图像分割的商空间粒度原理

The Granular Theorem of Quotient Space in Image Segmentation

从商空间粒度理论角度分析图像分割概念,研究已有的图像分割方法,提出图像分割的商空间粒度原理.用商空间的三元组(X,f,Γ)([X],[f],[Γ])来描述图像分割过程,阐述基于商空间粒度计算理论的图像分割原理及基于粒度分层、合成及其综合技术下图像分割的方法,并提出了基于粒度合成原理的复杂纹理图像的分割算法.该算法通过分别提取多纹理图像中纹理区域的方向性及粗细度特征,形成图像的不同粒度,然后根据粒度合成原则,对所形成的粒度进行合成,从而实现对纹理图像的分割,实验表明该算法对复杂纹理图像分割是有效的.

Based on the quotient space granular theorem,the image segmentation concept is analyzed and the image segmentation methods are studied, and then the quotient space granular theo- rem of image segmentation is demonstrated. The image segmentation problems are described with triple elements function of the quotient space model （X,f,Г）-（[X],[f],[Г]）, according to the quotient space granularity computing, the image segmentation theorem is presented. The methods of images segmentation based on hierarchical and synthesis and combinational technique are exploited and then the segmentation algorithm based granularity synthesis technique is proposed. In this technique, the features of directionality and roughness in texture images data set are firstly extracted respectively to form the different granularities of image, then the different granularity are synthesized according to the theorem of granularity synthesis, finally the texture images is segmented. The experimental results demonstrate that the algorithm is valid for the segmentation of complicated texture images.