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Mathematical Problems in Engineering
Volume 2014, Article ID 832837, 17 pages
Research Article

3D Facial Similarity Measure Based on Geodesic Network and Curvatures

1College of Information Science and Technology, Beijing Normal University, Engineering Research Center of Virtual Reality and Applications, Ministry of Education, Beijing 100875, China
2College of Software and Technology, Qingdao University, Qingdao 266071, China
3School of Computer Engineering, Nanyang Technological University, Singapore 999002

Received 3 June 2014; Revised 18 September 2014; Accepted 18 September 2014; Published 4 November 2014

Academic Editor: Massimo Scalia

Copyright © 2014 Junli Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Automated 3D facial similarity measure is a challenging and valuable research topic in anthropology and computer graphics. It is widely used in various fields, such as criminal investigation, kinship confirmation, and face recognition. This paper proposes a 3D facial similarity measure method based on a combination of geodesic and curvature features. Firstly, a geodesic network is generated for each face with geodesics and iso-geodesics determined and these network points are adopted as the correspondence across face models. Then, four metrics associated with curvatures, that is, the mean curvature, Gaussian curvature, shape index, and curvedness, are computed for each network point by using a weighted average of its neighborhood points. Finally, correlation coefficients according to these metrics are computed, respectively, as the similarity measures between two 3D face models. Experiments of different persons’ 3D facial models and different 3D facial models of the same person are implemented and compared with a subjective face similarity study. The results show that the geodesic network plays an important role in 3D facial similarity measure. The similarity measure defined by shape index is consistent with human’s subjective evaluation basically, and it can measure the 3D face similarity more objectively than the other indices.