The Granular Theorem of Quotient Space in Image Segmentation
Liu Ren, Xian Feng Huang · Chinese Journal of Computers · 2005
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 theorem of image segmentation is demonstrated. The image segmentation problems are described with triple elements function of the quotient space model (X,f,Γ)([X],[f],[Γ]), 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.