﻿ 基于正交Log-Gabor滤波二值模式的人脸识别算法
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 智能系统学报  2019, Vol. 14 Issue (2): 330-337  DOI: 10.11992/tis.201708015 0

引用本文

YANG Huixian, FU Yu, ZENG Jinfang, et al. Face recognition based on orthogonal Log-Gabor binary pattern[J]. CAAI Transactions on Intelligent Systems, 2019, 14(2): 330-337. DOI: 10.11992/tis.201708015.

文章历史

Face recognition based on orthogonal Log-Gabor binary pattern
YANG Huixian , FU Yu , ZENG Jinfang , XU Chang
School of Physics and Optoelectronic, Xiangtan University, Xiangtan 411105, China
Abstract: To eliminate the effect of varying illumination on face recognition, a novel method of face recognition based on orthogonal log-Gabor binary pattern (OLGBP) is proposed in this paper. First, the algorithm performs log-Gabor transform on the samples in the orthogonal direction. Then the log-Gabor feature image is decomposed into real and imaginary parts, and the OLGBP feature vectors are constructed by fusing them into a binary pattern in the same scale at different directions. These feature vectors then form a collaboratively representative dictionary D. Finally, sparse coefficients are obtained by collaboratively representing these feature vectors with the test samples based on the dictionary D, and the test samples are classified by reconstruction of errors. The results for experiments performed on AR, Extend Yale B, and CAS-PEAL-R1 face databases show that the OLGBP algorithm has good effect on a single sample with illumination variation, and the effectiveness of the algorithm is verified.
Key words: face recognition    Log-Gabor filter    collaborative representation    orthogonality    sparse coding    binary pattern    single sample    multi scale

1 相关工作 1.1 协同表征

Di=[vi,1 　 vi,2 　···　 vi, n] $\in {\mathbb{\bf R}^{m \times n}}$

 $\hat a = \mathop {\arg \min }\limits_a \{ \left\| {{ y} - { {Da}}} \right\|_2^2 - \lambda \left\| { a} \right\|_2^2\}$ (1)

 $\widehat a = {({{ D}^{\rm T}}{ D} + \lambda \cdot { I})^{ - 1}}{{ D}^{\rm T}}y$ (2)

 ${\rm identity}\left( { y} \right) = \mathop {\arg \min }\limits_i \left\{ {\frac{{{{\left\| {{ y} - {{ D}_i}\widehat {{{ a}_i}}} \right\|}_2}}}{{{{\left\| {\widehat { a}} \right\|}_2}}}} \right\}$ (3)
1.2 正交Log-Gabor滤波器组 1.2.1 Log-Gabor滤波器

Gabor滤波器良好的空间局部性和方向选择性，被用于提取人脸多个方向的结构特征和空间频率，同时对光照和光照变化具有良好的鲁棒性。但Gabor滤波器存在两点不足：1)有直流分量，2)带宽受限。因此，Field提出Log-Gabor滤波器[12]。Log-Gabor滤波器带宽与人类视觉通道的带宽更接近，更适合对图像编码。二维Log-Gabor在频域上定义为

 ${\rm LG}\left( {u,v} \right) = \exp \left( { - \frac{{{{\left( {\log \left( {\displaystyle\frac{{{u_1}}}{{{u_2}}}} \right)} \right)}^2}}}{{2{{\left( {\log \left( {\displaystyle\frac{k}{{{u_0}}}} \right)} \right)}^2}}}} \right) \cdot \exp \left( { - \frac{{v_1^2}}{{{{\left( {2{\sigma _v}} \right)}^2}}}} \right)$ (4)

 \left\{ \begin{aligned} &{u_1} = u\cos \;\theta + v\sin \;\theta \\ &{v_1} = - u\sin \;\theta + v\cos \;\theta \end{aligned} \right.

 ${\varphi _{u,v}}\left( {x,y} \right) = I\left( {x,y} \right) \otimes {{\rm {LG}}_{u,v}}\left( {x,y} \right)$ (5)

1.2.2 正交Log-Gabor滤波器组

Log-Gabor滤波器组所提取的特征维数过高，从而导致计算机内存占有率高，算法识别耗时长，效率低下。受文献[19]的启发，提出正交Log-Gabor滤波器组。

2 OLGBP 2.1 人脸的OLGBP特征

OLGBP特征提取过程：

1) 将样本分别与正交Log-Gabor滤波器组卷积，得到LG特征。

2) 首先对LG做虚、实分解，得到LGR和LGI。然后将LGR和LGI二值化，并进行同尺度不同方向的特征融合。最后，将融合特征转十进制。二值化模式定义为

 $P_{u,v}^{\operatorname{Re} }\left( {\textit{z}} \right) = \left\{ {\begin{array}{*{20}{c}} 1,&{\operatorname{Re} \left( {{{\rm {LG}}_{u,v}}\left( {\textit{z}} \right)} \right) > 0} \\ 0,&{\operatorname{Re} \left( {{{\rm {LG}}_{u,v}}\left( {\textit{z}} \right)} \right) \leqslant 0} \end{array}} \right.$ (6)
 $P_{u,v}^{\operatorname{Im} }\left( {\textit{z}} \right) = \left\{ {\begin{array}{*{20}{c}} 1,&{\operatorname{Im} \left( {{{\rm {LG}}_{u,v}}\left( {\textit{z}} \right)} \right) > 0} \\ 0,&{\operatorname{Im} \left( {{{\rm {LG}}_{u,v}}\left( {\textit{z}} \right)} \right) \leqslant 0} \end{array}} \right.$ (7)

 $T_u^{\operatorname{Re} }\left( {\textit{z}} \right) = \sum\limits_{v = 0}^{n - 1} {P_{u,v}^{\operatorname{Re} }\left( {\textit{z}} \right)} \times {2^v}$ (8)
 $T_u^{\operatorname{Im} }\left({\textit{z}} \right) = \sum\limits_{v = 0}^{n - 1} {P_{u,v}^{\operatorname{Im} }\left( {\textit{z}}\right) \times {2^v}}$ (9)

2.2 人脸特征匹配

3 正交Log-Gabor滤波二值模式

AR人脸库包含了126人的4 000多幅人脸图像，涵盖表情、光照和遮挡3种变化，原图像的尺寸为120×165。随机从库中选取50名男性和50名女性，每人4幅光照变化的图像进行实验。实验中，选择AR人脸库每个人的第1幅图像作为训练样本，剩余3幅做测试样本，图像尺寸为83×60，部分图像如图4所示。

 Download: 图 4 AR 人脸库部分图像 Fig. 4 Example images in AR database

Extend Yale B人脸库包含了38人正面姿态下的2 432幅图像，涵盖64种不同光照，原图像的尺寸为168×192。根据光照入射角度分为5个子集：子集1的入射角度为0°~12°(每人7幅)；子集2的入射角度为13°~25°(每人12幅)；子集3的入射角度为26°~50°(每人12幅)；子集4的入射角度为51°~77°(每人14幅)；子集5的入射角度大于77°(每人19幅)。实验中，选择子集1每个人的第1幅图像作为训练样本，其他子集做测试样本，图像尺寸为96×84，部分图像如图5所示。

 Download: 图 5 Extend Yale B 人脸库部分图像 Fig. 5 Example images in Extend Yale B database

CAS-PEAL-R1人脸库包含正面图像库和姿态图像库，由1 040名中国人的99 450幅人脸图像组成，原图像的尺寸为100×100。实验中，采用正面图像库的光照变化图像做实验，随机选取其中199人(每人9幅)，每人的第i(i=1,2,3,4,5)幅作为训练样本，其余为测试样本，图像尺寸为83×60，部分图像如图6所示。

3.1 参数对识别率的影响

1)滤波器尺度u与方向v对识别率的影响

 Download: 图 7 s、o在AR的实验结果 Fig. 7 s and o’s result in AR
 Download: 图 8 s、o在CAS-PEAL-R1的实验结果 Fig. 8 s and o’s result in CAS-PEAL-R1

2)正交特征和全局特征对识别率的影响

3)编码系数比较

3.2 不同算法的识别性能对比

3.3 特征维数与时间复杂度分析

 $t = {T_1} + {T_2}$

4 结束语

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