A distance measure between labeled combinatorial maps

Combinatorial maps are widely used in image representation and processing, however map matching problems have not been extensively researched. This paper addresses the problem of inexact matching between labeled combinatorial maps. First, the concept of edit distance is extended to combinatorial maps, and then used to define mapping between combinatorial maps as a sequence of edit operations that transforms one map into another. Subsequently, an optimal approach based on A^* algorithm and an approximate approach based on Greedy algorithm are proposed to compute the distance between combinatorial maps. Experimental results show that the proposed inexact map matching approach produces richer search results than the exact map matching technique by tolerating small difference between maps. The proposed approach performs better in practice than the previous approach based on maximum common submap which cannot be directly used for comparing labels on the maps.