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 智能系统学报  2018, Vol. 13 Issue (2): 261-268  DOI: 10.11992/tis.201609002 0

### 引用本文

LIU Shuaishi, GUO Wenyan, ZHANG Yan, et al. Recognition of facial expression in case of random shielding based on robust regularized coding[J]. CAAI Transactions on Intelligent Systems, 2018, 13(2): 261-268. DOI: 10.11992/tis.201609002.

### 文章历史

Recognition of facial expression in case of random shielding based on robust regularized coding
LIU Shuaishi, GUO Wenyan, ZHANG Yan, CHENG Xi
College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun 130000, China
Abstract: In order to improve facial expression recognition rate under the random shielding, a new face representation model was proposed: robust regularized coding. Regularized regression coefficients are used for carrying out robust regression for the given signals. Firstly, in order to reduce the influence of shielding on facial expression identification system, all pixels of the expression image to be identified will be assigned with different weights; then, because the occluded pixels should have lower weight values, hence, successive iteration is applied until the weight converges to the set weight threshold; finally, the sparse representation of image to be tested can be calculated by using the optimal weight matrix, in addition, the classified results of the expression image to be tested are determined by the minimal residual that the training samples approximate to the test image. The proposed method achieved an ideal performance in Japanese JAFFE expression database and Cohn-Kanade database, in addition, the experimental results show that the method is robust for the recognition of the facial expression randomly shielded.
Key words: random shielding    regularized coding    automatic update of weight    recognition of facial expression

1 鲁棒的正则化编码

 ${\hat{ \alpha }} = \arg \min {\left\| {{\alpha }} \right\|_1}{{s.t}}.\left\| {{{y}} - {{T\alpha }}} \right\|_2^2 \leqslant \varepsilon$ (1)

1.1 鲁棒的正则化编码模型

 ${\hat{ \alpha }} = \arg \max \left\{ {\ln P\left( {{{y}}|\left. {{\alpha }} \right) + \ln P\left( {{\alpha }} \right)} \right.} \right\}$ (2)

 ${\hat{\alpha }} = \arg \max \left\{ {\prod\limits_{i = 1}^n {{f_\theta }} \left( {{{{y}}_{{i}}} - {{{r}}_{{i}}}{{\alpha }}} \right)} + \prod\limits_{j = 1}^m {{f_0}} \left( {{{{\alpha }}_{{j}}}} \right)\right\}$ (3)

$\,{\rho _\theta }\left( {{e}} \right) = - \ln {f_\theta }\left( {{e}} \right)$ $\,{\rho _0}\left( {{\alpha }} \right) = - \ln {f_0}\left( {{\alpha }} \right)$ 式(3)转成：

 ${\hat{ \alpha }} = \arg \min \left\{ {\sum\limits_{i = 1}^n {{\rho _\theta }\left( {{{{y}}_{{i}}} - {{{r}}_{{i}}}{{\alpha }}} \right) + \sum\limits_{j = 1}^m {{\rho _0}\left( {{{{\alpha }}_{{j}}}} \right)} } } \right\}$ (4)

 ${f_0}\left( {{{{\alpha }}_{{j}}}} \right) = \beta \exp \left\{ { - {{\left( {\left| {{{{\alpha }}_{{j}}}} \right|/{\sigma _\alpha }} \right)}^\beta }} \right\}/\left( {2{\sigma _\alpha }\Gamma \left( {1/\beta } \right)} \right)$ (5)

1) ${\rho _\theta }\left( {0} \right)$ ${\rho _\theta }\left( {{e}} \right)$ 的局部最小值；

2) 对称性： ${\rho _\theta }\left( {{{{e}}_{{i}}}} \right) = {\rho _\theta }\left( { - {{{e}}_{{i}}}} \right)$

3) 单调性：当 $\left| {{{{e}}_{{1}}}} \right| > \left| {{{{e}}_{{2}}}} \right|$ 时， ${\rho _\theta }\left( {{{{e}}_{{1}}}} \right) > {\rho _\theta }\left( {{{{e}}_{{2}}}} \right)$ 。不失一般性，令 ${\rho _\theta }\left( {0} \right) =0$

1.2 迭代权重优化鲁棒的正则化编码模型

 ${\tilde F_\theta }\left( {{e}} \right) = {F_\theta }\left( {{{{e}}_{{0}}}} \right) + {\left( {{{e}} - {{{e}}_{{0}}}} \right)^{ T}}{F'_\theta }\left( {{{{e}}_{{0}}}} \right) + {R_1}\left( {{e}} \right)$ (6)

${F_\theta }\left( {{e}} \right)$ ${{e}} = 0$ 取得最小值的同时，它的近似值 ${\tilde F_\theta }\left( {{e}} \right)$ ${{e}} = 0$ 也应取得最小值。令 ${F'_\theta }\left( 0 \right) = 0$ ，可以得到 ${{W}}$ 的对角元素如式(7)：

 ${{{W}}_{{{{i}},{{i}}}}} = {\rho '_\theta }\left( {{{{e}}_{{{{0}},{{i}}}}}} \right)/{{{e}}_{{{{0}},{{i}}}}}$ (7)

 ${\hat{ \alpha }} = \arg \min \left\{ {\frac{1}{2}\left\| {{{{W}}^{1/2}}\left( {{{y}} - {{T\alpha }}} \right)} \right\|_2^2 + \sum\limits_{j = 1}^m {{\rho _0}\left( {{{{\alpha }}_{{j}}}} \right)} } \right\}$ (8)

1.3 权重W

${{{W}}_{{{{i}},{{i}}}}}$ 表示分配给待测表情图像 ${{y}}$ 每个像素点 $i$ 的权值。从人的感官认识出发，被遮挡部分的像素点应该具有较低的权重，这样可以减少它们对编码过程的影响。由于完备字典是由非遮挡的人脸表情图像构成的，可以很好地表征人脸表情，然而遮挡部分像素造成的异常值将具有较大的编码残差，因此，这些具有较大的编码残差像素点应具有较小的权重。通过观察式(7)可以得到 ${{{W}}_{{{{i}},{{i}}}}}$ ${{{e}}_{{i}}}$ 成反比，与 ${\rho '_\theta }\left( {{{{e}}_{{i}}}} \right)$ 成正比。由于ρθ可微、对称、单调并且在原点取得最小值，可以假设 ${{{W}}_{{{{i}},{{i}}}}}$ 是连续且对称的，与 ${{{e}}_{{i}}}$ 成反比而且有界。不失一般性，令 ${{{W}}_{{{{i}},{{i}}}}} \in \left[ {0,1} \right]$ ，综合多方面的考虑，逻辑函数是权重函数的最好选择。本文选用与逻辑函数具有相似性质的SVM hinge loss函数[12]作为权重函数。

 ${\left\| {{{{W}}^{\left( t \right)}} - {{{W}}^{\left( {t - 1} \right)}}} \right\|_2}/{\left\| {{{{W}}^{\left( {t - 1} \right)}}} \right\|_2} < \gamma$ (9)

 ${r_i}\left( {{y}} \right) = {\left\| {{{W}}_{{final}}^{1/2}\left( {{{y}} - {{T}}{{{\delta }}_{{i}}}\left( {{\hat{ \alpha }}} \right)} \right)} \right\|_2},i = 1,2, \cdots ,k$ (10)

 ${{identity}}\left( {{y}} \right) = \arg \mathop {\min }\limits_{i \in \left( {1, 2, \cdots ,k} \right)} \left( {{r_i}\left( {{y}} \right)} \right)$ (11)

 ${\hat{ \alpha }} = \arg \min \left\{ {\frac{1}{2}\left\| {{{P}}{{{W}}^{1/2}}\left( {{{y}} - {{T\alpha }}} \right)} \right\|_2^2 + \sum\limits_{j = 1}^m {{\rho _0}\left( {{{{\alpha }}_{{j}}}} \right)} } \right\}$ (12)
 Download: 图 2 权重收敛曲线 Fig. 2 The convergence curve of the weigh
 Download: 图 3 不同类别训练图像逼近待测图像的残差图 Fig. 3 The residual of each training class approximates the test image
2 实验描述与结果分析

2.1 实验描述

 Download: 图 4 实验用的两数据库中的部分随机遮挡表情图像 Fig. 4 Some samples of occluded facial images in two databases

2.2 结果分析