In order to solve the problem of fixed structure element in traditional mathematical morphology on graph space

the concept of similarity weight on graph space is put forward

and the adaptive structure graph is defined. The property of structure graph is analyzed and proved. The new adaptive morphological operator on graph space is advanced on this basis and the properties of the operator are put forward and analyzed theoretically. The new operator considers not only the local feature of image pixels but also the global features of continuous pixels. The experimental results show that the new operator is superior to existing color morphology in maintaining integrity and correlation of the image information

and can select threshold value and structure element according to the characteristics of the image

thus it has a broad application prospect in more sophisticated image processing aspects.