Many classification approaches first represent a test sample using the training samples of all the classes. This collaborative representation is then used to label the test sample. It was a common belief that sparseness of the representation is the key to success for this classification scheme. However, more recently, it has been claimed that it is the collaboration and not the sparseness that makes the scheme effective. This claim is attractive as it allows to relinquish the computationally expensive sparsity constraint over the representation. In this paper, we first extend the analysis supporting this claim and then show that sparseness explicitly contributes to improved classification, hence it should not be completely ignored for computational gains. Inspired by this result, we augment a dense collaborative representation with a sparse representation and propose an efficient classification method that capitalizes on the resulting representation. The augmented representation and the classification method work together meticulously to achieve higher accuracy and lower computational time compared to state-of-the-art collaborative representation based classification approaches. Experiments on benchmark face, object and action databases show the efficacy of our approach.
In SRC @cite_30 , @math in Eq. ), which encourages the computed representation @math to be sparse. In Superposed-SRC (SSRC), @cite_16 modified the residual computation step of SRC. For SSRC, @math consists of class centroids and sample-to-centroid differences. While computing the residuals, SSRC keeps the coefficients of @math corresponding to the sample-to-centroid differences fixed in each @math . The CR-based classifier proposed by @cite_5 uses @math and solves Eq. ) using the Regularized Least Squares (RLS) method, hence denoted as CRC-RLS. @cite_1 used @math in Eq. ) and solved it as the standard least squares problem for face recognition. Chi and Porikli @cite_31 used a linear combination of a CR-based classifier and a nearest subspace classifier @cite_7 for improved classification performance.
@cite_30 @cite_7 @cite_1 @cite_5 @cite_31 @cite_16
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We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims. Previous work has demonstrated that the image variation of many objects (human faces in particular) under variable lighting can be effectively modeled by low-dimensional linear spaces, even when there are multiple light sources and shadowing. Basis images spanning this space are usually obtained in one of three ways: a large set of images of the object under different lighting conditions is acquired, and principal component analysis (PCA) is used to estimate a subspace. Alternatively, synthetic images are rendered from a 3D model (perhaps reconstructed from images) under point sources and, again, PCA is used to estimate a subspace. Finally, images rendered from a 3D model under diffuse lighting based on spherical harmonics are directly used as basis images. In this paper, we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low-dimensional linear space and that this subspace is close to those acquired by the other methods. More specifically, there exist configurations of k point light source directions, with k typically ranging from 5 to 9, such that, by taking k images of an object under these single sources, the resulting subspace is an effective representation for recognition under a wide range of lighting conditions. Since the subspace is generated directly from real images, potentially complex and or brittle intermediate steps such as 3D reconstruction can be completely avoided; nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse (harmonic) light fields. We validate the use of subspaces constructed in this fashion within the context of face recognition. Compressive Sensing has become one of the standard methods of face recognition within the literature. We show, however, that the sparsity assumption which underpins much of this work is not supported by the data. This lack of sparsity in the data means that compressive sensing approach cannot be guaranteed to recover the exact signal, and therefore that sparse approximations may not deliver the robustness or performance desired. In this vein we show that a simple £2 approach to the face recognition problem is not only significantly more accurate than the state-of-the-art approach, it is also more robust, and much faster. These results are demonstrated on the publicly available YaleB and AR face datasets but have implications for the application of Compressive Sensing more broadly. As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l 1 -norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1-norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC. 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.