We propose a novel 3D shape descriptor, called the Advanced Global Point Signature (AGPS), which is based on spectral analysis and is obtained by linear combination of some scaled eigenfunctions of the Laplace�Beltrami operator. Since it is built upon the concept of Global Point Signature, AGPS inherits several useful properties such as robustness to noise, stability and scale invariance. An AGPS-based method for extracting salient features from semi-rigid objects represented by triangular mesh surfaces is introduced. Due to its discriminative power, the associated AGPS values with each point remain extremely stable, which allows for simple and efficient shape characterization and robust salient point extraction. To assert our method regarding its robustness against noise and topological modifications, experiments on multiple benchmark datasets under unfavorable circumstances were performed. The method is also compared to state of the art methods for shape classification and retrieval. © 2017 Elsevier B.V.