›› 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.

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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.

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