In this paper, we propose a new topology extraction approach for 3D objects. We choose a normalized robust
and simplified geodesic-based Morse function to define skeletal Reeb graphs of 3D objects. In addition to scale
invariance, we ensure, by using a geodesic distance, the invariance of these graphs to all isometric transforms.
In our Reeb graph construction procedure, we introduce important improvements and advantages over existing
techniques. We define an efficient sampling rate based on the characteristic resolution intrinsic to each 3D object.
Then, we provide a geometry preserving approach by replacing the traditional intervals of a Morse function by
its exact level curves. Moreover, we take advantage of the resulting ordered adjacency matrices that describe our
Reeb graphs, to introduce a new measure of similarity between the corresponding objects. Experimental results
illustrate the computational simplicity and efficiency of the proposed technique for topological Reeb graphs'
extraction. The experiments also show the robustness of this approach against noise and object remeshing.