RSC算法：提升人脸识别的鲁棒性
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更新于2024-09-08
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"这篇文档详细介绍了RSC(鲁棒稀疏编码)算法在人脸识别中的应用，作者包括Meng Yang、Lei Zhang、Jian Yang和David Zhang等人，来自香港理工大学和南京科技大等机构。RSC是针对SRC(基于稀疏表示的分类)的改进，旨在提高人脸识别的鲁棒性，特别考虑了编码残差的实际分布情况，以更有效地处理遮挡、噪声等问题。"
在人脸识别领域，稀疏表示或编码（SRC）已经成为一种有效的技术。SRC的基本原理是将测试图像表示为训练样本的稀疏线性组合，并通过$l_2$范数或$l_1$范数来衡量编码残差的保真度。然而，这种模型通常假设编码残差遵循高斯或拉普拉斯分布，这在实际应用中可能不够精确，无法充分描述编码错误。
论文中提出的鲁棒稀疏编码（RSC）算法则是对这一问题的改进。RSC将稀疏编码视为一个带稀疏约束的稳健回归问题，寻找稀疏编码问题的最大似然估计（MLE）解。这样做的好处在于RSC对异常值（如遮挡、噪声等）具有更高的鲁棒性。为了解决RSC模型，文中提出了一种有效的迭代重加权稀疏编码算法。
实验部分，作者在多个数据集上进行了广泛的实验，结果证明RSC在处理噪声、部分遮挡等情况下，相比于SRC，能提供更稳定、准确的人脸识别性能。这使得RSC算法在实际应用中，尤其是在复杂环境和条件下的人脸识别任务中，具有更强的实用性。
RSC算法是SRC的一个重要发展，它通过更精确地建模编码残差的分布，提高了人脸识别的准确性和鲁棒性。对于从事人脸识别研究和开发的人员来说，这份文档提供了有价值的技术见解和实现方法，是理解和应用RSC算法的重要参考资料。
Robust Sparse Coding for Face Recognition
Meng Yang Lei Zhang
∗
Hong Kong Polytechnic Univ.
Jian Yang
Nanjing Univ. of Sci. & Tech.
David Zhang
Hong Kong Polytechnic Univ.
Abstract
Recently the sparse representation (or coding) based
classification (SRC) has been successfully used in face
recognition. In SRC, the testing image is represented as
a sparse linear combination of the training samples, and
the representation fidelity is measured by the 𝑙
2
-norm or
𝑙
1
-norm of coding residual. Such a sparse coding model
actually assumes that the coding residual follows Gaus-
sian or Laplacian distribution, which may not be accurate
enough to describe the coding errors in practice. In this
paper, we propose a new scheme, namely the robust sparse
coding (RSC), by modeling the sparse coding as a sparsity-
constrained robust regression problem. The RSC seeks for
the MLE (maximum likelihood estimation) solution of the
sparse coding problem, and it is much more robust to out-
liers (e.g., occlusions, corruptions, etc.) than SRC. An
efficient iteratively reweighted sparse coding algorithm is
proposed to solve the RSC model. Extensive experiments
on representative face databases demonstrate that the RSC
scheme is much more effective than state-of-the-art meth-
ods in dealing with face occlusion, corruption, lighting and
expression changes, etc.
1. Introduction
As a powerful tool for statistical signal modeling, sparse
representation (or sparse coding) has been successfully used
in image processing applications [16], and recently has led
to promising results in face recognition [24, 25, 27] and
texture classification [15]. Based on the findings that nat-
ural images can be generally coded by structural primitives
(e.g., edges and line segments) that are qualitatively similar
in form to simple cell receptive fields [18], sparse coding
techniques represent a natural image using a small number
of atoms parsimoniously chosen out of an over-complete
dictionary. Intuitively, the sparsity of the coding coefficient
vector can be measured by the 𝑙
0
-norm of it (𝑙
0
-norm counts
the number of nonzero entries in a vector). Since the com-
binatorial 𝑙
0
-norm minimization is an NP-hard problem, the
∗
Corresponding author. This research is supported by the Hong Kong
General Research Fund (PolyU 5351/08E).
𝑙
1
-norm minimization, as the closest convex function to 𝑙
0
-
norm minimization, is widely employed in sparse coding,
and it was shown that 𝑙
0
-norm and 𝑙
1
-norm minimizations
are equivalent if the solution is sufficiently sparse [3]. In
general, the sparse coding problem can be formulated as
min
𝜶
∥𝜶∥
1
s.t. ∥𝒚 − 𝐷𝜶∥
2
2
≤ 𝜀, (1)
where 𝒚 is a given signal, 𝐷 is the dictionary of coding
atoms, 𝜶 is the coding vector of 𝒚 over 𝐷, and 𝜀>0 is a
constant.
Face recognition (FR) is among the most visible and
challenging research topics in computer vision and pattern
recognition [29], and many methods, such as Eigenfaces
[21], Fisherfaces [2] and SVM [7], have been proposed in
the past two decades. Recently, Wright et al. [25] applied
sparse coding to FR and proposed the sparse representation
based classification (SRC) scheme, which achieves impres-
sive FR performance. By coding a query image 𝒚 as a
sparse linear combination of the training samples via the
𝑙
1
-norm minimization in Eq. (1), SRC classifies the query
image 𝒚 by evaluating which class of training samples could
result in the minimal reconstruction error of it with the as-
sociated coding coefficients. In addition, by introducing an
identity matrix 𝐼 as a dictionary to code the outlier pixels
(e.g., corrupted or occluded pixels):
min
𝜶,𝜷
∥[𝜶; 𝜷]∥
1
s.t. 𝒚 =[𝐷, 𝐼] ⋅ [𝜶; 𝜷] , (2)
the SRC method shows high robustness to face occlusion
and corruption. In [9], Huang et al. proposed a sparse rep-
resentation recovery method which is invariant to image-
plane transformation to deal with the misalignment and
pose variation in FR, while in [22] Wagner et al. proposed
a sparse representation based method that could deal with
face misalignment and illumination variation. Instead of di-
rectly using original facial features, Yang and Zhang [27]
used Gabor features in SRC to reduce greatly the size of
occlusion dictionary and improve a lot the FR accuracy.
The sparse coding model in Eq. (1)iswidelyusedin
literature. There are mainly two issues in this model. The
first one is that whether the 𝑙
1
-norm constraint ∥𝜶∥
1
is good
enough to characterize the signal sparsity. The second one is
625
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