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Regularized Robust Coding for Face Recognition
Meng Yang, Lei Zhang, Jian Yang, David Zhang
TL;DR
Sparse representation face recognition relies on residual distributions that may not fit practical corruptions and uses a costly sparsity constraint. The paper proposes regularized robust coding with an iteratively reweighted solver, and reports stronger performance than prior sparse-representation methods with low computational cost.
Problem
SRC's Gaussian or Laplacian residual assumptions may be invalid under practical face variations, while its l1 sparsity constraint makes computation expensive.
Method
RRC robustly regresses signals with regularized coefficients and is solved efficiently using an iteratively reweighted regularized robust coding algorithm.
Results
RRC significantly outperforms previous state-of-the-art methods such as SRC, CESR, and GSRC; its l2-regularized version achieves high recognition rates with low computational cost.
Takeaways & Limitations
RRC is presented as a strong candidate scheme for robust face recognition under complicated face variations.
Takeaways & Limitations
The Gaussian or Laplacian priors on coding residuals may not hold well, especially when query face images contain occlusions, corruptions, or expression variations.
Abstract
from arXiv · showhide
Recently the sparse representation based classification (SRC) has been proposed for robust face recognition (FR). In SRC, the testing image is coded as a sparse linear combination of the training samples, and the representation fidelity is measured by the l2-norm or l1-norm of the coding residual. Such a sparse coding model assumes that the coding residual follows Gaussian or Laplacian distribution, which may not be effective enough to describe the coding residual in practical FR systems. Meanwhile, the sparsity constraint on the coding coefficients makes SRC's computational cost very high. In this paper, we propose a new face coding model, namely regularized robust coding (RRC), which could robustly regress a given signal with regularized regression coefficients. By assuming that the coding residual and the coding coefficient are respectively independent and identically distributed, the RRC seeks for a maximum a posterior solution of the coding problem. An iteratively reweighted regularized robust coding (IR3C) algorithm is proposed to solve the RRC model efficiently. Extensive experiments on representative face databases demonstrate that the RRC is much more effective and efficient than state-of-the-art sparse representation based methods in dealing with face occlusion, corruption, lighting and expression changes, etc.
1. Introduction
The introduction identifies two concerns with sparse representation for face recognition: high computational cost from l1 sparsity and limited residual modeling under practical corruptions. It motivates regularized robust coding as an alternative for robust recognition.
- Face recognition representation modeling remains challenging, particularly for holistic-feature methods that are not robust to face occlusion.
- SRC represents a query image as a sparse combination of all training samples and classifies it using class-specific reconstruction errors.
- SRC improves robustness to block occlusion, pixel corruption, and disguise by introducing an identity dictionary to code outlier pixels and modeling residuals with the l1-norm.
- The l1 sparsity constraint may be computationally expensive, while l2 regularization can perform equally well without imposing sparsity on the coding vector.
- Using l2- or l1-norm fidelity assumes Gaussian or Laplacian coding residuals, an assumption that may fail when query faces contain occlusions, corruptions, or expression variations.
- The paper proposes regularized robust coding and an iteratively reweighted solution, targeting occlusion, corruption, disguise, and large expression variations while avoiding the high cost of l1 sparsity.
2. Regularized Robust Coding (RRC)
RRC replaces fixed Gaussian or Laplacian residual modeling and l1 sparsity with a Bayesian robust coding objective using flexible residual fidelity and regularized coefficients. Its adaptive residual model fits heavy-tailed coding errors, while the resulting formulation supports efficient iterative optimization.
- Motivation: Gaussian or Laplacian residual priors can poorly describe coding errors in practical face images, especially under occlusion and corruption.The empirical residual distribution has a sharp peak near zero and a long tail caused mainly by occluded and corrupted pixels.
- Residual modeling: The proposed residual model fits the empirical heavy tail better than Gaussian and Laplacian models, which is more important than fitting the peak for robust face recognition.The paper links this tail-fitting behavior to robustness against outlier pixels.
- Motivation: SRC and RSC rely on l1-sparsity constraints, whose computational complexity is high, while l1 sparsity is not necessarily essential to SRC's success.RSC is described as a robust sparse-coding maximum-likelihood model, but its l1 constraint remains computationally expensive.
- RRC formulation: RSC is a specific RRC instantiation, whereas RRC permits more general regularization; Laplacian coefficient priors recover the l1-norm sparse constraint.The coefficient prior is modeled with a generalized Gaussian distribution, allowing regularization beyond the Laplacian case.
- RRC formulation: RRC formulates coding as a MAP problem with i.i.d. coding residuals and i.i.d. coding coefficients, combining a residual fidelity term with a prior-derived regularizer.The residual is modeled through a flexible distribution, while the coefficient prior determines the regularization term.
- Optimization: IR3C transforms RRC minimization into an iteratively reweighted regularized coding problem to obtain an approximate MAP solution efficiently.The residual distribution is adapted to the input query image, and the resulting weights assign smaller values to pixels with large residuals.
3. Algorithm of RRC
The IR3C algorithm iteratively updates robust-coding weights and regularized coefficients to minimize the RRC model, then classifies using class-specific reconstruction residuals. Its computational cost is lower than or comparable to SRC, especially for occluded or corrupted faces.
- IR3C algorithm: IR3C alternates updates of the weight matrices W and V with regularized coding-coefficient updates to minimize the RRC objective.The algorithm uses a locally optimal iterative procedure with a reasonable initialization for face recognition.
- Initialization: IR3C initializes the residual from y−Dα(1), where Dα(1) is the mean image of all training samples.The initial coding vector assigns equal coefficients to all training samples.
- Classification: After convergence, IR3C classifies y by selecting the class with the smallest weighted reconstruction residual.The residual uses each class sub-dictionary, final sub-coding vector, and final weight matrix.
- Computational complexity: IR3C with β=2 solves an l2-regularized least-squares problem using conjugate gradients, with per-solve complexity about O(k1nm).Here k1 is the conjugate-gradient iteration count; t outer iterations update W.
- Computational complexity: IR3C with β=1 has complexity about O(tn2m), while SRC with occlusion has complexity O(n2(m+n)1.3).The paper reports that IR3C with β=1 therefore has much lower complexity than SRC for face recognition with occlusion.
- Computational complexity: IR3C’s time consumption is lower than or comparable to SRC without occlusion and remains lower than or comparable to faster l1-norm solvers.With real disguise on AR, about 30% of pixels could be deleted because very small weights indicate outliers.
4. Experimental Results
Experiments across face databases evaluate RRC under ordinary variation, corruption, occlusion, disguise, validation, and computational cost. RRC_L1 generally provides the strongest recognition, while RRC_L2 offers similar accuracy with lower computation in high-dimensional settings.
- Recognition without occlusion: RRC_L1 achieves the best Extended Yale B recognition rate at 99.8%, exceeding SVM, SRC, LRC, LLC, and RRC_L2.The listed best recognition rates are 97.0%, 98.3%, 96.0%, 97.6%, 98.9%, and 99.8%, respectively.
- Recognition without occlusion: RRC_L1 achieves the highest AR recognition rates except at dimension 30, while RRC_L2 is generally second best.RRC performance is weaker with very low-dimensional features.
- Recognition without occlusion: RRC_L1 achieves the best performance across Multi-PIE tests, with average improvements of 6% over LLC and 2.3% for the reported comparison.Recognition declines from Session 1 to Session 3, but RRC_L1 and RRC_L2 drop less than competing methods.
- Recognition with occlusion: RRC methods outperform SRC under block occlusion, with more than 22% and 6% improvement at 50% and 40% occlusion, respectively.RRC_L2 achieves the best accuracy in the reported block-occlusion experiment and can match or exceed RRC_L1.
- Face validation: RRC_L2 obtains the best face-validation result, reaching a 95.8% true-positive rate at a 0.1 false-positive rate.The corresponding rates are 82.6% for CESR, 90.7% for SRC, and 93.3% for RRC_L1.
- Running time: RRC_L2 has the least computation time, while RRC_L1 is faster than SRC and GSRC and achieves higher recognition rates in almost all cases.Considering recognition and running time together, the authors identify RRC_L1 and RRC_L2 as the best methods.
5. Conclusion
The paper presents RRC and IR3C for robust face recognition, combining robustness to varied outliers with regularized coding. Experiments show strong recognition performance and lower computational cost, especially with l2-norm regularization.
- RRC and its IR3C algorithm provide a robust coding framework for face recognition under varied outlier conditions.The approach targets occlusion, corruption, expression changes, and other practical variations.
- IR3C adaptively reweights pixels according to coding residuals to identify outliers and reduce their effects on coding.
- l2-norm regularization is reported to be as powerful as l1-norm regularization in RRC while requiring much lower computational cost.
- RRC methods were evaluated under illumination, expression, occlusion, corruption, and face-validation conditions.
- RRC significantly outperforms previous state-of-the-art methods such as SRC, CESR, and GSRC.
- RRC with l2-norm regularization combines high recognition rate with low computational cost for practical robust face recognition systems.