Objectives  Quantitative expression of topological relations of contour is vital to spatial cognition, topological feature mining and map generalization. However, previous studies focus on the construction of contour tree and the generalization algorithm of contour. However, its lack of the quantitative expression of topological relations and the research of the quantitative relationship between it and map scale change, and it is still unknown whether the topological indexes of different geomorphic types vary with map scale change or not.

  Methods  By preprocessing of non-closed contour and constructing directed contour tree, such as topology checking, matching and non-closed contour closure, a quantitative expression model of them was proposed and constructed, and 60 groups multi-scale contour datasets from different geomorphic types in Gansu were used to explore the consistency of the relationship.

  Results and Conclusions  Experimental results show that the topological indexes change rules of adjacent scale is consistent with the space cognitive and reasoning, and the same power function can be used to express the quantitative relationship of contour from different geomorphic types, which further demonstrates that it is rationality and possibility to realization the completely automatic generalization of contour based on multi-scale spatial similarity relation.