Global three-dimensional-mesh indexing based on structural analysis and geometrical signatures

This study presents a new local feature matching approach that relies upon Reeb graph (RG)-based representation as well as a simple and accurate similarity estimation. The central contribution of this work is to reinforce the topological consistency conditions of the graph-based description. Formally, the RGs are enriched with geometry signatures based on parameterisation approaches. After RG construction, the shape is segmented into Reeb charts of controlled topology mapped to its canonical planar domain. Then, two stretching signatures, corresponding to the area and angle distortion, are determined and taken as three-dimensional-shape descriptor. The similarity estimation is performed in two steps. The first one consists in forming the pairs of similar Reeb charts, according to the minimal distance between their corresponding signatures. The second step is to measure the global similarity which quantifies the similitude degree between all the matched Reeb charts. Retrieval experiments conducted on four publicly available databases have shown that the proposed matching scheme yields satisfactory results. Among observations, it can be noticed that despite its rapidity, the method provides an overall retrieval efficiency gain compared to very recent state-of-the-art methods.