The paper offers readers information that is quite relevant to the improvement of image segmentation algorithms. A two-dimensional topological map is obtained by means of new algorithm constructions, based on local configurations called precodes. The extraction algorithm approach is said to be optimal.

The paper focuses on an interesting application of image processing, where a labeled image is processed in order to obtain a model for image representation. The authors are conducting innovative research, based on topological maps and the way they can be used to propose new segmentation algorithms, as well as to enhance existing techniques.

The authors claim that, even though Domenger and Braquelaire’s topological map [1], Fiorio’s topological graph of frontier (TGF) [2], and their proposed solution, based on combinatorial maps, have the same topological representation, the precode-based algorithm they present in this paper yields more efficient computations, despite similar memory usage. The authors’ experiments and analysis would have been improved if they had provided additional information about their algorithm implementations in terms of time complexity. A Web address containing more examples, for comparison with two-dimension labeled images, would also be valuable.

Since the authors agree that the topological map is a good model for image processing, it is not clear why they did not consider including an example (namely, a segmentation algorithm) that works on such a map. It would be valuable to see how the authors plan to define a complete image analysis software based on the topological map. For those interested in contour-based segmentation, this paper is worth reading.