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## 基于旋转主方向梯度直方图特征的判别稀疏图映射算法

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• #### 摘要

非约束环境下采集的人脸图像复杂多变, 将其直接作为字典原子用于稀疏表示分类(sparse representation based classification, SRC), 识别效果不理想. 针对该问题, 本文提出一种基于旋转主方向梯度直方图特征的判别稀疏图映射(discriminative sparse graph embedding based on histogram of rotated principal orientation gradients, DSGE-HRPOG)算法, 用于构建类内紧凑、类间分离的低维判别特征字典, 提高稀疏表示分类准确性. 首先, 采用旋转主方向梯度直方图(histogram of rotated principal orientation gradients, HRPOG)特征算子提取非约束人脸图像的多尺度多方向梯度特征, 有效去除外界干扰和像素间冗余信息, 构建稳定、鉴别的HRPOG特征字典; 其次, 引入判别稀疏图映射(discriminative sparse graph embedding, DSGE)算法, 以类内重构散度最小、类间重构散度最大为目标计算特征字典的最佳低维投影矩阵, 进一步增强低维特征字典的判别性、紧致性; 最后, 提出投影矩阵和稀疏重构关系交替迭代优化算法, 将维数约简过程伴随在稀疏图构建过程中, 使分类效果更理想. 在AR, Extended Yale B, LFW和PubFig这4个数据库上进行大量实验, 验证了本文算法在实验环境数据库和真实环境数据库上的有效性.

#### 作者及机构信息

###### 通信作者: 童莹, tongying@njit.edu.cn
• 基金项目: 国家自然科学基金(批准号: 61703201, KYTYJJG206),江苏省自然科学基金(批准号: BK20170765)和南京工程学院青年创新基金(批准号: CKJB201602)资助的课题

#### 参考文献

 [1] Qian J J, Luo L, Yang J, Zhang F L, Lin Z C 2015 Pattern Recognit. 48 3145 [2] Chen Y, Yang J, Luo L, Zhang H M, Qian J J, Tai Y, Zhang J 2016 Pattern Recognit. 59 26 [3] Wright J, Yang A Y, Ganesh A, Sastry S S, Ma Y 2009 IEEE Trans. Pattern Anal. Mach. Intell. 31 210 [4] Yang M, Zhang L, Feng X C, Zhang D 2014 Int. J. Comput. Vis. 109 209 [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 [8] Zheng H, Tao D P 2015 Neurocomputing 162 9 [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 [11] Li J, Tao D 2012 IEEE Trans. Image Process. 21 4830 [12] Yan Y, Ricci E, Subramanian R 2014 IEEE Trans. Image Process. 23 5599 [13] Yang M, Zhang L, Shiu S C K, Zhang D 2013 IEEE Trans. Neural Netw. Learn. Syst. 24 900 [14] Yang M, Zhang L, Shiu S C K, Zhang D 2013 Pattern Recognit. 46 1865 [15] Georgakis C, Panagakis Y, Pantic M 2016 IEEE Trans. Image Process. 25 2021 [16] Zafeiriou S, Tzimiropoulos G, Petrou M, Stathaki T 2012 IEEE Trans. Neural Netw. 23 526 [17] Tenenbaum J B, De Silva V, Langford J C 2000 Science 290 2319 [18] Roweis S T, Saul L K 2000 Science 290 2323 [19] Belkin M, Niyogi P 2003 Neural Comput. 15 1373 [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 [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 [29] Yuan X F, Ge Z Q, Ye L J, Song Z H 2016 J. Chemometr. 30 430 [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 [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 [34] Lai Z H, Wong W K, Xu Y, Yang J, Zhang D 2016 IEEE Trans. Neural Netw. Learn. Syst. 27 723 [35] Yin J, Lai Z H, Zeng W M, Wei L 2018 Multimed. Tools Appl. 77 1069 [36] Zhang Y P, Xiang M, Yang B 2016 Neurocomputing 173 518 [37] Lu G F, Jin Z, Zou J 2012 Knowl-Based Syst. 31 119 [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 [40] Yang J, Chu D L, Zhang L, Xu Y, Yang J Y 2013 IEEE Trans. Neural Netw. 24 1023 [41] Zheng J W, Yang P, Chen S Y, Shen G J, Wang W L 2017 IEEE Trans. Image Process. 26 2408 [42] Gao Q X, Wang Q Q, Huang Y F, Gao X B 2015 IEEE Trans. Image Process. 24 5684 [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 [45] Yang M, Zhang L, Shiu S C K, Zhang D 2012 IEEE Trans. on Information Forensics and Security 7 1738 [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 [48] Tzimiropoulos G, Zafeiriou S, Pantic M 2012 IEEE Trans. Pattern Anal. Mach. Intell. 34 2454 [49] Ding C X, Choi J, Tao D C, Davis L S 2016 IEEE Trans. Pattern Anal. Mach. Intell. 38 518 [50] Weng D W, Wang Y L, Gong M M, Tao D C 2015 IEEE Trans. Image Process. 24 2287 [51] Yin J, Zeng W M, Wei L 2016 Knowl-Based Syst. 99 112 [52] Huang K K, Dai D Q, Ren C X 2017 Pattern Recognit. 62 87 [53] Liu Y, Gao Q X, Miao S, Gao X B, Nie F, Li Y S 2017 IEEE Trans. Image Process. 26 684 [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

#### 施引文献

• 图 1  本文算法的实现流程

Fig. 1.  Flow chart of the proposed algorithm.

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

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

图 3  3-HRPOG算子的旋转梯度卷积模板

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

Fig. 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.

图 5  5-HRPOG算子的旋转主方向梯度模板

图 6  Ms-HRPOG特征提取示意图

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

图 7  LFW数据库中某一图像的SPP稀疏重构权值

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

图 8  AR数据库部分样本图像

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

图 9  Extended Yale B数据库部分样本图像

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

图 10  Extended Yale B数据库部分遮挡样本图像

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

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

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

图 12  不同初始投影矩阵${{{P}}_0}$的识别率

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

图 13  目标函数收敛曲线

Fig. 13.  Convergence curve of the objective function.

•  [1] Qian J J, Luo L, Yang J, Zhang F L, Lin Z C 2015 Pattern Recognit. 48 3145 [2] Chen Y, Yang J, Luo L, Zhang H M, Qian J J, Tai Y, Zhang J 2016 Pattern Recognit. 59 26 [3] Wright J, Yang A Y, Ganesh A, Sastry S S, Ma Y 2009 IEEE Trans. Pattern Anal. Mach. Intell. 31 210 [4] Yang M, Zhang L, Feng X C, Zhang D 2014 Int. J. Comput. Vis. 109 209 [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 [8] Zheng H, Tao D P 2015 Neurocomputing 162 9 [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 [11] Li J, Tao D 2012 IEEE Trans. Image Process. 21 4830 [12] Yan Y, Ricci E, Subramanian R 2014 IEEE Trans. Image Process. 23 5599 [13] Yang M, Zhang L, Shiu S C K, Zhang D 2013 IEEE Trans. Neural Netw. Learn. Syst. 24 900 [14] Yang M, Zhang L, Shiu S C K, Zhang D 2013 Pattern Recognit. 46 1865 [15] Georgakis C, Panagakis Y, Pantic M 2016 IEEE Trans. Image Process. 25 2021 [16] Zafeiriou S, Tzimiropoulos G, Petrou M, Stathaki T 2012 IEEE Trans. Neural Netw. 23 526 [17] Tenenbaum J B, De Silva V, Langford J C 2000 Science 290 2319 [18] Roweis S T, Saul L K 2000 Science 290 2323 [19] Belkin M, Niyogi P 2003 Neural Comput. 15 1373 [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 [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 [29] Yuan X F, Ge Z Q, Ye L J, Song Z H 2016 J. Chemometr. 30 430 [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 [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 [34] Lai Z H, Wong W K, Xu Y, Yang J, Zhang D 2016 IEEE Trans. Neural Netw. Learn. Syst. 27 723 [35] Yin J, Lai Z H, Zeng W M, Wei L 2018 Multimed. Tools Appl. 77 1069 [36] Zhang Y P, Xiang M, Yang B 2016 Neurocomputing 173 518 [37] Lu G F, Jin Z, Zou J 2012 Knowl-Based Syst. 31 119 [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 [40] Yang J, Chu D L, Zhang L, Xu Y, Yang J Y 2013 IEEE Trans. Neural Netw. 24 1023 [41] Zheng J W, Yang P, Chen S Y, Shen G J, Wang W L 2017 IEEE Trans. Image Process. 26 2408 [42] Gao Q X, Wang Q Q, Huang Y F, Gao X B 2015 IEEE Trans. Image Process. 24 5684 [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 [45] Yang M, Zhang L, Shiu S C K, Zhang D 2012 IEEE Trans. on Information Forensics and Security 7 1738 [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 [48] Tzimiropoulos G, Zafeiriou S, Pantic M 2012 IEEE Trans. Pattern Anal. Mach. Intell. 34 2454 [49] Ding C X, Choi J, Tao D C, Davis L S 2016 IEEE Trans. Pattern Anal. Mach. Intell. 38 518 [50] Weng D W, Wang Y L, Gong M M, Tao D C 2015 IEEE Trans. Image Process. 24 2287 [51] Yin J, Zeng W M, Wei L 2016 Knowl-Based Syst. 99 112 [52] Huang K K, Dai D Q, Ren C X 2017 Pattern Recognit. 62 87 [53] Liu Y, Gao Q X, Miao S, Gao X B, Nie F, Li Y S 2017 IEEE Trans. Image Process. 26 684 [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
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##### 出版历程
• 收稿日期:  2019-02-20
• 修回日期:  2019-07-29
• 上网日期:  2019-11-26
• 刊出日期:  2019-10-01

## 基于旋转主方向梯度直方图特征的判别稀疏图映射算法

• 1. 中国人民解放军陆军工程大学, 通信工程学院, 南京　210007
• 2. 南京工程学院, 信息与通信工程学院, 南京　211167
• ###### 通信作者: 童莹, tongying@njit.edu.cn
基金项目: 国家自然科学基金(批准号: 61703201, KYTYJJG206),江苏省自然科学基金(批准号: BK20170765)和南京工程学院青年创新基金(批准号: CKJB201602)资助的课题

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