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Vol1-CVIM-172 No.7 21/5/27 1 Proposal on Ringing Detector for Image Restoration Chika Inoshita, Yasuhiro Mukaigawa and Yasushi Yagi 1 A lot of methods have been proposed for restoring blurred images due to motion of the camera or subjects. The major problem of the restoration process is that the deblurred images include wave-like artifacts called ringing. In this paper, we propose a ringing detector for distinguish the artifact from some textures included in natural images. To design the ringing detector, we focused attention on the fact that the ringings are caused by null frequency of the point spread function. Ringings are detected by evaluating whether the deblurred image includes sine waves corresponding the null frequencies across the entire image with uniform phase. By combining the ringing detector with a debluring process, we can reduce ringing artifacts in the restores images. We demonstrate the effectiveness of the proposed ringing detector by some experiments using synthetic images and real images. 1. 2 Shan 1) Yuan 2) PSF 1 Insutitute of Scientific and Industrial Research, Osaka University 1 c 21 Information Processing Society of Japan

Vol1-CVIM-172 No.7 21/5/27 2. 2 Shan 1) 2 2)3) 2 2.3 1 Yuan 4) Ancuti 5) Agrawal 6) 2.4 Ben-Ezra 7)8) Raskar 9) Image domain Blur image l PSF b / = F(l) F(b) F(f) Frequency domain 1 3. Inverse Deblurred image ( PSF ) l = f b (1) f b PSF l PSF (1) (1) F (l) = F ( f )F (b) (2) F (g) g (2) PSF ( ) F (l) r = F 1 F (b) F 1 (g) g r PSF (3) 1 (3) 2 c 21 Information Processing Society of Japan

Vol1-CVIM-172 No.7 21/5/27 (a) (b) 2 3 1 (a) (b) 4 4. 4 3 2 3 2 PSF (2) 3 1 PSF 2 (3) 4 PSF PSF ( ) r(x, y) = f (x, y) + e i (x, y) (4) i r(x, y) f (x, y) e i (x, y) (5) e i (x, y) = k i cos(2π(a i x + b i y) + c i ) (5) a i x b i y PSF k i c i 2 (4) 4.3 4 4(a) 2 4(b) (a) (b) 3 c 21 Information Processing Society of Japan

PSF (b) 1 (b) 2 ( 1 ) ( 2 ) (1) (6) (7) g(x, y) = r(x s, y t)w(s, t) (6) s,t w(x, y) = 1 x 2 +y 2 2πd 2 e 2d 2 cos(2π(ax + by)) (7) d a x b y g(x, y) 5 1 (2) e i (x, y) c i k i k i 1 C i (c) c C i (c) = error wave error wave * (a) * (b) 5 (g i (x, y) g i (x, y))(e i (x, y, c) e i (x, y, c)) x,y (8) (g i (x, y) g i (x, y)) 2 (e i (x, y, c) e i (x, y, c)) 2 x,y x,y g i (x, y) = r(x s, y t)w i (s, t) (9) s,t w i (x, y) = 1 x 2 +y 2 2πd 2 e 2d 2 cos(2π(a i x + b i y)) (1) e i (x, y, c) = cos(a i x + b i y + c) (11) g i (x, y) g i (x, y) = (12) N x,y e i (x, y, c) e i (x, y, c) = (13) N i,x,y N Vol1-CVIM-172 No.7 21/5/27 C i (c) 1 1 5 1 (b) 4 c 21 Information Processing Society of Japan

Vol1-CVIM-172 No.7 21/5/27 1. Image restoration in frequency domain 2. Search Image domain non-invertible frequency 3. Apply ringing detector 3 25 Blur image l(known) PSF b(known) Deblurred image Inverse F(b) Small value Deblurred image Large value s e 2 tim f o r 15 e b m u 1 n 5 / = 4. Minimize ringing artifact 2. 4. 6. 8. 2 4 6 8 output of ringing detector 2 4 6 8.3 F(l) Frequency domain F(b) 7 (a=25,b=25) Deblurred image Refined image 6 4.4 PSF PSF 6 1 (3) 2 PSF 3 2 4 c i k i 4-1 e i (x, y) c i (8) c 4-2 k i k i 4-3 c i k i 2 4 PSF 5. 5 (1) x y a i, b i,,25,,5 x y 1 frickr(http://www.flickr.com/) 6 scene, flower, animal, building, human 7 x y 25 7 1 1 5 c 21 Information Processing Society of Japan

Vol1-CVIM-172 No.7 21/5/27 1 x-axis frequency a 25 5 6 9 1 6 3.7.9.9 y-axis frequency 25.34 3 1 2 b 3.7.9.6 5 9 3.7 (a) PSF1 (b) PSF1 (c) PSF1 (a) building (b) desk (c) road (d) PSF2 (e) PSF2 (f) PSF2 8 9 PSF 5 PSF PSF (1) 8 9 PSF 9(c) 9(f) PSF PSNR. RL 1) 11) 2 3 PSNR PSF1 PSF2 PSNR 1 building PSF1 11 PSF2 PSF1 PSF2 2 PSF1 PSNR[dB] RL building 35.43 511 355 32.85 desk 45.78 53.51 35 35.61 road 4.65 53 29.93 29 3 PSF2 PSNR[dB] RL building 323 35.45 334 3.9 desk 3.42 35.92 336 31.7 road 31.69 34.92 27.77 25.79 RL 6 c 21 Information Processing Society of Japan

Vol1-CVIM-172 No.7 21/5/27 (a) (b) (c) RL (d) 1 PSF1 (a) (b) 14 13 (a) (b) (c) RL (d) 11 (a) PSF2 12 PSF1 (b) PSF1 PSF2 12 PSF1 ( ) 1(a) PSF 5.3 PSF PSF PSF 13 14 PSF 15 PSF PSF PSF 7 c 21 Information Processing Society of Japan

(a) (b) (c) 15 5.4 PSF PSF 5 PSF 5 5.3 PSF PSF PSF 5 PSF2 MATLAB 1 6. PSF PSF PSF PSF Vol1-CVIM-172 No.7 21/5/27 1) Q.Shan, J.Jia, and A.Agarwala, High-quality motion deblurring from a single image, ACM Transactions on Graphics, Vol. 27, No. 3, Article 73, 28. 2) L.Yuan, J.Sun, L.Quan, and H.-Y.Shum, Progressive Inter-scale and Intra-scale Non-blind Image Deconvolution, ACM Transactions on Graphics, Vol. 27, No. 3, Article 74, 28. 3),,,, D, Vol. J92-D, No. 8, pp128-122, 28. 4) L.Yuan, J.Sun, L.Quan, and H.-Y.Shum, Image Deblurring with Blurred/Noisy Image Pairs, ACM Transactions on Graphics, Vol. 26, No. 3, Article 1, 27. 5) C.Ancuti, C.O.Ancuti, and P.Bekaert, Deblurring by Matching, EUROGRAPHICS, Vol. 28, No. 2, 29. 6) A.Agrawal, Y.Xu, and R.Raskar, Invertible Motion Blur In Video, ACM Transactions on Graphics, Vol. 28, Issue 3, 29 7) M.Ben-Ezra, and S.K.Nayar, Motion Deblurring using Hybrid Imaging, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 1-8, 23. 8) M.Ben-Ezra, and S.K.Nayar, Motion-Based Motion Deblurring, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 26, No. 6, 24. 9) R.Raskar, A.Agrawal, and J.Tumblin, Coded Exposure Photography: Motion Deblurring using Fluttered Shutter, ACM Transactions on Graphics, Vol. 25, Issue 3, 26 1) W.H.Richardson, Bayesian-Based Iterative Method of Image Restoration, Journal of Optical Society of America, Vol. 62, No. 1, 1972 11) N.Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press, 1964 8 c 21 Information Processing Society of Japan

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