This paper presents a Surface Geodesic Pattern (SGP) representation for matching textured 3D deformable surfaces. SGP encodes the local variations of the surface texture derivatives to extract local information from distinctive textural relationships contained in a geodesic neighborhood. Thus, SGP derives its strength from the fusion of surface texture and shape information at the data level in a way that is invariant to non-rigid deformations. We also propose Gabor Topography Wavelet (GTW) for direct feature extraction from the range data. Both features are combined using a multi-view sparse representation to achieve higher discrimination capability while matching non-rigid 3D surfaces. The performance of the proposed method is evaluated extensively on the Bosphorus face database, the FRGC v2 face database, and the PolyU contact-free hand database and the results are compared to state-of-the-art methods. Experimental results show the effectiveness and superiority of the proposed method in recognizing objects under non-rigid surface deformations.