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Published byBlanca Shafto Modified over 10 years ago
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Overview Definition of Norms Low Rank Matrix Recovery Low Rank Approaches + Deformation Optimization Applications
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Definition of Norms
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L1 vs L2 Norm L1 Norm induces sparsity
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Matrix Norms
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Low Rank Matrix Recovery
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Surveillance Example Candès, Li, Ma, and W., JACM 2011.
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Low Rank Matrix Recovery + Deformation
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Problem Setting
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Modeling Misalignment Approach Target Definitions
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Iterative Linearization Optimization Problem Definitions
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Results – Face Alignment
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Aligning Natural Faces
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Stabilization of faces in the video
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Comparison of aligning handwritten digits
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Aligning planar homographies
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OPTIMIZATION
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Improvement of Algorithms
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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
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Applications
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TILT: Transform Invariant Low-rank Textures [Zhang, Liang, Ganesh, Ma, ACCV’10]
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TILT: All Types of Regular Geometric Structures in Images [Zhang, Liang, Ganesh, Ma, ACCV’10]
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TILT: Shape from Patterns and Textures [Zhang, Liang, Ganesh, Ma, ACCV’10]
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TILT: Examples of Natural Objects with Bilateral Symmetry [Zhang, Liang, Ganesh, Ma, ACCV’10]
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TILT: Examples of Characters, Signs, and Texts [Zhang, Liang, Ganesh, Ma, ACCV’10]
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TILT: More Examples [Zhang, Liang, Ganesh, Ma, ACCV’10]
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Camera Calibration with Radial Distortion [Zhang, Matsushita, and Ma, in CVPR 2011]
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Camera Calibration with Radial Distortion
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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
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