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Image Deblurring with Optimizations

Image Deblurring with Optimizations. University of Washington The Chinese University of Hong Kong Adobe Systems, Inc. Qi Shan Leo Jiaya Jia Aseem Agarwala. The Problem. 2. An Example. Previous Work (1). Hardware solutions:. [Ben-Ezra and Nayar 2004]. [Levin et al. 2008].

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Image Deblurring with Optimizations

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  1. Image Deblurring with Optimizations University of Washington The Chinese University of Hong Kong Adobe Systems, Inc. Qi Shan Leo Jiaya Jia Aseem Agarwala

  2. The Problem 2

  3. An Example

  4. Previous Work (1) Hardware solutions: [Ben-Ezra and Nayar 2004] [Levin et al. 2008] [Raskar et al. 2006] 4

  5. [Jia et al. 2004] [Rav-Acha and Peleg 2005] [Petschnigg et al. 2004] [Yuan et al. 2007] Previous Work (2) Multi-frame solutions: 5

  6. Previous Work (3) Single image solutions: [Fergus et al. 2006] [Jia 2007] [Levin et al. 2007] 6

  7. Most recent work on Single Image Deblurring Qi Shan, Jiaya Jia, and Aseem Agarwala High-Quality Motion Deblurring From a Single Image. SIGGRAPH 2008 Lu Yuan, Jian Sun, Long Quan and Heung-Yeung Shum Progressive Inter-scale and intra-scale Non-blind Image Deconvolution. SIGGRAPH 2008. Joshi, N., Szeliski, R. and Kriegman, D. PSF Estimation using Sharp Edge Prediction, CVPR 2008. A. Levin, Y. Weiss, F. Durand, W. T. Freeman Understanding and evaluating blind deconvolution algorithms. CVPR 2009 Sunghyun Cho and Seungyong Lee, Fast Motion Deblurring. SIGGRAPH ASIA 2009 And many more...

  8. Some take home ideas 1. Using hierarchical approaches to estimate kernel in different scales 2. Realize the importance of strong edges 3. Bilateral filtering to suppress ringing artifacts 4. RL deconvolution is good, but we've got better chioces 5. Stronger prior does a better job 6. Deblurring by assuming spatially variant kernel is a good way to go

  9. Today's topic How to apply natural image statistics, image local smoothness constraints, and kernel sparsity prior in a MAP process Short discussion on 1. the stability of a non-blind deconvolution process 2. noise resistant non-blind deconvolution and denoising

  10. Image Global Statistics … 10

  11. Image Global Statistics … 11

  12. Image Global Statistics 12

  13. Image Local Constraint 13

  14. Image Local Constraint 14

  15. Image Local Constraint 15

  16. Image Local Constraint 16

  17. Kernel Statistics exponentially distributed 17

  18. Combining All constraints L f n Two-step iterative optimization • Optimize L • Optimize f 18

  19. Optimization Process Optimize L Idea: separate convolution replace with 19

  20. Optimization Process Optimize L Idea: separate convolution replace with 20

  21. Updating L Adding a new constraint to make Removing terms that are not relevant to An easy quadratic optimization problem with a closed form solution in the frequency domain 21

  22. Updating Removing terms that are not relevant to 22

  23. each only contains a single variable Ψi It is then a set of easy single variable optimization problems 23

  24. Iteration 0 (initialization) 24

  25. Time: about 30 seconds for an 800x600 image Iteration 8 (converge) 25

  26. A comparison RL deconvolution 26

  27. A comparison Our deconvolution 27

  28. Two-step iterative optimization • Optimize L • Optimize f Optimization with a total variation regularization 28

  29. Results 29

  30. Results 30

  31. 31

  32. 32

  33. More results 33

  34. More results 34

  35. Today's topic How to apply natural image statistics, image local smoothness constraints, and kernel sparsity prior in a MAP process Short discussion on 1. the stability of a non-blind deconvolution process 2. noise resistant non-blind deconvolution and denoising

  36. Stability Considering the simplest case: Wiener Filtering How about if And

  37. Stability Thus where is the frequency domain representation of is the variance of the noise Observation: the noise in the blur image is magnified in the deconvolved image. And the Noise Magnification Factor (NMF) is solely determined by the filter

  38. Some examples

  39. Some examples Dense kernels are less stable for deconvolution than sparse ones

  40. Noise resistant deconvolution and denoising With Jiaya Jia, Singbing Kang and Zenlu Qin In CVPR 2010 See you in San Francisco! Blind and non-blind image deconvolution software is available online and will be updated soon! 40

  41. Thank You

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