Abstract: This study presents a new local feature matching approach based Reeb graph (RG). The central contribution is to reinforce the topological consistency of the graph-based description. 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 taken as three-dimensional-shape descriptor. The similarity estimation is performed in two steps. The first is forming the pairs of similar Reeb charts, according to the minimal distance between their corresponding signatures. Then to measure the global similarity which quantifies the similitude degree between all the matched Reeb charts. Retrieval experiments have shown that the proposed matching scheme provides an overall retrieval efficiency gain compared to recent advanced methods.