Robust multi-dimensional Null Space representation for image retrieval and classification

This paper presents a novel system for image retrieval and classification based on a robust multi-dimensional view invariant representation and a linear classifier algorithm. Specifically, multi-dimensional null space invariant (NSI) matrix representation has been derived. Moreover, the robustness of null space representation has been investigated with perturbation analysis in terms of the error ratio and SNR. The proposed representation is invariant to affine transformations and preserves the null space matrix. We use principal component null space analysis (PCNSA) of the NSI operator for recognition, indexing, and retrieval of 2D and 3D images. We rely on PCNSA to determine the distance of a query image to the centroid of the class, which is a statistical information vector in the PCNSA algorithm representing the corresponding class of the object. Our results shows that NSI provides a robust and powerful approach to image recognition and classification even when the query image or the stored image has been subjected to unknown affine transformations due to camera motions.