Digital Image Restoration

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1 Digital Image Restoration Blur as a chance and not a nuisance Filip Šroubek sroubekf@utia.cas.cz Institute of Information Theory and Automation Academy of Sciences of the Czech Republic Prague CMP

2 CMP

3 Image Degradation Model channel original image u noise + n acquired image = z convolution CMP

4 Energy Minimization CMP

5 Energy Minimization Data term CMP

6 Energy Minimization Data term Blur has different shapes Compact support Non-negative Preserve energy CMP 2017 Blur regularization Motion blur Out-of-focus & Abberations 6

7 Energy Minimization Data term Image regularization CMP

8 Statistics of sharp images Intensity Gradient CMP

9 Statistics of blurred images Intensity Gradient CMP

10 Regularization CMP

11 Energy Minimization NO-BLUR solution: WHY? Regularization favors blurred images CMP

12 Regularization favors blur CMP

13 Regularization favors blur Artificially sparsify images CMP

14 Ad-hoc steps! To avoid no-blur solution: Artificial sharpening Remove spikes Adjusting priors on the fly Hierarchical approach Chan TIP98 Shan SigGraph08 Cho SigGraph09 Xu ECCV09, CVPR13 Almeida TIP10 Krishnan CVPR11 Zhong CVPR13 Sun ICCP13 Michaeli ECCV14 Perrone PAMI15 Pan CVPR16 CMP

15 Artificial Sharpening Blurred image Shock filter Blur prediction h-step Deconvolution u-step CMP 2017 Cho et al., SIGGRAPH

16 Remove Spiky Objects Xu et al., ECCV 2010 CMP

17 Remove Spiky Objects Mask out small objects Xu et al., ECCV 2010 CMP

18 Remove Spiky Objects Reconstructed image with small objects removed Xu et al., ECCV 2010 CMP

19 Hierarchical Deconvolution Scale N-2 Scale N-1 Scale N image blur CMP

20 Bayesian Paradigm a posteriori distribution unknown likelihood given by our problem a priori distribution our prior knowledge CMP

21 Blind deconvolution with MAP CMP

22 Bayesian Paradigm revisited Marginalize the posterior Maximize the marginalized prob. Then maximize the posterior CMP

23 1 no-blur solution correct solution CMP

24 How to marginalize? If Gaussian distributions analytic solution exists in the form of Gaussian distribution If not (our case) approximation Laplace approximation Factorization with Variational Bayes CMP

25 Variational Bayes Factorization of the posterior and then marginalization is trivial. Every factor q depends on moments of other variables => must be solved iteratively. Miskin AICA00 Fergus SIGGRAPH06 Tzikas TIP09 Whyte IJCV12 Levin PAMI11 Babacan ECCV12 Wipf JMLR14 CMP

26 Marginalization in blind deconvolution CMP

27 Limitations of BD Gaussian noise original SNR=20dB SNR=50dB CMP

28 Limitations of BD Model discrepancies original 7% discrepancy CMP

29 Automatic Relevance Determination (Students t-distribution) Standard data term replaced by CMP

30 CMP

31 Space-variant Blur Object motion Camera motion Optical aberrations Scene depth CMP

32 Approximation of SV Blur Patch-wise convolution General SV PSF Locally convolution may not hold Parametric model (Blur Basis) More accurate Model may not hold Conversion to space-invariant HW design Local object motion Segmentation Line blur Joshi CVPR08, Sorel ICIP09, Ji CVPR12,Sun CVPR15 Whyte CVPR10, Gupta ECCV10, Hirsch ICCV11, Zhang NIPS13 Levin SIGGRAPH08, Ben-Ezra PAMI04, Tai PAMI10, Wavefront coding Levin NIPS06, Shan ICCV07, Dai CVPR08, Chakrabarti CVPR10, Kim CVPR14 CMP

33 Fast Moving Objects D.R.,J.K.,F.S.,L.N.,J.M. arxiv: FMO moves over a distance exceeding its size within exposure time CMP

34 Formation model Alpha matting CMP

35 FMO Appearance Estimation CMP

36 FMO Localization The pipeline consists of three stages: 1) Explorer 2) Detector 3) Tracker CMP

37 Input FMO Video CMP

38 FMO Tracking + Reconstruction CMP

39 Temporal SR - Table tennis CMP

40 Temporal SR - Darts CMP

41 Rotating FMOs Simple convolution replaced by space-variant convolution is a function of trajectory and angular velocity is a 3D object (sphere) Gradient descent w.r.t Exhaustive search w.r.t angular velocity CMP

42 Temporal SR with Rotation Input video frame Estimated high-speed video CMP

43 Limitations Poor collaboration between tracking and restoration Estimated blur and FMO appearance improve tracking Unstable FMO appearance estimation Combine multiple video frames Track multiple FMOs CMP

44 Thank You For Your Attention CMP

45

46 Multichannel Model channel K channel 2 channel 1 original image noise acquired images [u u * h k ] + n k = z k CMP

47 Multichannel Model Acquisition model: Optimization problem Data term Gaussian noise L2 norm CMP 2017 Image regularization term Blur Regularization term 47

48 Multichannel Blur Regularization u z 1 = u * h 1 h 2 * u = z 2 z 1 * = u * h 1 * * h 2 * u = * z 2 0 CMP

49 Camera motion CMP

50 Astronomical images Degraded images Reconstructed image PSF estimation CMP

51 MC Model with Decimation channel K channel 2 channel 1 original image noise acquired images D [u u * h k ] + n k = z k CMP

52 Robustness to misalignment original image PSF degraded image CMP

53 Super-resolution rough registration Superresolved image (2x) CMP 2017 Optical zoom (ground truth) 53

54 original 8 images SR 2x SR 3x CMP

55 Video Super-resolution Input video Super-resolution CMP

56 Embedded Systems CMP

57 Acquired blurred image CMP

58 Blur estimation CMP

59 Patch-wise Deconvolution CMP

60 Super-resolution JPEG SR CMP

61 Embedded Super-Resolution Input image SR from 5 images SR from 10 images CMP

62 Patch-wise restoration CMP

63 CMP

64 Regularization CMP

65 Adjusting priors Start with an overestimated noise level and slowly decrease it to the correct level. Start with p<<1 and slowly increase it to p=1. CMP

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