Title :
Reconstruction and Recognition of Tensor-Based Objects With Concurrent Subspaces Analysis
Author :
Xu, Dong ; Yan, Shuicheng ; Zhang, Lei ; Lin, Stephen ; Zhang, Hong-Jiang ; Huang, Thomas S.
Author_Institution :
Nanyang Technol. Univ., Singapore
Abstract :
Principal components analysis (PCA) has traditionally been utilized with data expressed in the form of 1-D vectors, but there exists much data such as gray-level images, video sequences, Gabor-filtered images and so on, that are intrinsically in the form of second or higher order tensors. For representations of image objects in their intrinsic form and order rather than concatenating all the object data into a single vector, we propose in this paper a new optimal object reconstruction criterion with which the information of a high-dimensional tensor is represented as a much lower dimensional tensor computed from projections to multiple concurrent subspaces. In each of these subspaces, correlations with respect to one of the tensor dimensions are reduced, enabling better object reconstruction performance. Concurrent subspaces analysis (CSA) is presented to efficiently learn these subspaces in an iterative manner. In contrast to techniques such as PCA which vectorize tensor data, CSA´s direct use of data in tensor form brings an enhanced ability to learn a representative subspace and an increased number of available projection directions. These properties enable CSA to outperform traditional algorithms in the common case of small sample sizes, where CSA can be effective even with only a single sample per class. Extensive experiments on images of faces and digital numbers encoded as second or third order tensors demonstrate that the proposed CSA outperforms PCA-based algorithms in object reconstruction and object recognition.
Keywords :
Gabor filters; image reconstruction; image representation; image resolution; image sequences; object recognition; principal component analysis; tensors; video signal processing; 1D vectors; Gabor-filtered image; concurrent subspaces analysis; gray-level images; image representations; object recognition; object reconstruction; principal components analysis; tensor-based objects; video sequences; Concurrent Subspaces Analysis; Concurrent subspaces analysis (CSA); Dimensionality Reduction; Object Reconstruction; Object Representation; Principal Components Analysis; dimensionality reduction; object reconstruction; object representation; principal components analysis (PCA);
Journal_Title :
Circuits and Systems for Video Technology, IEEE Transactions on
DOI :
10.1109/TCSVT.2007.903317