Sparse and Dense Hybrid Representation via Dictionary Decomposition for Face Recognition

Sparse representation provides an effective tool for classification under the conditions that every class has sufficient representative training samples and the training data are uncorrupted. These conditions may not hold true in many practical applications. Face identification is an example where we have a large number of identities but sufficient representative and uncorrupted training images cannot be guaranteed for every identity. A violation of the two conditions leads to a poor performance of the sparse representation-based classification (SRC). This paper addresses this critic issue by analyzing the merits and limitations of SRC. A sparse- and dense-hybrid representation (SDR) framework is proposed in this paper to alleviate the problems of SRC. We further propose a procedure of supervised low-rank (SLR) dictionary decomposition to facilitate the proposed SDR framework. In addition, the problem of the corrupted training data is also alleviated by the proposed SLR dictionary decomposition. The application of the proposed SDR-SLR approach in face recognition verifies its effectiveness and advancement to the field. Extensive experiments on benchmark face databases demonstrate that it consistently outperforms the state-of-the-art sparse representation based approaches and the performance gains are significant in most cases.

[1]  Xudong Jiang,et al.  Enhanced maximum likelihood face recognition , 2006 .

[2]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[3]  Michael Elad,et al.  Sparse Representation for Color Image Restoration , 2008, IEEE Transactions on Image Processing.

[4]  Xudong Jiang,et al.  Eigenfeature Regularization and Extraction in Face Recognition , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Vincent Lepetit,et al.  Are sparse representations really relevant for image classification? , 2011, CVPR 2011.

[6]  Jen-Tzung Chien,et al.  Discriminant Waveletfaces and Nearest Feature Classifiers for Face Recognition , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Stan Z. Li,et al.  Face recognition based on nearest linear combinations , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[9]  Yu-Chiang Frank Wang,et al.  Low-rank matrix recovery with structural incoherence for robust face recognition , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[10]  Guillermo Sapiro,et al.  Sparse Representation for Computer Vision and Pattern Recognition , 2010, Proceedings of the IEEE.

[11]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[12]  Xudong Jiang,et al.  Complete discriminant evaluation and feature extraction in kernel space for face recognition , 2008, Machine Vision and Applications.

[13]  G. Sapiro,et al.  A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. , 2013, Journal of structural biology.

[14]  Yihong Gong,et al.  Locality-constrained Linear Coding for image classification , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[15]  Xudong Jiang,et al.  Modular Weighted Global Sparse Representation for Robust Face Recognition , 2012, IEEE Signal Processing Letters.

[16]  Jian Yang,et al.  Regularized Robust Coding for Face Recognition , 2012, IEEE Transactions on Image Processing.

[17]  Hyeonjoon Moon,et al.  The FERET evaluation methodology for face-recognition algorithms , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[19]  Xudong Jiang,et al.  Human Detection by Quadratic Classification on Subspace of Extended Histogram of Gradients , 2014, IEEE Transactions on Image Processing.

[20]  Stephen Lin,et al.  Graph Embedding and Extensions: A General Framework for Dimensionality Reduction , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  D. Donoho For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution , 2006 .

[22]  Lei Zhang,et al.  Sparse representation or collaborative representation: Which helps face recognition? , 2011, 2011 International Conference on Computer Vision.

[23]  Pascal Frossard,et al.  Dictionary Learning , 2011, IEEE Signal Processing Magazine.

[24]  Aleix M. Martinez,et al.  The AR face database , 1998 .

[25]  Sébastien Marcel,et al.  A Scalable Formulation of Probabilistic Linear Discriminant Analysis: Applied to Face Recognition , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Ran He,et al.  Maximum Correntropy Criterion for Robust Face Recognition , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  Yaakov Tsaig,et al.  Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse , 2008, IEEE Transactions on Information Theory.

[28]  David J. Kriegman,et al.  Clustering appearances of objects under varying illumination conditions , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[29]  Yueting Zhuang,et al.  Sparse representation using nonnegative curds and whey , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[30]  Ronen Basri,et al.  Lambertian Reflectance and Linear Subspaces , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[31]  Guillermo Sapiro,et al.  Classification and clustering via dictionary learning with structured incoherence and shared features , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[32]  Guillermo Sapiro,et al.  Discriminative learned dictionaries for local image analysis , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[33]  Larry S. Davis,et al.  Learning Structured Low-Rank Representations for Image Classification , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[34]  Xudong Jiang,et al.  Noise-Resistant Local Binary Pattern With an Embedded Error-Correction Mechanism , 2013, IEEE Transactions on Image Processing.

[35]  Chunheng Wang,et al.  Sparse representation for face recognition based on discriminative low-rank dictionary learning , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[36]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[37]  John Wright,et al.  RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[38]  Yi Ma,et al.  The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices , 2010, Journal of structural biology.

[39]  David J. Kriegman,et al.  Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection , 1996, ECCV.

[40]  Arvind Ganesh,et al.  Fast Convex Optimization Algorithms for Exact Recovery of a Corrupted Low-Rank Matrix , 2009 .

[41]  David Zhang,et al.  Fisher Discrimination Dictionary Learning for sparse representation , 2011, 2011 International Conference on Computer Vision.

[42]  Anders P. Eriksson,et al.  Is face recognition really a Compressive Sensing problem? , 2011, CVPR 2011.

[43]  Mohammed Bennamoun,et al.  Linear Regression for Face Recognition , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[44]  Arvind Ganesh,et al.  Fast algorithms for recovering a corrupted low-rank matrix , 2009, 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[45]  A. Martínez,et al.  The AR face databasae , 1998 .

[46]  Takeo Kanade,et al.  Multi-PIE , 2008, 2008 8th IEEE International Conference on Automatic Face & Gesture Recognition.

[47]  Jian Yang,et al.  KPCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and recognition , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[48]  Jun Guo,et al.  In Defense of Sparsity Based Face Recognition , 2013, 2013 IEEE Conference on Computer Vision and Pattern Recognition.

[49]  David J. Kriegman,et al.  Acquiring linear subspaces for face recognition under variable lighting , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[50]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[51]  Guillermo Sapiro,et al.  Supervised Dictionary Learning , 2008, NIPS.

[52]  Baback Moghaddam,et al.  Principal Manifolds and Probabilistic Subspaces for Visual Recognition , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[53]  Xudong Jiang,et al.  Asymmetric Principal Component and Discriminant Analyses for Pattern Classification , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[54]  Hossein Mobahi,et al.  Toward a Practical Face Recognition System: Robust Alignment and Illumination by Sparse Representation , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[55]  M. Turk,et al.  Eigenfaces for Recognition , 1991, Journal of Cognitive Neuroscience.

[56]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[57]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[58]  Yuxiao Hu,et al.  Face recognition using Laplacianfaces , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[59]  Xudong Jiang,et al.  LBP-Based Edge-Texture Features for Object Recognition , 2014, IEEE Transactions on Image Processing.

[60]  Xudong Jiang,et al.  Linear Subspace Learning-Based Dimensionality Reduction , 2011, IEEE Signal Processing Magazine.

[61]  Yong Yu,et al.  Robust Recovery of Subspace Structures by Low-Rank Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[62]  Larry S. Davis,et al.  Learning a discriminative dictionary for sparse coding via label consistent K-SVD , 2011, CVPR 2011.

[63]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[64]  Stan Z. Li,et al.  Face recognition using the nearest feature line method , 1999, IEEE Trans. Neural Networks.

[65]  Jun Guo,et al.  Extended SRC: Undersampled Face Recognition via Intraclass Variant Dictionary , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[66]  Peng Zhao,et al.  On Model Selection Consistency of Lasso , 2006, J. Mach. Learn. Res..

[67]  Lei Zhang,et al.  Gabor Feature Based Sparse Representation for Face Recognition with Gabor Occlusion Dictionary , 2010, ECCV.