Digital Image Restoration
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- Allan Reynolds
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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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