Prof. Feng Liu. Spring /12/2017

Transcription

1 Prof. Feng Liu Spring /12/2017

2 Last Time Filters and its applications

3 Today De-noise Median filter Bilateral filter Non-local mean filter Video de-noising

4 Filter Re-cap noisy image naïve denoising Gaussian blur better denoising edge-preserving filter Slide credit: Sylvain Paris and Frédo Durand

5 Median Filter Replace piel by the median value of its neighbors No new piel values introduced Removes spikes: good for impulse, salt & pepper noise Slide credit: C. Dyer

6 Median Filter Salt and pepper noise Median filtered Slide credit: M. Hebert, C. Dyer Plots of a row of the image Matlab: output im = medfilt2(im, [h w])

7 Median Filter Median filter is edge preserving Slide credit: C. Dyer

8 Slide credit: C. Dyer

9 input 1919 median filter output Slide credit: C. Dyer images by J. Plush

10 Bilateral filter Tomasi and Manduci CCV98.pdf Related to SUSAN filter [Smith and Brady 95] Digital-TV [Chan, Osher and Chen 2001] sigma filter Slide credit: F. Durand

11 Start with Gaussian filtering Here, input is a step function + noise J f I output Slide credit: F. Durand input

12 Gaussian filter as weighted average Weight of depends on distance to J() f (,) I() output input Slide credit: F. Durand

13 The problem of edges Here, It is too different J() pollutes our estimate J() f (,) I() output input Slide credit: F. Durand

14 Principle of Bilateral filtering [Tomasi and Manduchi 1998] Penalty g on the intensity difference J() 1 k() f (,) g(i() I()) I() I() output Slide credit: F. Durand input

15 Bilateral filtering [Tomasi and Manduchi 1998] Spatial Gaussian f J() 1 k() f (,) g(i() I()) I() output input Slide credit: F. Durand

16 Bilateral filtering [Tomasi and Manduchi 1998] Spatial Gaussian f Gaussian g on the intensity difference 1 f (,) k() J() g(i() I()) I() I() output input Slide credit: F. Durand

17 Normalization factor [Tomasi and Manduchi 1998] k()= J() 1 k() f (,) f (,) g(i() I()) g(i() I()) I() output input Slide credit: F. Durand

18 Blur from averaging across edges input * output * * Same Gaussian kernel everywhere. Slide credit: P. Sylvain

19 Bilateral filter: no averaging across edges input * output * * The kernel shape depends on the image content. Slide credit: P. Sylvain

20 Parameter for intensity difference Gaussian g s r = 0.1 s r = 0.25 s r = (Gaussian blur) input s s = 2 Parameter for spatial distance Gaussian f s s = 6 s s = 18 Slide credit: P. Sylvain

21 Parameter for intensity difference Gaussian g s r = 0.1 s r = 0.25 s r = (Gaussian blur) input s s = 2 Parameter for spatial distance Gaussian f s s = 6 s s = 18 Slide credit: P. Sylvain

22 Result Input Output Tomasi and Manduchi 1998

23 Other view The bilateral filter uses the 3D distance Slide credit: F. Durand

24 Speed Direct bilateral filtering is slow (minutes) Accelerations eist: Subsampling in space & range Durand & Dorsey 2002 Paris & Durand 2006 Limit to bo kernel & intelligent maintenance of histogram Weiss 2006 Slide credit: F. Durand

25 Local filters Compute a new value at each piel using its neighboring piels Bo filter Gaussian filter Median filter Bilateral filter

26 Non-local means filter Compute a new value at each piel from the whole image final value at piel i weight of piel j value at piel j Buades, A., Coll, B., Morel, J.-M. A non-local algorithm for image denoising. CVPR 2005

27 Weight : patch centered at piel i : patch centered at piel j Similar piel neighborhoods give a large weight Reprint from Buades et al. 2005

28 Input Gaussian Anisotropic Total variation Neighborhood NL-means Reprint from Buades et al. 2005

29 Non-local means filter High-quality Slow Fast non-local means algorithms available

30 Video de-noise We know how to de-noise an image How about video? E. P. Bennett and L. McMillan. Video Enhancement using Per-piel Virtual Eposures SIGGRAPH 2005

31 Gaussian filter in video cube Blurring artifacts Not edge-preserving Motion blur

32 Bilateral filter in video cube Cannot remove shot noise Reprint from [Bennett and McMillan 2005]

33 ASTA Filter [Bennett and McMillan 05] Build upon bilateral filter Find similar piels in a video cube for filtering Patch-based similarity measurement Adaptive Spatial-temporal Accumulation Filter Prefer temporal neighbors

34 Patch-based similarity measurement frame pt frame st

35 Similarity measure Reprint from [Bennett and McMillan 2005]

36 Adaptive Filtering Reprint from [Bennett and McMillan 2005]

37 Results (filtering + tone mapping) Input Naïve method ASTA Reprint from [Bennett and McMillan 2005]

38 Net Time Color Lighting