Sparse representation (or coding)-based classification (SRC) has gained great success in face recognition in recent years. However, SRC emphasizes the sparsity too much and overlooks the correlation information which has been demonstrated to be critical in real-world face recognition problems. Besides, some paper considers the correlation but overlooks the discriminative ability of sparsity. Different from these existing techniques, in this paper, we propose a framework called adaptive sparse representation-based classification (ASRC) in which sparsity and correlation are jointly considered. Specifically, when the samples are of low correlation, ASRC selects the most discriminative samples for representation, like SRC; when the training samples are highly correlated, ASRC selects most of the correlated and discriminative samples for representation, rather than choosing some related samples randomly. In general, the representation model is adaptive to the correlation structure that benefits from both l 1 -norm and l 2 -norm. Extensive experiments conducted on publicly available data sets verify the effectiveness and robustness of the proposed algorithm by comparing it with the state-of-the-art methods.
However, SRC is under the assumption that the query image @math and the training images are well aligned. It is indicated that with sufficient training samples that cover nearly all the possible variations, @math can be correctly represented and robust to variations @cite_3 . Thus, SRC may fail in the case that the query image is misaligned or the dictionary has a small number of samples. Meanwhile, due to the sparsity, SRC may have the instability problem when samples are highly correlated. If the subjects correlated to the query image look similar, the SRC method tends to select one at random for representation rather than selecting them all. It indicates that SRC fails to capture the correlation structure of the dictionary which is critical in face recognition @cite_30 .
@cite_30 @cite_3
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Recently, sparse representation based classification (SRC) and collaborative representation based classification (CRC) have been successfully used for visual recognition and have demonstrated impressive performance. Given a test sample, SRC or CRC formulates its linear representation with respect to the training samples and then computes the residual error for each class. SRC or CRC assumes that the training samples from each class contribute equally to the dictionary in the corresponding class, i.e., the dictionary consists of the training samples in that class. This, however, leads to high residual error and instability. To overcome this limitation, we propose a class specific dictionary learning algorithm. To be specific, by introducing the dual form of dictionary learning, an explicit relationship between the basis vectors and the original image features is represented, which also enhances the interpretability. SRC or CRC can be thus considered as a special case of the proposed algorithm. Blockwise coordinate descent algorithm and Lagrange multipliers are then adopted to optimize the corresponding objective function. Extensive experimental results on five benchmark face recognition datasets show that the proposed algorithm achieves superior performance compared with conventional classification algorithms. HighlightsA novel class specific dictionary learning (CSDL) approach is proposed, where the standard collaborative representation based classification (CRC) or sparse representation based classification (SRC) can be considered as its special cases.The dual form of dictionary learning is proposed to enhance the interpretability.Our proposed CSDL achieves superior face recognition performance on several benchmark datasets. Sparse representation (or coding)-based classification (SRC) has gained great success in face recognition in recent years. However, SRC emphasizes the sparsity too much and overlooks the correlation information which has been demonstrated to be critical in real-world face recognition problems. Besides, some paper considers the correlation but overlooks the discriminative ability of sparsity. Different from these existing techniques, in this paper, we propose a framework called adaptive sparse representation-based classification (ASRC) in which sparsity and correlation are jointly considered. Specifically, when the samples are of low correlation, ASRC selects the most discriminative samples for representation, like SRC; when the training samples are highly correlated, ASRC selects most of the correlated and discriminative samples for representation, rather than choosing some related samples randomly. In general, the representation model is adaptive to the correlation structure that benefits from both l 1 -norm and l 2 -norm. Extensive experiments conducted on publicly available data sets verify the effectiveness and robustness of the proposed algorithm by comparing it with the state-of-the-art methods. The success of sparse representation based classification (SRC) has largely boosted the research of sparsity based face recognition in recent years. A prevailing view is that the sparsity based face recognition performs well only when the training images have been carefully controlled and the number of samples per class is sufficiently large. This paper challenges the prevailing view by proposing a prototype plus variation'' representation model for sparsity based face recognition. Based on the new model, a Superposed SRC (SSRC), in which the dictionary is assembled by the class centroids and the sample-to-centroid differences, leads to a substantial improvement on SRC. The experiments results on AR, FERET and FRGC databases validate that, if the proposed prototype plus variation representation model is applied, sparse coding plays a crucial role in face recognition, and performs well even when the dictionary bases are collected under uncontrolled conditions and only a single sample per classes is available. Sparse representation based classification (SRC) has recently been proposed for robust face recognition. To deal with occlusion, SRC introduces an identity matrix as an occlusion dictionary on the assumption that the occlusion has sparse representation in this dictionary. However, the results show that SRC's use of this occlusion dictionary is not nearly as robust to large occlusion as it is to random pixel corruption. In addition, the identity matrix renders the expanded dictionary large, which results in expensive computation. In this paper, we present a novel method, namely structured sparse representation based classification (SSRC), for face recognition with occlusion. A novel structured dictionary learning method is proposed to learn an occlusion dictionary from the data instead of an identity matrix. Specifically, a mutual incoherence of dictionaries regularization term is incorporated into the dictionary learning objective function which encourages the occlusion dictionary to be as independent as possible of the training sample dictionary. So that the occlusion can then be sparsely represented by the linear combination of the atoms from the learned occlusion dictionary and effectively separated from the occluded face image. The classification can thus be efficiently carried out on the recovered non-occluded face images and the size of the expanded dictionary is also much smaller than that used in SRC. The extensive experiments demonstrate that the proposed method achieves better results than the existing sparse representation based face recognition methods, especially in dealing with large region contiguous occlusion and severe illumination variation, while the computational cost is much lower.