Low-Rank Matrix Fitting Based on Subspace Perturbation Analysis with Applications to Structure from Motion

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 31; no. 5; pp. 841 - 854
• Main Authors: Hongjun Jia, Martinez, A.M.
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.05.2009; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Algorithms; Applied sciences; Artificial Intelligence; Bioinformatics; Computer graphics; Computer science; control theory; systems; Computer vision; Criteria; Data engineering; Exact sciences and technology; Fittings; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Imaging, Three-Dimensional - methods; Intelligence; Low-rank matrix; Mathematical analysis; Matrices; Matrix methods; matrix perturbation; missing data; Motion; Motion analysis; Movement; Noise; Optical noise; Pattern analysis; Pattern recognition; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Photography - methods; random matrix; Reproducibility of Results; Sensitivity and Specificity; structure from motion; Studies; subspace analysis; Upper bound; noise; matrix perturbation; subspace analysis; structure from motion; Additive noise; Occlusion; Validation; Computer vision; Random matrix; Low-rank matrix; Pattern recognition; Modeling; Missing data; Upper bound; Perturbation method; Vector space; Incomplete information; Pattern analysis; Artificial intelligence; Occultation

The task of finding a low-rank (r) matrix that best fits an original data matrix of higher rank is a recurring problem in science and engineering. The problem becomes especially difficult when the original data matrix has some missing entries and contains an unknown additive noise term in the remain...