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首页> 外文会议>International Symposium on Computer and Information Sciences(ISCIS 2006); 20061101-03; Istanbul(TR) >Neighborhood Decomposition of Convex Structuring Elements for Mathematical Morphology on Hexagonal Grid
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Neighborhood Decomposition of Convex Structuring Elements for Mathematical Morphology on Hexagonal Grid

机译：六边形网格上用于数学形态学的凸结构元素的邻域分解

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摘要

In this paper, we present a new technique to find the optimal neighborhood decomposition for convex structuring elements used in morphological image processing on hexagonal grid. In neighborhood decomposition, a structuring element is decomposed into a set of neighborhood structuring elements, each of which consists of the combination of the origin pixel and its six neighbor pixels. Generally, neighborhood decomposition reduces the amount of computation required to perform morphological operations such as dilation and erosion. Firstly, we define a convex structuring element on a hexagonal grid and formulate the necessary and sufficient condition to decompose a convex structuring element into the set of basis convex structuring elements. Secondly, decomposability of a convex structuring element into the set of primal bases is also proved. Furthermore, cost function is used to represent the amount of computation or execution time required for performing dilations on different computing environments and by different implementation methods. The decomposition condition and the cost function are applied to find the optimal neighborhood decomposition of a convex structuring element, which guarantees the minimal amount of computation for morphological operations. Example decompositions show that the decomposition results in great reduction in the amount of computation for morphological operations.
机译：在本文中，我们提出了一种新技术，用于寻找六角形网格上形态图像处理中使用的凸结构元素的最佳邻域分解。在邻域分解中，结构元素被分解为一组邻域结构元素，每个邻域结构元素都由原始像素及其六个相邻像素的组合组成。通常，邻域分解会减少执行诸如膨胀和腐蚀之类的形态运算所需的计算量。首先，我们在六边形网格上定义了一个凸结构元素，并提出了将凸结构元素分解为基础凸结构元素集合的充要条件。其次，还证明了凸结构元素可分解为原始基数的集合。此外，成本函数用于表示在不同的计算环境上并通过不同的实现方法执行膨胀所需的计算量或执行时间。利用分解条件和代价函数来寻找凸结构元素的最优邻域分解，从而保证了形态运算的最小计算量。示例分解表明，分解导致形态运算的计算量大大减少。

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