›› 2018, Vol. 33 ›› Issue (1): 207-222.doi: 10.1007/s11390-018-1814-7

Special Issue: Artificial Intelligence and Pattern Recognition; Computer Graphics and Multimedia

• Regular Paper • Previous Articles     Next Articles

3D Face Similarity Measure by Fréchet Distances of Geodesics

Jun-Li Zhao1,2, Member, CCF, Zhong-Ke Wu3, Member, CCF, Zhen-Kuan Pan4,*, Member, CCF, Fu-Qing Duan3, Member, CCF, Jin-Hua Li1, Member, CCF, Zhi-Han Lv1, Kang Wang5, Yu-Cong Chen3   

  1. 1 School of Data Science and Software Engineering, Qingdao University, Qingdao 266071, China;
    2 College of Automation and Electrical Engineering, Qingdao University, Qingdao 266071, China;
    3 College of Information Science and Technology, Beijing Normal University, Beijing 100087, China;
    4 College of Computer Science and Technology, Qingdao University, Qingdao 266071, China;
    5 School of Management, Capital Normal University, Beijing 100048, China
  • Received:2017-06-20 Revised:2017-12-09 Online:2018-01-05 Published:2018-01-05
  • Contact: Zhen-Kuan Pan E-mail:zkpan@126.com
  • About author:Jun-Li Zhao is an associate professor and master supervisor in School of Data Science and Software Engineering, Qingdao University, Qingdao. She received her Ph.D. degree in computer applied technology in 2015 from Beijing Normal University, Beijing. She is a member of CCF. She is currently engaged in postdoctoral research on computer graphics, computer vision, and virtual reality research.
  • Supported by:

    This work was supported by the National Natural Science Foundation of China under Grant Nos. 61702293, 61772294, and 61572078, the Open Research Fund of the Ministry of Education Engineering Research Center of Virtual Reality Application of China under Grant No. MEOBNUEVRA201601. It was also partially supported by the National High Technology Research and Development 863 Program of China under Grant No. 2015AA020506, and the National Science and Technology Pillar Program during the 12th Five-Year Plan Period of China under Grant No. 2013BAI01B03.

3D face similarity is a critical issue in computer vision, computer graphics and face recognition and so on. Since Fréchet distance is an effective metric for measuring curve similarity, a novel 3D face similarity measure method based on Fréchet distances of geodesics is proposed in this paper. In our method, the surface similarity between two 3D faces is measured by the similarity between two sets of 3D curves on them. Due to the intrinsic property of geodesics, we select geodesics as the comparison curves. Firstly, the geodesics on each 3D facial model emanating from the nose tip point are extracted in the same initial direction with equal angular increment. Secondly, the Fréchet distances between the two sets of geodesics on the two compared facial models are computed. At last, the similarity between the two facial models is computed based on the Fréchet distances of the geodesics obtained in the second step. We verify our method both theoretically and practically. In theory, we prove that the similarity of our method satisfies three properties:reflexivity, symmetry, and triangle inequality. And in practice, experiments are conducted on the open 3D face database GavaDB, Texas 3D Face Recognition database, and our 3D face database. After the comparison with iso-geodesic and Hausdorff distance method, the results illustrate that our method has good discrimination ability and can not only identify the facial models of the same person, but also distinguish the facial models of any two different persons.

[1] Daoudi M, Srivastava A, Veltkamp R. 3D Face Modeling, Analysis and Recognition. John Wiley & Sons, 2013.

[2] Adan A, Adan M. A flexible similarity measure for 3D shapes recognition. IEEE Trans. Pattern Analysis and Machine Intelligence, 2004, 26(11):1507-1520.

[3] Stephan C N, Arthur R S. Assessing facial approximation accuracy:How do resemblance ratings of disparate faces compare to recognition tests? Forensic Science International, 2006, 159(Suppl 1):S159-S163.

[4] Quatrehomme G, Balaguer T, Staccini P, Alunni-Perret V. Assessment of the accuracy of three-dimensional manual craniofacial reconstruction:A series of 25 controlled cases. International Journal of Legal Medicine, 2007, 121(6):469-475.

[5] Li H Y, Wu Z K, Zhou M Q. A iso-geodesic stripes based similarity measure method for 3D face. In Proc. the 4th Int. Conf. Biomedical Engineering and Informatics (BMEI), October 2011, pp.2114-2118.

[6] Moorthy A K, Mittal A, Jahanbin S, Grauman K, Bovik A C. 3D facial similarity:Automatic assessment versus perceptual judgments. In Proc. the 4th IEEE Int. Conf. Biometrics:Theory Applications and Systems (BTAS), September 2010.

[7] Bowyer K W, Chang K, Flynn P. A survey of approaches and challenges in 3D and multi-modal 3D +2D face recognition. Computer Vision and Image Understanding, 2006, 101(1):1-15.

[8] Scheenstra A, Ruifrok A, Veltkamp R C. A survey of 3D face recognition methods. In Proc. the 5th Int. Conf. Audio-and Video-Based Biometric Person Authentication, July 2005, pp.891-899.

[9] Nagamine T, Uemura T, Masuda I. 3D facial image analysis for human identification. In Proc. the 11th IAPR Int. Conf. Pattern Recognition, Computer Vision and Applications, September 1992, pp.324-327.

[10] Wu Y J, Pan G, Wu Z H. Face authentication based on multiple profiles extracted from range data. In Proc. the 4th Int. Conf. Audio-and Video-Based Biometric Person Authentication, Jun. 2003, pp.515-522.

[11] ter Haar F B, Veltkampy R C. SHREC' 08 entry:3D face recognition using facial contour curves. In Proc. IEEE Int. Conf. Shape Modeling and Applications, June 2008, pp.259-260.

[12] Jahanbin S, Choi H, Liu Y, Bovik A C. Three dimensional face recognition using iso-geodesic and iso-depth curves. In Proc. the 2nd IEEE Int. Conf. Biometrics:Theory, Applications and Systems, October 2008.

[13] Bronstein A M, Bronstein M M, Kimmel R. Threedimensional face recognition. International Journal of Computer Vision, 2005, 64(1):5-30.

[14] Berretti S, Del Bimbo A, Pala P. Description and retrieval of 3D face models using iso-geodesic stripes. In Proc. the 8th ACM Int. Workshop on Multimedia Information Retrieval, October 2006, pp.13-22.

[15] Berretti S, Del Bimbo A, Pala P. 3D face recognition using iso-geodesic stripes. IEEE Trans. Pattern Analysis and Machine Intelligence, 2010, 32(12):2162-2177.

[16] Mpiperis I, Malassiotis S, Strintzis M G. 3-D face recognition with the geodesic polar representation. IEEE Trans. Information Forensics and Security, 2007, 2(3):537-547.

[17] Achermann B, Bunke H. Classifying range images of human faces with hausdorff distance. In Proc. the 15th Int. Conf. Pattern Recognition, September 2000, pp.809-813.

[18] Lee Y H, Shim J C. Curvature based human face recognition using depth weighted hausdorff distance. In Proc. Int. Conf. Image Processing, October 2004, pp.1429-1432.

[19] Shahbaz K. Applied similarity problems using Fréchet distance[Ph.D. Thesis]. Carleton University, Ottawa, 2013.

[20] Hu Y L, Duan F Q, Yin B C, Zhou M Q, Sun Y F, Wu Z K, Geng G H. A hierarchical dense deformable model for 3D face reconstruction from skull. Multimedia Tools and Applications, 2013, 64(2):345-364.

[21] Mitchell J S B, Mount D M, Papadimitriou C H. The discrete geodesic problem. SIAM Journal on Computing, 1987, 16(4):647-668.

[22] Xin S Q, Wang G J. Improving Chen and Han's algorithm on the discrete geodesic problem. ACM Trans. Graphics (TOG), 2009, 28(4):Article No. 104.

[23] Ying X, Xin S Q, He Y. Parallel Chen-Han (PCH) algorithm for discrete geodesics. ACM Trans. Graphics (TOG), 2014, 33(1):Article No. 9.

[24] Ying X, Wang X N, He Y. Saddle vertex graph (SVG):A novel solution to the discrete geodesic problem. ACM Trans. Graphics (TOG), 2013, 32(6):Article No. 170.

[25] Surazhsky V, Surazhsky T, Kirsanov D, Gortler S J, Hoppe H. Fast exact and approximate geodesics on meshes. ACM Trans. Graphics (TOG), 2005, 24(3):553-560.

[26] Fréchet M M. Sur quelques points du calcul fonctionnel. Rendiconti del Circolo Matematico di Palermo (1884-1940), 1906, 22(1):1-72. (in German)

[27] Alt H, Godau M. Computing the Fréchet distance between two polygonal curves. International Journal of Computational Geometry & Applications, 1995, 5(01n02):75-91.

[28] Rote G. Computing the Fréchet distance between piecewise smooth curves. Computational Geometry:Theory and Applications, 2007, 37(3):162-174.

[29] Eiter T, Mannila H. Computing discrete Fréchet distance. Technical Report CD-TR 94/64. http://citeseerx.ist.psu.edu/viewdoc/download?doi=, April 1994.

[30] Moreno A, Sánchez A. GavabDB:A 3D face database. In Proc. the 2nd COST Workshop on Biometrics on the Internet, March 2004, pp.75-80.

[31] Gupta S, Castleman K R, Markey M K, Bovik A C. Texas 3D face recognition database. In Proc. IEEE Southwest Symp. Image Analysis & Interpretation (SSIAI), May 2010, pp.97-100.

[32] Liu Y J. Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures. Computer-Aided Design, 2013, 45(3):695-704.

[33] Xu C X, Wang T Y, Liu Y J, Liu L G, He Y. Fast Wavefront Propagation (FWP) for computing exact geodesic distances on meshes. IEEE Trans. Visualization and Computer Graphics, 2015, 21(7):822-834.
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