# American Institute of Mathematical Sciences

## A new face feature point matrix based on geometric features and illumination models for facial attraction analysis

 School of Information Science and Technology, Northwest University, Xi'an, China

* Corresponding author: Jian Zhao

Received  July 2017 Revised  December 2017 Published  November 2018

Fund Project: The first author is supported by the National Natural Science Foundation of China grant 61379010, 61772421

In this paper, we propose a 81-point face feature points template that used for face attraction analysis. This template is proposed that based on the AAM model, according to the geometric characteristics and the illumination model. The experimental results demonstrate that, the attraction of human face can be analyzed by the feature vector analysis of human face image quantification and the influence of light intensity on the attraction of human face. By taking the appropriate algorithm, the concept of facial beauty attractiveness can be learned by machine with numeric expressions.

Citation: Jian Zhao, Fang Deng, Jian Jia, Chunmeng Wu, Haibo Li, Yuan Shi, Shunli Zhang. A new face feature point matrix based on geometric features and illumination models for facial attraction analysis. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2019073
##### References:
 [1] A. Asthana, S. Zafeiriou, S. Cheng and M. Pantic, Robust discriminative response map fitting with constrained local models, IEEE Conference on Computer Vision and Pattern Recognition, (2013), 3444-3451. [2] R. Basri and D. W. Jacobs, Lambertian reflectance and linear subspaces, IEEE Transactions on Pattern Analysis & Machine Intelligence, 25 (2003), 218-233. [3] F. Chen and D. Zhang, A benchmark for geometric facial beauty study, Lecture Notes in Computer Science, 6165 (2010), 21-32. [4] Y. Cheon and D. Kim, Natural facial expression recognition using differential-AAM and manifold learning, Pattern Recognition, 42 (2009), 1340-1350. [5] T. F. Cootes, G. J. Edwards and C. J. Taylor, Active appearance models, European Conference on Computer Vision, (2001), 484-498. [6] J. H. Langlois and L. A. Roggman, Attractive Faces Are Only Average, Psychological Science, 1 (1990), 115-121. [7] X.-F. Lu, Chinese research facial pattern types and techniques, China Academy of Fine Arts doctoral dissertation, 2010. [8] X.-F. Lu, Yuan Dynasty painter Wang Yi's "writing like a secret" and portrait program, Fine Arts., 18 (2005), 72-73. [9] H.-Y. Mao, Facial beauty attractive characteristics of the analysis and machine learning, South China University of Technology, 2011. [10] I. Matthews and S. Baker, Active appearance models revisited, International Journal of Computer Vision, 6165 (2004), 135-164. [11] S. C. Rhee and S. H. Koo, An objective system for measuring facial attractiveness, Plastic & Reconstructive Surgery, 119 (2006), 1953-1954. [12] A. J. Rubenstein, J. H. Langlois and L. A. Roggman, What makes a face attractive and why: The role of averageness in defining facial beauty, G Rhodes & L 62 Zebrowitz, Facial Attractiveness: Evolutionary, Cognitive, & Social Perspectives, 2002. [13] Y. Sato, M. D. Wheeler and K. Ikeuchi, Object Shape and Reflectance Modeling from Observation, Modeling from Reality. Springer US, (2001), 95-116. [14] G. Tzimiropoulos and M. Pantic, Optimization Problems for Fast AAM Fitting in-the-Wild, IEEE International Conference on Computer Vision, (2014), 593-600. [15] X.-M. Zhang, China United States, Beijing: Xinhua Publishing House, 2005.

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##### References:
 [1] A. Asthana, S. Zafeiriou, S. Cheng and M. Pantic, Robust discriminative response map fitting with constrained local models, IEEE Conference on Computer Vision and Pattern Recognition, (2013), 3444-3451. [2] R. Basri and D. W. Jacobs, Lambertian reflectance and linear subspaces, IEEE Transactions on Pattern Analysis & Machine Intelligence, 25 (2003), 218-233. [3] F. Chen and D. Zhang, A benchmark for geometric facial beauty study, Lecture Notes in Computer Science, 6165 (2010), 21-32. [4] Y. Cheon and D. Kim, Natural facial expression recognition using differential-AAM and manifold learning, Pattern Recognition, 42 (2009), 1340-1350. [5] T. F. Cootes, G. J. Edwards and C. J. Taylor, Active appearance models, European Conference on Computer Vision, (2001), 484-498. [6] J. H. Langlois and L. A. Roggman, Attractive Faces Are Only Average, Psychological Science, 1 (1990), 115-121. [7] X.-F. Lu, Chinese research facial pattern types and techniques, China Academy of Fine Arts doctoral dissertation, 2010. [8] X.-F. Lu, Yuan Dynasty painter Wang Yi's "writing like a secret" and portrait program, Fine Arts., 18 (2005), 72-73. [9] H.-Y. Mao, Facial beauty attractive characteristics of the analysis and machine learning, South China University of Technology, 2011. [10] I. Matthews and S. Baker, Active appearance models revisited, International Journal of Computer Vision, 6165 (2004), 135-164. [11] S. C. Rhee and S. H. Koo, An objective system for measuring facial attractiveness, Plastic & Reconstructive Surgery, 119 (2006), 1953-1954. [12] A. J. Rubenstein, J. H. Langlois and L. A. Roggman, What makes a face attractive and why: The role of averageness in defining facial beauty, G Rhodes & L 62 Zebrowitz, Facial Attractiveness: Evolutionary, Cognitive, & Social Perspectives, 2002. [13] Y. Sato, M. D. Wheeler and K. Ikeuchi, Object Shape and Reflectance Modeling from Observation, Modeling from Reality. Springer US, (2001), 95-116. [14] G. Tzimiropoulos and M. Pantic, Optimization Problems for Fast AAM Fitting in-the-Wild, IEEE International Conference on Computer Vision, (2014), 593-600. [15] X.-M. Zhang, China United States, Beijing: Xinhua Publishing House, 2005.
68 feature points detected face map
7-dimensional geometric features
The feature points of the geometric features in this paper
The feature point diagram of the illumination model
Improved light intensity map
7-dimensional distance feature vector description.
 Feature quantity number Feature quantity symbol Feature quantity description 1 F1 Nose and ears width (nose up to the top of the ear) 4 F4 Nose to the height of the forehead center 5 F5 Nose to the eyes of the angle 6 F6 Forehead center to the side of the distance 7 F7 The distance on both sides of the forehead
 Feature quantity number Feature quantity symbol Feature quantity description 1 F1 Nose and ears width (nose up to the top of the ear) 4 F4 Nose to the height of the forehead center 5 F5 Nose to the eyes of the angle 6 F6 Forehead center to the side of the distance 7 F7 The distance on both sides of the forehead
The slope of the nose of the ears
 Experimental sample Slope 1 Slope 2 Difference 1 0.0280 0.0399 -0.0119 3 0.0196 -0.0402 0.0598 4 -00476 -0.0562 0.0086 5 0.0840 0.0224 0.0616 6 0.1369 0.1168 0.0201
 Experimental sample Slope 1 Slope 2 Difference 1 0.0280 0.0399 -0.0119 3 0.0196 -0.0402 0.0598 4 -00476 -0.0562 0.0086 5 0.0840 0.0224 0.0616 6 0.1369 0.1168 0.0201
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