Several work have shown that a topological map is a good tool to describe and handle a labeled image. Indeed, it allows describing the full topology of the image: its subdivision in cells (vertices, edges, faces) and all the incidence and adjacency relations between these cells, contrary to simpler models like region adjacency graphs. Thanks to this description, a topological map allows computing and updating several features that can mix topological and geometrical information. One major problem of topological map, that often limits its use, is the memory size required by its representation. In this paper, we solve this drawback by proposing two compact representations of topological maps that offer different space/time efficiency compromises. These two representations are based on the links between topological maps and linel maps, where each edge corresponds to a linel, and on an implicit encoding of linel darts. Our experiments show a major reduction on memory space comparing to previous encoding, and allows us to envisage to process big images without memory constraint.