从积分几何中的概念出发,证明了凸集形态和运算的一个重要性质F(S,u)=F(A,u) F(B,u),并推广到非凸集的情况,从而将两物体的形态和,归结为法矢相同点集的形态和.同时提出了法矢球的概念,进而将两物体的形态运算转化为两法矢球的合并.通过引入负物体的概念,依靠三者的结合,从理论上推导出图形形态算子的统一模型,从而在算法理论上统一了二维、三维实体的形态和、差运算,并保证了该模型理论的正确性.

In this paper, the important property of convex object morphology addition is proved that F(S,u)=F(A,u) F(B,u) based on integral geometry, this can be popularized to concave set, then the two objects' morphology operator can be calculated through the two point sets' Minkowsky addition which have the same normal vector. The concept of vector sphere is provided, and the Minkowsky operator can be turned to the combination of two vector spheres. With the introduction of“Negative Object”, a unified model of graphic morphology operators is developed by combining the three concepts. This model unifies the morphology addition, subtraction of 2D and 3D objects in algorithm theory, and guaranties the correctness of the model' s theory.