Jianjun Qian

Nuclear Norm Based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes

Recently, regression analysis has become a popular tool for face recognition. Most existing regression methods use the one-dimensional, pixel-based error model, which characterizes the representation error individually, pixel by pixel, and thus neglects the two-dimensional structure of the error image. We observe that occlusion and illumination changes generally lead, approximately, to a low-rank error image. In order to make use of this low-rank structural information, this paper presents a two-dimensional image-matrix-based error model, namely, nuclear norm based matrix regression (NMR), for face representation and classification. NMR uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the regression coefficients. We further develop a fast ADMM algorithm to solve the approximate NMR model and show it has a quadratic rate of convergence. We experiment using five popular face image databases: the Extended Yale B, AR, EURECOM, Multi-PIE and FRGC. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression-based methods for face recognition in the presence of occlusion and illumination variations.

Robust nuclear norm regularized regression for face recognition with occlusion

Recently, regression analysis based classification methods are popular for robust face recognition. These methods use a pixel-based error model, which assumes that errors of pixels are independent. This assumption does not hold in the case of contiguous occlusion, where the errors are spatially correlated. Furthermore, these methods ignore the whole structure of the error image. Nuclear norm as a matrix norm can describe the structural information well. Based on this point, we propose a nuclear-norm regularized regression model and use the alternating direction method of multipliers (ADMM) to solve it. We thus introduce a novel robust nuclear norm regularized regression (RNR) method for face recognition with occlusion. Compared with the existing structured sparse error coding models, which perform error detection and error support separately, our method integrates error detection and error support into one regression model. Experiments on benchmark face databases demonstrate the effectiveness and robustness of our method, which outperforms state-of-the-art methods. We propose a nuclear norm regularized regression model (NR) and use ADMM to solve it.We also provide the complexity analysis and convergence analysis of NR.The robust NR based classification (RNR) is introduced for face recognition.Experimental results demonstrate the advantages of our method.

Discriminative histograms of local dominant orientation (D-HLDO) for biometric image feature extraction

This paper presents a simple and robust method, namely discriminative histograms of local dominant orientation (D-HLDO), for biometric image feature extraction. In D-HLDO, the local dominant orientation map and the corresponding relative energy map are obtained by applying the singular value decomposition (SVD) to the collected gradient vectors over a local patch. The dominant orientation map and the relative energy map are then used to construct the concatenated histogram features. Local mean based nearest neighbor discriminant analysis (LM-NNDA) is finally employed to reduce the redundancy information and get the low-dimensional and discriminative features. The proposed method is applied to face, finger-knuckle-print and Palm biometrics and is examined using the AR, CMU PIE and FRGCv2.0 face image databases, the PolyU Palmprint database, and the PolyU Finger-Knuckle-Print database. Experimental results demonstrate the effectiveness of the proposed D-HLDO method.

Nuclear Norm-Based 2-DPCA for Extracting Features From Images

The 2-D principal component analysis (2-DPCA) is a widely used method for image feature extraction. However, it can be equivalently implemented via image-row-based principal component analysis. This paper presents a structured 2-D method called nuclear norm-based 2-DPCA (N-2-DPCA), which uses a nuclear norm-based reconstruction error criterion. The nuclear norm is a matrix norm, which can provide a structured 2-D characterization for the reconstruction error image. The reconstruction error criterion is minimized by converting the nuclear norm-based optimization problem into a series of F-norm-based optimization problems. In addition, N-2-DPCA is extended to a bilateral projection-based N-2-DPCA (N-B2-DPCA). The virtue of N-B2-DPCA over N-2-DPCA is that an image can be represented with fewer coefficients. N-2-DPCA and N-B2-DPCA are applied to face recognition and reconstruction and evaluated using the Extended Yale B, CMU PIE, FRGC, and AR databases. Experimental results demonstrate the effectiveness of the proposed methods.

Local Structure-Based Image Decomposition for Feature Extraction With Applications to Face Recognition

This paper presents a robust but simple image feature extraction method, called image decomposition based on local structure (IDLS). It is assumed that in the local window of an image, the macro-pixel (patch) of the central pixel, and those of its neighbors, are locally linear. IDLS captures the local structural information by describing the relationship between the central macro-pixel and its neighbors. This relationship is represented with the linear representation coefficients determined using ridge regression. One image is actually decomposed into a series of sub-images (also called structure images) according to a local structure feature vector. All the structure images, after being down-sampled for dimensionality reduction, are concatenated into one super-vector. Fisher linear discriminant analysis is then used to provide a low-dimensional, compact, and discriminative representation for each super-vector. The proposed method is applied to face recognition and examined using our real-world face image database, NUST-RWFR, and five popular, publicly available, benchmark face image databases (AR, Extended Yale B, PIE, FERET, and LFW). Experimental results show the performance advantages of IDLS over state-of-the-art algorithms.

Matrix Variate Distribution-Induced Sparse Representation for Robust Image Classification

Sparse representation learning has been successfully applied into image classification, which represents a given image as a linear combination of an over-complete dictionary. The classification result depends on the reconstruction residuals. Normally, the images are stretched into vectors for convenience, and the representation residuals are characterized by I2-norm, which actually assumes that the elements in the residuals are independent and identically distributed variables. However, it is hard to satisfy the hypothesis when it comes to some structural errors, such as illuminations, occlusions, and so on. In this paper, we represent the image data in their intrinsic matrix form rather than concatenated vectors. The representation residual is considered as a matrix variate following the matrix elliptically contoured distribution, which is robust to dependent errors and has long tail regions to fit outliers. Then, we seek the maximum a posteriori probability estimation solution of the matrix-based optimization problem under sparse regularization. An alternating direction method of multipliers (ADMMs) is derived to solve the resulted optimization problem. The convergence of the ADMM is proven theoretically. Experimental results demonstrate that the proposed method is more effective than the state-of-the-art methods when dealing with the structural errors.

Face Recognition With Pose Variations and Misalignment via Orthogonal Procrustes Regression

A linear regression-based method is a hot topic in face recognition community. Recently, sparse representation and collaborative representation-based classifiers for face recognition have been proposed and attracted great attention. However, most of the existing regression analysis-based methods are sensitive to pose variations. In this paper, we introduce the orthogonal Procrustes problem (OPP) as a model to handle pose variations existed in 2D face images. OPP seeks an optimal linear transformation between two images with different poses so as to make the transformed image best fits the other one. We integrate OPP into the regression model and propose the orthogonal Procrustes regression (OPR) model. To address the problem that the linear transformation is not suitable for handling highly non-linear pose variation, we further adopt a progressive strategy and propose the stacked OPR. As a practical framework, OPR can handle face alignment, pose correction, and face representation simultaneously. We optimize the proposed model via an efficient alternating iterative algorithm, and experimental results on three popular face databases, such as CMU PIE database, CMU Multi-PIE database, and LFW database, demonstrate the effectiveness of our proposed method.

Nuclear-L1 norm joint regression for face reconstruction and recognition with mixed noise

Abstract Occlusion, real disguise and illumination are still the common difficulties encountered in face recognition. The sparse representation based classifier (SRC) has shown a great potential in handling pixel-level sparse noise, while the nuclear norm based matrix regression (NMR) model has been demonstrated to be powerful for dealing with the image-wise structural noise. Both methods, however, might be not very effective for handling the mixed noise: the structural noise plus the sparse noise. In this paper, we present two nuclear-L 1 norm joint matrix regression (NL 1 R) models for face recognition with mixed noise, which are derived by using MAP (maximum a posteriori probability estimation). The first model considers the mixed noise as a whole, while the second model assumes the mixed noise is an additive combination of two independent componenral nts: sparse noise and structuoise. The proposed models can be solved by the alternating direction method of multipliers (ADMM). We validate the effectiveness of the proposed models through a series of experiments on face reconstruction and recognition.

Nearest Orthogonal Matrix Representation for Face Recognition

Abstract This paper presents a simple but effective method for face recognition, named nearest orthogonal matrix representation (NOMR). Specifically, the specific individual subspace of each image is estimated and represented uniquely by the sum of a set of basis matrices generated via singular value decomposition (SVD), i.e. the nearest orthogonal matrix (NOM) of original image. Then, the nearest neighbor criterion is introduced for recognition. Compared with the current specific individual subspace based methods (e.g. the sparse representation based classifier, the linear regression based classifier and so on), the proposed NOMR is more robust for alleviating the effect of illumination and heterogeneous (e.g. sketch face recognition), and more intuitive and powerful for handling the small sample size problem. To evaluate the performance of the proposed method, a series of experiments were performed on several face databases: Extended Yale B, CMU-PIE, FRGCv2, AR and CUHK Face Sketch database (CUFS). Experimental results demonstrate that the proposed method achieves encouraging performance compared with the state-of-the-art methods.

Weighted sparse coding regularized nonconvex matrix regression for robust face recognition

Most existing regression based classification methods for robust face recognition usually characterize the representation error using L1-norm or Frobenius-norm for the pixel-level noise or nuclear norm for the image-level noise, and code the coefficients vector by l1-norm or l2-norm. To our best knowledge, nuclear norm can be used to describe the low-rank structural information but may lead to the suboptimal solution, while l1-norm or l2-norm can promote the sparsity or cooperativity but may neglect the prior information (e.g., the locality and similarity relationship) among data. To solve these drawbacks, we propose two weighted sparse coding regularized nonconvex matrix regression models including weighted sparse coding regularized matrix -norm based matrix regression (WSMR) for the structural noise and weighted sparse coding regularized matrix -norm plus minimax concave plus (MCP) function based matrix regression (WSM2R) for the mixed noise (e.g, structural noise plus sparse noise). The MCP induced nonconvex function can overcome the imbalanced penalization of different singular values and entries of the error image matrix, and the weighted sparse coding can consider the prior information by borrowing a novel distance metric. The variants of inexact augmented Lagrange multiplier (iALM) algorithm including nonconvex iALM (NCiALM) and majorization-minimization iALM (MMiALM) are developed to solve the proposed models, respectively. The matrix -norm based classifier is devised for classification. Finally, experiments on four popular face image databases can validate the superiority of our methods compared with the-state-of-the-art regression methods.