In this paper, two new approaches for the topological feature matching problem are proposed. The first one consists of estimating a combinatorial map between block structures (pixels, windows) of given binary images which is then analyzed for topological correspondence using the concept of homology of maps. The second approach establishes a matching by using a similarity measure between two sets of boundary representations of the connected components extracted from two given binary images. The similarity measure is applied on all oriented boundary components of given features. A number of experiments are carried out on both synthetic and real images to validate the two approaches.