2. Overview Definition of Norms Low Rank Matrix Recovery Low Rank Approaches + Deformation Optimization Applications

3. Definition of Norms

4. L1 vs L2 Norm L1 Norm induces sparsity

5. Matrix Norms

6. Low Rank Matrix Recovery

10. Surveillance Example Candès, Li, Ma, and W., JACM 2011.

11. Low Rank Matrix Recovery + Deformation

12. Problem Setting

13. Modeling Misalignment Approach Target Definitions

14. Iterative Linearization Optimization Problem Definitions

17. Results – Face Alignment

19. Aligning Natural Faces

20. Stabilization of faces in the video

21. Comparison of aligning handwritten digits

22. Aligning planar homographies

23. OPTIMIZATION

24. Improvement of Algorithms

25. 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

26. Applications

27. TILT: Transform Invariant Low-rank Textures [Zhang, Liang, Ganesh, Ma, ACCV’10]

28. TILT: All Types of Regular Geometric Structures in Images [Zhang, Liang, Ganesh, Ma, ACCV’10]

29. TILT: Shape from Patterns and Textures [Zhang, Liang, Ganesh, Ma, ACCV’10]

30. TILT: Examples of Natural Objects with Bilateral Symmetry [Zhang, Liang, Ganesh, Ma, ACCV’10]

31. TILT: Examples of Characters, Signs, and Texts [Zhang, Liang, Ganesh, Ma, ACCV’10]

32. TILT: More Examples [Zhang, Liang, Ganesh, Ma, ACCV’10]

33. Camera Calibration with Radial Distortion [Zhang, Matsushita, and Ma, in CVPR 2011]

34. Camera Calibration with Radial Distortion

37. 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