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Overview. Definition of Norms Low Rank Matrix Recovery Low Rank Approaches + Deformation Optimization Applications. Definition of Norms. L1 vs L2 Norm. L1 Norm induces sparsity. Matrix Norms. Low Rank Matrix Recovery. Low Rank Matrix Recovery. Low Rank Matrix Recovery.
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Overview • Definition of Norms • Low Rank Matrix Recovery • Low Rank Approaches + Deformation • Optimization • Applications
L1 vs L2 Norm • L1 Norm induces sparsity
Surveillance Example Candès, Li, Ma, and W., JACM 2011.
Modeling Misalignment Definitions Target Approach
Iterative Linearization Definitions Optimization Problem
Drawbacks • Many SDP solvers exist but they are not very efficient for nuclear norm minimization. • Accelerated Proximal Gradient Algorithms exist but no general purpose tools
TILT: Transform Invariant Low-rank Textures [Zhang, Liang, Ganesh, Ma, ACCV’10]
TILT: All Types of Regular Geometric Structures in Images [Zhang, Liang, Ganesh, Ma, ACCV’10]
TILT: Shape from Patterns and Textures [Zhang, Liang, Ganesh, Ma, ACCV’10]
TILT: Examples of Natural Objects with Bilateral Symmetry [Zhang, Liang, Ganesh, Ma, ACCV’10]
TILT: Examples of Characters, Signs, and Texts [Zhang, Liang, Ganesh, Ma, ACCV’10]
TILT: More Examples [Zhang, Liang, Ganesh, Ma, ACCV’10]
Camera Calibration with Radial Distortion [Zhang, Matsushita, and Ma, in CVPR 2011]
Conclusions • Low rank minimization is a nice way for finding regularities within the data • Nuclear norm is an efficient (fast and scalable) and effective (good proxy for low-rank) way for low rank minimization • Impressive results for handling occlusion • Not many available tools support nuclear norm minimization