素用于3-D数学形态运算，如侵蚀、膨胀等。因此没有代数框架来系统地生成3-D结构元素。本文所讨论的工作是利用几何滤子(G-滤子)系统地生成三维结构元素。本文首先给出了定义在三维矩形像素网格上的几何滤镜(G-滤镜)的新概念。利用这些G-滤子，生成了256个凸多面体。利用这256个凸多面体可以生成256个不同的结构元素。这些G滤波器对体图像的处理具有潜在的应用价值。此外，通过构造一个由3x3x3像素网格构成的凸多面体格，简要地描述了G-滤子的代数。本文提出了一种新的自动生成255个凸多面体的算法，它的初始集合A包含3×3×3矩形网格的全部8个角点。本文还提出了一种层次路径枚举算法，用于可视化凸多面体集合与其对应的其他凸多面体子集之间的关系。最后，提出了一种从选定的凸多面体生成三维结构元素的算法。
Three dimensional (3-D) structuring elements plays a vital role in the processing of three dimensional volumetric images such as 3-D medical images. These structuring elements are used in 3-D mathematical morphological operations such as erosion, dilation etc. There is no algebraic framework as such to systematically generate the 3-D structuring elements. The work discussed in this paper is systematically generating the 3-D structuring elements by using geometric filters (G-Filters). This paper initially gives a novel concept of what we call as geometric filters (G-Filters) defined over a 3-D rectangular grid of pixels. By using these G-Filters, 256 convex Polyhedrons are generated. The 256 different structuring elements could be created by using the 256 convex polyhedrons. These G-Filters have potential applications to processing of volumetric images. In addition, the paper describes in brief the algebra of G-Filters by formulating a lattice of convex polyhedrons constructed in a 3X3X3 grid of pixels. This paper proposes a new algorithm for automatic generation of 255 convex polyhedrons from its initial set named A containing all eight corners of the 3x3x3 rectangular grid. This paper also proposes an algorithm for hierarchal path enumeration used in visualizing the relationships between convex polyhedron sets and their corresponding subsets of other convex polyhedrons. Finally, an algorithm is proposed to generate 3D structuring element from a selected convex polyhedron.