The formal model of the spatial directional relation is one of the most important parts in the area of spatial relation. However

the research on the expression method of special directional relation is still immature. In this paper

the characteristics and defects of the recent special directional relation models are analyzed first; Second the basic idea

and the construction method of the quadtree histogram are introduced; third a new expression method to judge the special directional relation based on quadtree histogram is described in detail; finally

to prove the correctness of the method

several contrast experiments are given based on synthetic and real images. The experimental results show that the model can get close to the verdict like human cognition for special directional relation and overcome the problems of the existing models.