14.基于数学形态学的分形维数分析法及其应用

陈成钢[1]艾涛²

（1.天津城建大学理学院天津 300384；

2.上海中兴通讯技术有限责任公司 上海 201203）

摘要：数学形态学是分析几何形状和结构的数学方法，广泛应用于各类图像形状和结构的分析与处理. 图像的分数维特征描述了纹理的复杂度和粗糙度，本文将Peleg的分数维形态学计算方法应用于纹理分形特征的计算，在Peleg基础上进行改进，采用的结构元是圆对称性的结构元，将膨胀和腐蚀的作用分开考虑，从而得到两组纹理特征．试验表明，该方法可以更好地描述图像的纹理特征．

关键词：数学形态学、分数维；纹理特征；分形

中图分类号：TP391文献标识码：A

The fractal dimension of mathematical morphology analysis method and its application

Chen Cheng-gang¹AiTao²

(1.Department of Fundamental Subject,TIUC,Tianjin 300384, China )

(2. Shanghai Zhongxing Communication Technology Limited liability company, Shanghai 201203，China)

Abstract：Mathematical morphology is a mathematical method that could be used to analyze geometry and structure, which is widely used in all kinds of image analysis and processing of shapes and structures. Fractal dimension feature of image describes the complexity and roughness of the image texture. Peleg fractal morphology calculation method was applied to calculate the fractal texture features, which was improved on the basis of the Peleg. The circular symmetry of the structure element in structuring element was used ,and the expansion and corrosion effects were considered separately, resulting in the rise of two sets of texture features . Experiments show that this method can be well applied in describing the texture feature of the image．