Image recognition via two-dimensional random projection and nearest constrained subspace

• A feature extraction scheme using two-dimensional random projection, called 2DCS, is proposed.
• A new classifier, called NCSC (including it fast version NCSC-II), is proposed.
• Classifiers of NN, NFL and NS are the special cases of NCSC.
• With tuned parameter, NCSC/NCSC-II outperforms NN, NFL, NS and the Orthonormal ℓ2-norm method.

We consider the problem of image recognition via two-dimensional random projection and nearest constrained subspace. First, image features are extracted by a two-dimensional random projection. The two-dimensional random projection for feature extraction is an extension of the 1D compressive sampling technique to 2D and is computationally more efficient than its 1D counterpart and 2D reconstruction is guaranteed. Second, we design a new classifier called NCSC (Nearest Constrained Subspace Classifier) and apply it to image recognition with the 2D features. The proposed classifier is a generalized version of NN (Nearest Neighbor) and NFL (Nearest Feature Line), and it has a close relationship to NS (Nearest Subspace). For large datasets, a fast NCSC, called NCSC-II, is proposed. Experiments on several publicly available image sets show that when well-tuned, NCSC/NCSC-II outperforms its rivals including NN, NFL, NS and the orthonormal ℓ2ℓ2-norm classifier. NCSC/NCSC-II with the 2D random features also shows good classification performance in noisy environment.