Discriminative sparsity graph embedding based on histogram of rotated princial orientation gradients

Tong Ying; Shen Yue-Hong; Wei Yi-Min

doi:10.7498/aps.68.20190224

Abstract

The unconstrained face images collected in the real environments include many complicated and changeable interference factors, and sparsity preserving projections (SPP) cannot well obtain the low-dimensional intrinsic structure embedded in the high-dimensional samples, which is important for subsequent sparse representation classifier (SRC). To deal with this problem, in this paper we propose a new method named discriminative sparsity graph embedding based on histogram of rotated principal orientation gradients (DSGE-HRPOG). Firstly, it extracts multi-scale and multi-directional gradient features of unconstrained face images by HRPOG feature descriptor and incorporates them into a discriminative feature dictionary of sparse representation classifier. Secondly, it seeks an optimal subspace of HRPOG feature dictionary in which the atoms in intra-classes are as compact as possible, while the atoms in inter-classes are as separable as possible by adopting the proposed DSGE dimensionality reduction method. Finally, an optimal algorithm is presented in which the low-dimensional projection and the sparse graph construction are iteratively updated, and the accuracy of unconstrained face recognition is further improved. Extensive experimental results on AR, Extended Yale B, LFW and PubFig databases demonstrate the effectiveness of our proposed method.

Keywords:

Authors and contacts

1.
College of Communication Engineering, The Army Engineering University of PLA, Nanjing 210007, China
2.
School of Information and Communication Engineering, Nanjing Institute of Technology, Nanjing 211167, China

Corresponding author: Tong Ying, tongying@njit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61703201, KYTYJJG206), the Natural Science Foundation of Jiangsu Province, China (Grant No.BK20170765), and the NIT fund for Young Scholar, China (Grant No.CKJB201602)

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References

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[4]	Yang M, Zhang L, Feng X C, Zhang D 2014 Int. J. Comput. Vis. 109 209 Google Scholar
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[12]	Yan Y, Ricci E, Subramanian R 2014 IEEE Trans. Image Process. 23 5599 Google Scholar
[13]	Yang M, Zhang L, Shiu S C K, Zhang D 2013 IEEE Trans. Neural Netw. Learn. Syst. 24 900 Google Scholar
[14]	Yang M, Zhang L, Shiu S C K, Zhang D 2013 Pattern Recognit. 46 1865 Google Scholar
[15]	Georgakis C, Panagakis Y, Pantic M 2016 IEEE Trans. Image Process. 25 2021 Google Scholar
[16]	Zafeiriou S, Tzimiropoulos G, Petrou M, Stathaki T 2012 IEEE Trans. Neural Netw. 23 526 Google Scholar
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[49]	Ding C X, Choi J, Tao D C, Davis L S 2016 IEEE Trans. Pattern Anal. Mach. Intell. 38 518 Google Scholar
[50]	Weng D W, Wang Y L, Gong M M, Tao D C 2015 IEEE Trans. Image Process. 24 2287 Google Scholar
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Cited By

图 1 本文算法的实现流程

Figure 1. Flow chart of the proposed algorithm.

DownLoad: Full-Size Img PowerPoint

图 2 3-HRPOG算子的梯度卷积模板示意图　(a) ${h_x}$模板; (b) ${h_y}$模板

Figure 2. Gradient convolution masks of 3-HRPOG feature descriptor: (a) ${h_x}$ mask; (b) ${h_y}$ mask.

DownLoad: Full-Size Img PowerPoint

图 3 3-HRPOG算子的旋转梯度卷积模板

Figure 3. Rotated gradient convolution masks of 3-HRPOG feature descriptor.

DownLoad: Full-Size Img PowerPoint

图 4 旋转不变性分析　(a) 原图及HOG和3-HRPOG的梯度矢量值; (b) 旋转${45^ \circ }$图像及HOG和3-HRPOG的梯度矢量值

Figure 4. Rotation invariance analysis: (a) Original binary image and gradient vectors of HOG and 3-HRPOG; (b) rotated ${45^ \circ }$ binary image and gradient vectors of HOG and 3-HRPOG.

DownLoad: Full-Size Img PowerPoint

图 5 5-HRPOG算子的旋转主方向梯度模板

Figure 5. Rotated dominant direction gradient masks of 5-HRPOG feature descriptor.

DownLoad: Full-Size Img PowerPoint

图 6 Ms-HRPOG特征提取示意图

Figure 6. The sketch of Ms-HRPOG feature descriptor.

DownLoad: Full-Size Img PowerPoint

图 7 LFW数据库中某一图像的SPP稀疏重构权值

Figure 7. Sparsity reconstruction weights of one sample with SPP algorithm on the LFW database.

DownLoad: Full-Size Img PowerPoint

图 8 AR数据库部分样本图像

Figure 8. Samples of one person in the AR database.

DownLoad: Full-Size Img PowerPoint

图 9 Extended Yale B数据库部分样本图像

Figure 9. Samples of one person in the Extended Yale B database

DownLoad: Full-Size Img PowerPoint

图 10 Extended Yale B数据库部分遮挡样本图像

Figure 10. Occlusion samples of one person in the Extended Yale B database.

DownLoad: Full-Size Img PowerPoint

图 11 部分样本图像　(a) LFW数据库部分样本; (b) PubFig数据库部分样本

Figure 11. Samples of one person: (a) LFW database; (b) PubFig database.

DownLoad: Full-Size Img PowerPoint

图 12 不同初始投影矩阵${{{P}}_0}$的识别率

Figure 12. Recognition rates based on different initial matrix${{{P}}_0}$.

DownLoad: Full-Size Img PowerPoint

图 13 目标函数收敛曲线

Figure 13. Convergence curve of the objective function.

DownLoad: Full-Size Img PowerPoint

表 1 AR数据库在表情、光照和时间干扰因素下的实验结果

Table 1. Experimental results on the AR database with the interference factors of expression, illumination and time.

Method	LPP^[22]	NPE^[23]	SPP^[33]	DSNPE^[37]	DP-NFL^[51]	SRC-DP^[40]	DSGE-pixels	DSGE-HRPOG
Method	LPP^[22]	NPE^[23]	SPP^[33]	DSNPE^[37]	DP-NFL^[51]	SRC-DP^[40]	DSGE-pixels	3-HRPOG	5-HRPOG	Ms-HRPOG
Recognition Rate/%	67.14	68.69	68.21	76.07	71.8	75.2	76.79	88.45	88.21	88.81
Dimension	115	311	220	140	63	63	322	777	754	774

DownLoad: CSV

表 2 AR数据库在遮挡干扰因素下的实验结果

Table 2. Experimental results of AR database with the occlusion interference.

	Experiment 1/%	Experiment 2/%	Experiment 3/%
LPP^[22]	71.39	68.68	69.46
NPE^[23]	72.64	71.81	71.08
SPP^[33]	75.90	72.92	74.07
DSNPE^[37]	80.28	78.26	78.14
SRC-DP^[40]	78.35	76.50	77.80
SRC-FDC^[42]	80.90	79.90	80.30
DSGE-pixels	79.03	78.75	82.65
DSGE-HRPOG (3-HRPOG)	88.54	89.51	90.53
DSGE-HRPOG (5-HRPOG)	89.31	89.58	90.98
DSGE-HRPOG (Ms-HRPOG)	89.31	90.00	91.06

DownLoad: CSV

表 3 AR数据库在混合干扰因素下的实验结果

Table 3. Experimental results on the AR database with the mix interference factors.

	Mean/%	Std/%	Dimension
LPP^[22]	95.90	0.38	141
NPE^[23]	95.87	0.55	311
SPP^[33]	90.39	0.90	151
DSNPE^[37]	98.02	0.33	200
Wang^[54]	97.85	0.93	—
Gao^[53]	98.59	0.53	—
DSGE-pixels	98.45	0.27	202
DSGE-HRPOG (3-HRPOG)	99.45	0.17	1350
DSGE-HRPOG (5-HRPOG)	99.37	0.12	1297
DSGE-HRPOG (Ms-HRPOG)	99.55	0.13	1385

DownLoad: CSV

表 4 Extended Yale B数据库在光照干扰因素下的实验结果

Table 4. Experimental results of Extended Yale B database with the illumination interference.

Method	LPP^[22]	NPE^[23]	SPP^[33]	DSNPE^[37]	GRSDA^[39]	RCDA^[52]	DSGE-pixels	DSGE-HRPOG
Method	LPP^[22]	NPE^[23]	SPP^[33]	DSNPE^[37]	GRSDA^[39]	RCDA^[52]	DSGE-pixels	3-HRPOG	5-HRPOG	Ms-HRPOG
Recognition Rate/%	87.86	89.31	85.79	85.74	82.7	92	86.03	91.35	89.77	92.48
Dimension	65	160	95	85	266	—	83	355	345	351

DownLoad: CSV

表 5 Extended Yale B数据库在遮挡干扰因素下的实验结果

Table 5. Experimental results of Extended Yale B database with the occlusion interference.

	Experiment 1/%	Experiment 2/%
LPP^[22]	95.51 ± 0.40	96.78 ± 0.72
NPE^[23]	96.43 ± 0.23	97.85 ± 0.31
SPP^[33]	92.57 ± 0.84	93.05 ± 0.77
DSNPE^[37]	94.18 ± 0.48	95.29 ± 0.54
Gao^[53]	86.91 ± 1.07	88.23 ± 0.91
DSGE-pixels	95.83 ± 0.66	96.21 ± 0.21
DSGE-HRPOG(3-HRPOG)	97.30 ± 0.20	97.73 ± 0.35
DSGE-HRPOG (5-HRPOG)	96.85 ± 0.38	96.93 ± 0.60
DSGE-HRPOG G(Ms-HRPOG)	97.98 ± 0.50	98.10 ± 0.31

DownLoad: CSV

表 6 LFW和PubFig数据库的实验结果

Table 6. Experimental results on the LFW database and PubFig database.

	LFW/%	PubFig/%
LPP^[22]	35.32	24.00
NPE^[23]	35.19	25.00
SPP^[33]	31.52	29.00
DSNPE^[37]	44.05	30.90
WGSC^[58]	47.60	37.50
RSRC^[3]	42.80	47.00
RRC^[57]	53.20	42.20
IRGSC^[41]	56.30	48.50
DSGE-pixels	51.52	38.60
DSGE-HOG	69.62	49.00
DSGE-HRPOG(3-HRPOG)	76.71	54.20
DSGE-HRPOG (5-HRPOG)	76.58	53.30
DSGE-HRPOG (Ms-HRPOG)	73.80	53.70

DownLoad: CSV

表 7 PubFig数据库上有联合优化和无联合优化的实验结果

Table 7. Experimental results with joint optimization and without joint optimization on the PubFig database.

	DSGE-HRPOG
	3-HRPOG	5-HRPOG	Ms-HRPOG
with joint optimization	54.20 (630)	53.30 (473)	53.70 (514)
without joint optimization	53.50 (514)	50.90 (423)	53.20 (514)

DownLoad: CSV

[1]	Qian J J, Luo L, Yang J, Zhang F L, Lin Z C 2015 Pattern Recognit. 48 3145 Google Scholar
[2]	Chen Y, Yang J, Luo L, Zhang H M, Qian J J, Tai Y, Zhang J 2016 Pattern Recognit. 59 26 Google Scholar
[3]	Wright J, Yang A Y, Ganesh A, Sastry S S, Ma Y 2009 IEEE Trans. Pattern Anal. Mach. Intell. 31 210 Google Scholar
[4]	Yang M, Zhang L, Feng X C, Zhang D 2014 Int. J. Comput. Vis. 109 209 Google Scholar
[5]	Vu T H, Monga V 2016 The 23rd IEEE International Conference on Image Processing Phoenix, Arizona, USA, September 25-28, 2016 p4428
[6]	Babaee M, Wolf T, Rigoll G 2016 The 23rd IEEE International Conference on Image Processing Phoenix, Arizona, USA, September 25-28, 2016 p704
[7]	Huang K K, Dai D Q, Ren C X, Lai Z R 2017 IEEE Trans. Neural Netw. 28 1082 Google Scholar
[8]	Zheng H, Tao D P 2015 Neurocomputing 162 9 Google Scholar
[9]	Cai S J, Zuo W M, Zhang L, Feng X C, Wang P 2014 The 13th European Conference on Computer Vision Zurich, Switzerland, September 6−12, 2014 p624
[10]	Yang J M, Yang M H 2017 IEEE Trans. Pattern Anal. Mach. Intell. 39 576 Google Scholar
[11]	Li J, Tao D 2012 IEEE Trans. Image Process. 21 4830 Google Scholar
[12]	Yan Y, Ricci E, Subramanian R 2014 IEEE Trans. Image Process. 23 5599 Google Scholar
[13]	Yang M, Zhang L, Shiu S C K, Zhang D 2013 IEEE Trans. Neural Netw. Learn. Syst. 24 900 Google Scholar
[14]	Yang M, Zhang L, Shiu S C K, Zhang D 2013 Pattern Recognit. 46 1865 Google Scholar
[15]	Georgakis C, Panagakis Y, Pantic M 2016 IEEE Trans. Image Process. 25 2021 Google Scholar
[16]	Zafeiriou S, Tzimiropoulos G, Petrou M, Stathaki T 2012 IEEE Trans. Neural Netw. 23 526 Google Scholar
[17]	Tenenbaum J B, De Silva V, Langford J C 2000 Science 290 2319 Google Scholar
[18]	Roweis S T, Saul L K 2000 Science 290 2323 Google Scholar
[19]	Belkin M, Niyogi P 2003 Neural Comput. 15 1373 Google Scholar
[20]	Lin B B, He X F, Zhang C Y, Ji M 2013 J. Mach. Learn. Res. 14 2945
[21]	Lin B B, Yang J, He X F, Ye J P 2014 Int. Conf. Mach. Learn. 145
[22]	He X, Niyogi P 2004 Advances in Neural Information Processing Systems 153
[23]	He X, Cai D, Yan S 2005 Proc. IEEE Int. Conf. Comput. Vis. 2 1208
[24]	Dornaika F, Raduncanu B 2013 The 26th IEEE Conference on Computer Vision and Pattern Recognition Portland, Oregon, USA, Jun 23-28, 2013 p862
[25]	Huang S C, Zhuang L 2016 Neurocomputing 218 373
[26]	Wan M H, Yang G W, Gai S, Yang Z J 2017 Multimed. Tools Appl. 76 355 Google Scholar
[27]	Liang J Z, Chen C, Yi Y F, Xu X X, Ding M 2017 IEEE Access 17201
[28]	Wang R, Nie F P, Hong R C, Chang X J, Yang X J, Yu W Z 2017 IEEE Trans. Image Process. 26 5019 Google Scholar
[29]	Yuan X F, Ge Z Q, Ye L J, Song Z H 2016 J. Chemometr. 30 430 Google Scholar
[30]	Yan S C, Xu D, Zhang B Y, Zhang H J, Yang Q, Lin S 2007 IEEE Trans. Pattern Anal. Mach. Intell. 29 40 Google Scholar
[31]	Belkin M, Niyogi P 2013 Neural Comput. 15 1373
[32]	Cortes C, Mohri M 2007 Advances in Neural Information Processing Systems Vancouver, Canada, December 3-8 2007 p305
[33]	Qiao L S, Chen S C, Tan X Y 2010 Pattern Recognit. 43 331 Google Scholar
[34]	Lai Z H, Wong W K, Xu Y, Yang J, Zhang D 2016 IEEE Trans. Neural Netw. Learn. Syst. 27 723 Google Scholar
[35]	Yin J, Lai Z H, Zeng W M, Wei L 2018 Multimed. Tools Appl. 77 1069 Google Scholar
[36]	Zhang Y P, Xiang M, Yang B 2016 Neurocomputing 173 518 Google Scholar
[37]	Lu G F, Jin Z, Zou J 2012 Knowl-Based Syst. 31 119 Google Scholar
[38]	Wei L, Xu F F, Wu A H 2014 Knowl-Based Syst. 136
[39]	Lou S J, Zhao X M, Chuang Y L, Yu H T, Zhang S Q 2016 Neurocomputing 173 290 Google Scholar
[40]	Yang J, Chu D L, Zhang L, Xu Y, Yang J Y 2013 IEEE Trans. Neural Netw. 24 1023 Google Scholar
[41]	Zheng J W, Yang P, Chen S Y, Shen G J, Wang W L 2017 IEEE Trans. Image Process. 26 2408 Google Scholar
[42]	Gao Q X, Wang Q Q, Huang Y F, Gao X B 2015 IEEE Trans. Image Process. 24 5684 Google Scholar
[43]	Zhang G Q, Sun H J, Xia G Y, Sun Q S 2016 IEEE Trans. Image Process. 25 4271
[44]	Ren C X, Dai D Q, Li X X, Lai Z R 2014 IEEE Trans. on Image Processing 23 725 Google Scholar
[45]	Yang M, Zhang L, Shiu S C K, Zhang D 2012 IEEE Trans. on Information Forensics and Security 7 1738 Google Scholar
[46]	Dalal N, Triggs B 2005 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition San Diego, California, June 20-26 2005 p886
[47]	Tian S X, Bhattacharya U, Lu S J, Su B L, Wang Q Q, Wei X H, Lu Y, Tan C L 2016 Pattern Recognit. 51 125 Google Scholar
[48]	Tzimiropoulos G, Zafeiriou S, Pantic M 2012 IEEE Trans. Pattern Anal. Mach. Intell. 34 2454 Google Scholar
[49]	Ding C X, Choi J, Tao D C, Davis L S 2016 IEEE Trans. Pattern Anal. Mach. Intell. 38 518 Google Scholar
[50]	Weng D W, Wang Y L, Gong M M, Tao D C 2015 IEEE Trans. Image Process. 24 2287 Google Scholar
[51]	Yin J, Zeng W M, Wei L 2016 Knowl-Based Syst. 99 112 Google Scholar
[52]	Huang K K, Dai D Q, Ren C X 2017 Pattern Recognit. 62 87 Google Scholar
[53]	Liu Y, Gao Q X, Miao S, Gao X B, Nie F, Li Y S 2017 IEEE Trans. Image Process. 26 684 Google Scholar
[54]	Wang H, Nie F P, Huang H 2014 The 31st International Conference on Machine Learning Beijing, China, June 21-26, 2014 p1836
[55]	Learned-Miller E, Huang G B, Roy C A, Li H X, Hua G 2016 Advances in Face Detection and Facial Image Analysis. 189
[56]	Kumar N, Berg A C, Belhumeur P N, Nayar S K 2009 Proc. IEEE Int. Conf. Comput. Vis. 365
[57]	Yang M, Zhang L, Yang J, Zhang D 2013 IEEE Trans. Image Process. 1753
[58]	Tang X, Feng G C, Cai J X 2014 Neurocomputing 402
[59]	Li F, Jiang M Y 2018 Neural Process. Lett. 47 661
[60]	Tao D P, Guo Y N, Li Y T, Gao X B 2018 IEEE Trans. Image Process. 27 325 Google Scholar

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Vol. 68, Issue 19 - 2019-10-05

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