caa a22 4500 467914958 CHVBK 20180406152859.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s11263-006-6659-9 doi (NATIONALLICENCE)springer-10.1007/s11263-006-6659-9 An Analysis of Linear Subspace Approaches for Computer Vision and Pattern Recognition [Elektronische Daten] [Pei Chen, David Suter] Linear subspace analysis (LSA) has become rather ubiquitous in a wide range of problems arising in pattern recognition and computer vision. The essence of these approaches is that certain structures are intrinsically (or approximately) low dimensional: for example, the factorization approach to the problem of structure from motion (SFM) and principal component analysis (PCA) based approach to face recognition. In LSA, the singular value decomposition (SVD) is usually the basic mathematical tool. However, analysis of the performance, in the presence of noise, has been lacking. We present such an analysis here. First, the "denoising capacity” of the SVD is analysed. Specifically, given a rank-r matrix, corrupted by noise—how much noise remains in the rank-r projected version of that corrupted matrix? Second, we study the "learning capacity” of the LSA-based recognition system in a noise-corrupted environment. Specifically, LSA systems that attempt to capture a data class as belonging to a rank-r column space will be affected by noise in both the training samples (measurement noise will mean the learning samples will not produce the "true subspace”) and the test sample (which will also have measurement noise on top of the ideal clean sample belonging to the "true subspace”). These results should help one to predict aspects of performance and to design more optimal systems in computer vision, particularly in tasks, such as SFM and face recognition. Our analysis agrees with certain observed phenomenon, and these observations, together with our simulations, verify the correctness of our theory. Springer Science + Business Media, LLC., 2006 singular value decomposition nationallicence linear subspaces nationallicence principal component analysis nationallicence structure from motion nationallicence factorization method nationallicence homography nationallicence face recognition nationallicence matrix perturbation nationallicence first-order perturbation nationallicence multiple eigenvalue/singular value nationallicence Chen Pei ARC Centre for Perceptive and Intelligent Machines in Complex Environments, Department of Electrical and Computer Systems Engineering, Monash University, 3800, Australia aut Suter David ARC Centre for Perceptive and Intelligent Machines in Complex Environments, Department of Electrical and Computer Systems Engineering, Monash University, 3800, Australia aut International Journal of Computer Vision Kluwer Academic Publishers 68/1(2006-06-01), 83-106 0920-5691 68:1<83 2006 68 11263 https://doi.org/10.1007/s11263-006-6659-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-006-6659-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Pei ARC Centre for Perceptive and Intelligent Machines in Complex Environments, Department of Electrical and Computer Systems Engineering, Monash University, 3800, Australia aut NATIONALLICENCE 700 1- Suter David ARC Centre for Perceptive and Intelligent Machines in Complex Environments, Department of Electrical and Computer Systems Engineering, Monash University, 3800, Australia aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 68/1(2006-06-01), 83-106 0920-5691 68:1<83 2006 68 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer