计算二维图像欧拉数的新公式

欧拉数是拓扑学的重要特征参数,在二维数字图像中,由局部性质计算图像欧拉数的公式,对于四连通和八连通是不同的.文章在定义图段和相邻数概念的基础上,提出了由局部性质计算二值图像欧拉数的一种新公式,并进行了证明.该算法基于逐行扫描,分图段计算,每段所对应的相邻上一行的段数不同,会引起图像欧拉数的变化,累加求和即可得到整个二值图像的欧拉数.新算法最重要的特点是将四连通和八连通统一在一个公式之中,这是以往局部算法所没有的.

A New Formula for 2D Image Euler Number

Euler Number is one of the most important characteristics in topological. In two dimensions digital images, the Euler characteristic is locally computable. The form of Euler Number formula is different for 4-connected and 8- connected. In this paper, a new formula of the Euler Number computing is proposed and is proved, based on the definition of the Figure Segment and Neighbor Number. This formula is calculated based on both scanning image line by line and computing Neighbor Number for each Figure Segment. The Euler Number of whole image is summed by 1 minus the Neighbor Number of Figure Segment. The most important feature of this formula is unifying the form of 4-connected and 8-connected, which is still lacking in traditional locally computing formulas.