计算机应用   2017, Vol. 37 Issue (4): 1185-1188,1192  DOI: 10.11772/j.issn.1001-9081.2017.04.1185 0

### 引用本文

FANG Yiguang, LIU Wu, ZHANG Ji, ZHANG Lingchen, YUAN Meigui, QU Lei. Learning based kernel image differential filter for face recognition[J]. Journal of Computer Applications, 2017, 37(4): 1185-1188,1192. DOI: 10.11772/j.issn.1001-9081.2017.04.1185.

### 文章历史

1. 国网安徽省电力公司 安全监察质量部, 合肥 230022;
2. 国网安庆供电公司 安全监察质量部, 安徽 安庆 246000;
3. 安徽南瑞继远电网技术有限公司, 合肥 230088;
4. 安徽大学 电子信息工程学院, 合肥 230601

Learning based kernel image differential filter for face recognition
FANG Yiguang1, LIU Wu2, ZHANG Ji3, ZHANG Lingchen4, YUAN Meigui4, QU Lei4
1. Safety Supervision Quality Department, State Grid Anhui Electric Power Supply Company, Hefei Anhui 230022, China;
2. Safety Supervision Quality Department, State Grid Anqing Electric Power Supply Company, Anqing Anhui 246000, China;
3. Anhui Jiyuan Electric Power System Technology Company Limited, Hefei Anhui 230088, China;
4. School of Electronics and Information Engineering, Anhui University, Hefei Anhui 230601, China
Abstract: For the applications of face recognition, a learning based kernel image differential filter was proposed. Firstly, instead of designing the image filter in a handcrafted or analytical way, the new image filter was designed by dynamically learning from the training data. By integrating the idea of Linear Discriminant Analysis (LDA) into filter learning, the intra-class difference of filtered image was attenuated and the inter-class difference was amplified. Secondly, the second order derivative operator and kernel trick were introduced to better extract the image detail information and cope with the nonlinear feature space problem. As a result, the filter is adaptive and more discriminative feature description can be obtained. The proposed algorithm was experimented on AR and ORL face database and compared with linearly learning image filter named IFL, kernel image filter without differential information, and kernel image filter considering only one order differential information. The experimental results validate the effectiveness of the proposed method.
Key words: filter learning    Linear Discriminant Analysis (LDA)    kernel space    second order derivative    face recognition
0 引言

1 基于学习的线性判别滤波器

 图 1 图像块转为图像块向量 Figure 1 Converting image block to image block vector

 \begin{align} & df{{(\mathit{\boldsymbol{I}})}^{\mathit{\boldsymbol{p}}}}=[f{{(\mathit{\boldsymbol{I}})}^{{{\mathit{\boldsymbol{p}}}_{1}}}}-f{{(\mathit{\boldsymbol{I}})}^{\mathit{\boldsymbol{p}}}}, f{{(\mathit{\boldsymbol{I}})}^{{{\mathit{\boldsymbol{p}}}_{2}}}}-f{{(\mathit{\boldsymbol{I}})}^{\mathit{\boldsymbol{p}}}}, \cdots, \\ & \ \ \ \ \ \ \ \ \ \ \ \ f{{(\mathit{\boldsymbol{I}})}^{{{\mathit{\boldsymbol{p}}}_{d}}}}-f{{(\mathit{\boldsymbol{I}})}^{\mathit{\boldsymbol{p}}}}] \\ \end{align} (1)

 $df{{(\mathit{\boldsymbol{I}})}_{ij}}=[df(\mathit{\boldsymbol{I}})_{ij}^{1}, df(\mathit{\boldsymbol{I}})_{ij}^{2}, \cdots, df(\mathit{\boldsymbol{I}})_{ij}^{L}]$ (2)

 ${{\mathit{\boldsymbol{S}}}_{\rm{w}}}=\sum\limits_{i=1}^{C}{\sum\limits_{j=1}^{{{N}_{i}}}{(df{{(\mathit{\boldsymbol{I}})}_{ij}}-\overline{df{{(\mathit{\boldsymbol{I}})}_{i}}})}}{{(df{{(\mathit{\boldsymbol{I}})}_{ij}}-\overline{df{{(\mathit{\boldsymbol{I}})}_{i}}})}^{\rm{T}}}$ (3)
 ${{\mathit{\boldsymbol{S}}}_{\rm{b}}}=\sum\limits_{i=1}^{C}{{{N}_{i}}}(\overline{df{{(\mathit{\boldsymbol{I}})}_{i}}}-\overline{df(\mathit{\boldsymbol{I}})}){{(\overline{df{{(\mathit{\boldsymbol{I}})}_{i}}}-\overline{df(\mathit{\boldsymbol{I}})})}^{\rm{T}}}$ (4)

 $f{{(\mathit{\boldsymbol{I}})}^{\mathit{\boldsymbol{p}}}}={{\mathit{\boldsymbol{w}}}^{\rm{T}}}{{\mathit{\boldsymbol{I}}}^{\mathit{\boldsymbol{p}}}}$ (5)
 $df{{(\mathit{\boldsymbol{I}})}_{ij}}={{\mathit{\boldsymbol{w}}}^{\rm{T}}}d{{\mathit{\boldsymbol{I}}}_{ij}}$ (6)

 ${{\mathit{\boldsymbol{S}}}_{\rm{w}}}={{\mathit{\boldsymbol{w}}}^{\rm{T}}}(\sum\limits_{i=1}^{C}{\sum\limits_{j=1}^{{{N}_{i}}}{(d{{\mathit{\boldsymbol{I}}}_{ij}}-\overline{{{\mathit{\boldsymbol{I}}}_{i}}})}}{{(d{{\mathit{\boldsymbol{I}}}_{ij}}-\overline{{{\mathit{\boldsymbol{I}}}_{i}}})}^{\rm{T}}})\mathit{\boldsymbol{w}}={{\mathit{\boldsymbol{w}}}^{\rm{T}}}{{{\mathit{\boldsymbol{\hat{S}}}}}_{\rm{w}}}\mathit{\boldsymbol{w}}$ (7)
 ${{\mathit{\boldsymbol{S}}}_{\rm{b}}}={{\mathit{\boldsymbol{w}}}^{\rm{T}}}(\sum\limits_{i=1}^{C}{{{N}_{i}}}(\overline{{{\mathit{\boldsymbol{I}}}_{i}}}-\overline{\mathit{\boldsymbol{I}}}){{(\overline{{{\mathit{\boldsymbol{I}}}_{i}}}-\overline{\mathit{\boldsymbol{I}}})}^{\rm{T}}})\mathit{\boldsymbol{w}}={{\mathit{\boldsymbol{w}}}^{\rm{T}}}{{{\mathit{\boldsymbol{\hat{S}}}}}_{\rm{b}}}\mathit{\boldsymbol{w}}$ (8)

2 基于学习的核图像微分滤波器

2.1 图像块向量的微分信息扩充

 图 2 图像块向量的微分信息扩充 Figure 2 Differential information extension of image block vector

 \left\{\begin{align} & \frac{\partial \mathit{\boldsymbol{I}}(i, j)}{\partial x}=\mathit{\boldsymbol{I}}(i+1, j)-\mathit{\boldsymbol{I}}(i, j) \\ & \frac{\partial \mathit{\boldsymbol{I}}(i, j)}{\partial y}=\mathit{\boldsymbol{I}}(i, j+1)-\mathit{\boldsymbol{I}}(i, j) \\ \end{align} \right. (9)

 \left\{\begin{align} & \frac{{{\partial }^{2}}\mathit{\boldsymbol{I}}(i, j)}{\partial {{x}^{2}}}=\mathit{\boldsymbol{I}}(i+1, j)-2\mathit{\boldsymbol{I}}(i, j)+\mathit{\boldsymbol{I}}(i-1, j) \\ & \frac{{{\partial }^{2}}\mathit{\boldsymbol{I}}(i, j)}{\partial {{y}^{2}}}=\mathit{\boldsymbol{I}}(i, j+1)-2\mathit{\boldsymbol{I}}(i, j)+\mathit{\boldsymbol{I}}(i, j-1) \\ \end{align} \right. (10)

2.2 核图像微分滤波器学习

Iij为第i个人的第j个样本图像, Vijp为图像Iijp点处的经过2.1节微分信息扩充后的图像块向量。如果IijL个待处理像素, 如图 3所示, 可将这L个像素的图像块向量拼合成图像块向量矩阵${{\mathit{\boldsymbol{M}}}_{ij}}=[\mathit{\boldsymbol{V}}_{ij}^{1}, \mathit{\boldsymbol{V}}_{ij}^{2}, \cdots, \mathit{\boldsymbol{V}}_{ij}^{L}]$, 该矩阵中就包含了第i个人第j个样本图像所有局部区域的亮度以及一阶和二阶微分信息。

 图 3 图像块向量矩阵构建 Figure 3 Construction of image block matrix

 ${{\mathit{\boldsymbol{S}}}_{\rm{w}}}=\sum\limits_{i=1}^{C}{\sum\limits_{j=1}^{{{N}_{i}}}{({{\mathit{\boldsymbol{M}}}_{ij}}-{{\overline{\mathit{\boldsymbol{M}}}}_{i}})}}{{({{\mathit{\boldsymbol{M}}}_{ij}}-{{\overline{\mathit{\boldsymbol{M}}}}_{i}})}^{\rm{T}}}$ (11)
 ${{\mathit{\boldsymbol{S}}}_{\rm{b}}}=\sum\limits_{i=1}^{C}{{{N}_{i}}}({{\mathit{\boldsymbol{M}}}_{i}}-\overline{\mathit{\boldsymbol{M}}}){{({{\mathit{\boldsymbol{M}}}_{i}}-\overline{\mathit{\boldsymbol{M}}})}^{\rm{T}}}$ (12)

 $\varphi {{\mathit{\boldsymbol{S}}}_{\rm{w}}}=\sum\limits_{i=1}^{C}{\sum\limits_{j=1}^{{{N}_{i}}}{(\varphi {{\mathit{\boldsymbol{M}}}_{ij}}-\varphi {{\overline{\mathit{\boldsymbol{M}}}}_{i}})}}{{(\varphi {{\mathit{\boldsymbol{M}}}_{ij}}-\varphi {{\overline{\mathit{\boldsymbol{M}}}}_{i}})}^{\rm{T}}}$ (13)
 $\varphi {{\mathit{\boldsymbol{S}}}_{\rm{b}}}=\sum\limits_{i=1}^{C}{{{N}_{i}}}(\varphi {{\mathit{\boldsymbol{M}}}_{i}}-\varphi \overline{\mathit{\boldsymbol{M}}}){{(\varphi {{\mathit{\boldsymbol{M}}}_{i}}-\varphi \overline{\mathit{\boldsymbol{M}}})}^{\rm{T}}}$ (14)

3 实验结果及分析

3.1 直观比较实验

 图 4 基于学习的微分核图像滤波器的滤波效果 Figure 4 Results after applying learning based kernel image differential filter
3.2 AR库上的实验

AR库共有100人, 每人14张图片。图 5给出该库中的部分样本图像, 可以看出AR库存在明显的光照和表情变化, 这些因素引入的特征非线性有利于验证本文结合核运算的图像滤波器的有效性。

 图 5 AR库人脸样本图像 Figure 5 Sample images of AR dataset

3.3 ORL库上的实验

ORL库共有40人, 每人10张图片。表 2中给出了本文算法同其他算法的平均识别率对比。可以看出, 本文算法在不同度量方法下的识别率均优于其他算法, 这也说明了本文引入二阶微分和核运算的有效性。

4 结语

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