? 基于测地线Fréchet距离的三维人脸相似性度量
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Journal of Computer Science and Technology 2018, Vol. 33 Issue (1) :207-222    DOI: 10.1007/s11390-018-1814-7
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基于测地线Fréchet距离的三维人脸相似性度量
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 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
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 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

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摘要 三维人脸相似性度量是计算机视觉、计算机图形学和人脸识别中的一个关键问题。由于Fréchet距离是测量曲线相似性的一个有效度量,因此本文提出了一种通过在人脸模型上计算测地线的Fréchet距离来度量三维人脸相似度的新方法。在我们的方法中,通过两组3D曲线之间的相似度来测量两个3D曲面之间的相似性。由于测地线的内蕴属性,我们选择测地线作为对比曲线。首先,以相同的角度间隔和相同的初始方向在每个三维人脸模型上提取从鼻尖点出发的测地线。第二步,计算两组待比较人脸模型的两组测地线之间的Fréchet距离。最后,基于第二步获得的测地线的Fréchet距离计算两个人脸模型之间的相似度。我们已从理论和实践两方面验证了我们的方法。理论上,我们证明了该方法定义的相似度满足三个属性:自反性、对称性和三角不等式属性。实践上,在公开的三维人脸数据库Gavadb、德克萨斯3D人脸识别数据库和我们自己的3D人脸数据库中进行了实验。与等测地带和Hausdorff距离的方法相比,结果表明我们的方法具有良好的辨别能力,不仅可以识别同一人的面部模型,还可以区分不同人的面部模型。
关键词三维人脸   相似性度量   Fréchet距离   测地线     
Abstract: 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.
Keywords3D face   similarity measure   Fréchet distance   geodesic     
Received 2017-06-20;
本文基金:

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.

通讯作者: Zhen-Kuan Pan     Email: 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.
引用本文:   
Jun-Li Zhao, Zhong-Ke Wu, Zhen-Kuan Pan, Fu-Qing Duan, Jin-Hua Li, Zhi-Han Lv, K.基于测地线Fréchet距离的三维人脸相似性度量[J]  Journal of Computer Science and Technology , 2018,V33(1): 207-222
Jun-Li Zhao, Zhong-Ke Wu, Zhen-Kuan Pan, Fu-Qing Duan, Jin-Hua Li, Zhi-Han Lv, Kang Wang, Yu-Cong Chen.3D Face Similarity Measure by Fréchet Distances of Geodesics[J]  Journal of Computer Science and Technology, 2018,V33(1): 207-222
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