Two-dimensional relaxed representation

In this paper, a novel classification framework called two-dimensional relaxed representation (2DRR) is proposed for image classification. Different from recent popular vector-based representations with/without sparsity which encode a vector signal as a sparse/nonsparse linear combination of elementary vector signals, 2DRR is based on 2D image matrices, where each column of the input matrix signal is represented by a combination of the corresponding columns of the elementary matrices. In order to preserve the global linear coding relationship between the input matrix and these elementary matrices, the proposed 2DRR constrains the coding coefficients corresponding to each column of the input matrix to be locally close. Then two algorithms are derived from the 2DRR framework under the l(2) norm and the l(1) norm respectively. Extensive experimental results show the effectiveness of the proposed algorithms in comparison to three existing algorithms. (C) 2013 Elsevier B.V. All rights reserved.