204/3 Vol. J97 A o. 3 HDR HDR wavelet-shrinkage wavelet wavelet wavelet-shrinkage wavelet RGB wavelet wavelet wavelet HDR wavelet 2.

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1 HDR Multiple Exposure Image Fusion with oise Reduction for HDR Acquisition Ryo MATSUOKA, Takao JIO, and Masahiro OKUDA HDR (High Dynamic Range) HDR LDR (Low Dynamic Range) HDR HDR HDR. (Human Visual System (HVS)) CCD CMOS High Dynamic Range Image (HDR ) HDR CG The University of Kitakyushu, Kitakyushu-shi, Japan Toyohashi University of Technology, Toyohashi-shi, Japan [] HDR [2] [8] HDR ISO HDR A Vol. J97 A o. 3 pp c

2 204/3 Vol. J97 A o. 3 HDR HDR wavelet-shrinkage wavelet wavelet wavelet-shrinkage wavelet RGB wavelet wavelet wavelet HDR wavelet 2. 2 R Y () [4] Y = R t, () t Y i i RGB 8bit [0, ] i = g (Y ) (2) () (2) R R = f (i) /t (3) f (x) f (x) =g (x) Mitsunaga [4] f f Fig. Our method flow. 20

3 HDR 2 Fig. 2 Inverse camera response curve. CAO EOS 20D f 2 f RGB f G n= I m = ωm(n)rm(n) n= ωm(n), (4) R m(n) n m ω m(n) wavelet waveletshrinkage ( ) ( ) shrinkage (3) (5) (6) L H M(n)M(n +)(Rm(n)+Rm(n +)) L m(n) =, 2 (5) M(n)M(n +)(Rm(n) Rm(n +)) H m(n) =, 2 (6) n =,, n n = R m (n) n m = {R, G, B} M(n) n R, G, B 0( ) ( ) 0 (6) H m (n) { Hm(n) 0, if H m=g (n) < threshold =, H m(n), otherwise (7) (7) Hm (n) 0 ( ) G 0 R, B 0 RGB G RGB R m (n) =L m (n)+h m (n). (8) HDR 2

4 204/3 Vol. J97 A o. 3 3 : ( ) ( ) Fig. 3 By multiple exposure image noise removal: (left) low exposure image, (right) denoising result. ωm(n) M(n)M(n +)(ωm(n)+ωm(n + )), 2 = if H m=g(n) < threshold M(n)ω m(n). otherwise (9) (4) wavelet (3) R m(n) R m (n) =ω m (n) R m (n). (0) n =,..., (8) (9) n = (3) (0) Haar wavelet wavelet-shrinkage wavelet 3. 3 wavelet-shrinkage HDR HDR wavelet-shrinkage (0) Haar wavelet wavelet wavelet (L) (H) (LL, HL, LH, HH) LL wavelet-shrinkage wavelet wavelet [9] [2] wavelet-shrinkage Hard Shrinkage [] min h 0 + λ(h l) 2, λ > 0, () h l wavelet h wavelet λ () wavelet h 0, if l < /λ =, (2) l, otherwise (2) wavelet wavelet 0 waveletshrinkage 22

5 HDR wavelet-shrinkage min E (h) = h 0 + λ h (h l(n)) 2, (3) n= l(n) (0) n wavelet (HL, LH, HH) wavelet h HDR wavelet λ shrinkage m wavelet ( ) 2 0, if λ h n= = l(n) >0. n= l(n), otherwise (4) (2) waveletshrinkage [9] [2] wavelet 0 = (4) (2) (4) wavelet-shrinkage (4) (4) [2] [6] [2], [3] CCD CMOS 4 : ( ) Hat ( ) Fig. 4 Conventional two weight functions: (left) Hat-type, (right) Gauss-type. ( [3]) Y = x + a σ + a 2σ 2 x, (5) x Y σ σ 2 a a y y = g(y )+σ q σ q y f(y) =f (g (Y )+σ q), f(y) x f(g(y )+σ q) x f(g(y )) + f (g(y ))σ q x = Y + f (g(y ))σ q x = a σ + a 2σ 2 x + f (g(y ))σ q (6) g f f(g(y )) = Y t n n = ( a σ + a 2σ 2 x + f (g (Y )) σ q ) /t. (7) 23

6 204/3 Vol. J97 A o. 3 ω 0(i) =m(i) ((a σ +a 2σ 2 x+f (g(y ))σ q)/t) m(i) ((a σ +a 2σ 2 Y +f (g(y ))σ q)/t) = m(i) ((a σ +a 2σ 2 f(i)+f (i)σ q)/t) (8) m (i) i 0 0 x x Y RAW (8) (8) ω (i) =m (i) (b + b 2f (i)+b 3f (i)) /t (9) 2 3 b, b 2, b 3 b =0.00, b 2 =0.99, b 3 =0.0 b 3 b 2 5. Bilateral Filter [4] BM3D [5] 5. CAO EOS 20D 3 ISO ISO ISO600 Ground truth (HDR ) 5 ( 3 5 = 45 ) 5 (scene, scene2) scene /8sec, /2sec, 2sec, scene2 /50sec, /3sec, /3sec HDR HDR LDR 5 HDR Ground truth HDR (oisy image) 5 HDR (scene, scene2) Fig. 5 Tonemapped HDR sample images (scene, scene2). 24

7 HDR Bilateral Filter [4] BM3D [5] oisy image HDR Bilateral Filter [4] HDR LDR PSR SSIM [7] LDR (7) % (7) Hard Shrinkage [] HDR MATLAB tonemap LDR Ward [6] 6 Bilateral Filter [4] (a) (b) (c) 6 HDR : ( ) Ground truth Bilateral Filter BM3D Fig. 6 Tonemapped HDR images: (from left to right) Ground truth, oisy image, our method, Bilateral Filter, BM3D. 25

8 204/3 Vol. J97 A o. 3 BM3D [5] 6(a) BM3D [5] BM3D [5] BM3D [5] 6(b) BM3D [5] 6(c) shrinkage BM3D [5] 5. 3 PSR SSIM [7] PSR ( ) MAX 2 PSR =0 log 0 (20) (Ildr I ldr )2 I ldr Ground truth I ldr HDR Bilateral Filter [4] BM3D [5] oisy image Ground truth oisy image 4.2. HDR oisy image Ground truth PSR Table Value of PSR, (R.L.T.: Reinhard Local Tonemap, R.G.T.: Reinhard Global Tonemap). Tone-mapping R.L.T. R.G.T. CLAHE MATLAB oisy image (scene) (scene2) our method (scene) (scene2) Bilateral Filter (scene) (scene2) BM3D (scene) (scene2) SSIM Table 2 Value of SSIM, (R.L.T.: Reinhard Local Tonemap, R.G.T.: Reinhard Global Tonemap). Tone-mapping R.L.T. R.G.T. CLAHE MATLAB oisy image (scene) (scene2) our method (scene) (scene2) Bilateral Filter (scene) (scene2) BM3D (scene) (scene2) Reinhard [8], CLAHE [9], MATLAB tonemap 2 HDR LDR HDR SR SR HDR HDR HDR-VDP-2 [20] HDR-VDP-2 [20] 2 Reinhard [8] 7 Reinhard [8] 26

9 HDR 7 Reinhard [8] HDR : ( ) Ground truth Bilateral Filter BM3D Fig. 7 Tonemapped HDR images by Reinhard Local Tonemap: (from left to right) Ground truth, oisy image, our method, Bilateral Filter, BM3D. 7 BM3D [5] Bilateral Filter [4] CLAHE [9] MATLAB BM3D [5] Bilateral Filter [4] Reinhard [8] MATLAB Bilateral Filter [4] BM3D [5] CLAHE [9] 8 Hat Fig. 8 (upper) conventional method (Fig. 2 left: Hat function), (lower left) our method quantization noise suppression, (lower right) our method sensor noise suppression. SSIM [7] PSR 5. 4 CLAHE [9] 8 Hat b =0.00, b 2 =0.0, b 3 =0.95 b =0.00, b 2 =0.99, b 3 =0.0 27

10 204/3 Vol. J97 A o. 3 9 : ( ) ( ) Fig. 9 Proposed two weight functions: (left) quantization noise suppression, (right) sensor noise suppression Ground truth HDR Ground truth onlinearsr (SR) HDR-VDP-2 [20] HDR SR HDR HDR SR s(x) =L 2 x max (2) x +2.6x Table 3 Quantitative evaluation using multiple exposure image with additional Gaussian noises (BRF: Bilateral Filter). oisy our BRF BM3D SR (scene) (scene2) HDR-VDP-2 (scene) (scene2) s x L max (2) Daly [2] HDR-VDP-2 [20] Rafal HDR 3 HDR- VDP-2 [20] 3 Bilateral Filter [4] BM3D 0 HDR Reinhard [8] LDR 0 Bilateral Filter [4] BM3D [5] BM3D [5] MATLAB ( ) sec BM3D [5] 36sec BM3D [5] 28

11 HDR 0 Reinhard [8] HDR : ( ) Ground truth Bilateral Filter BM3D Fig. 0 Tonemapped HDR images by Reinhard Global Tonemap: (from left to right) Ground truth, oisy image, our method, Bilateral Filter, BM3D. Bilateral Filter [4] 6. HDR wavelet-shrinkage HDR wavelet-shrinkage BM3D [5] (BM3D [5]) (B)( ), JST A-step KDDI [] E. Reinhard, S. Pattanaik, G. Ward, and P. Debevec, High Dynamic Range Imaging: Acquisition, Display, and Image-Based Lighting (Morgan Kaufmann Series in Computer Graphics and Geometric Modeling), Morgan Kaufmann Publisher, [2] P.E. Debevec and J. Malik, Recovering high dynamic range radiance maps from photographs, Proc. SIGGRAPH 97, Computer Graphics Proceedings, pp , 997. [3] S. Mann and R. Picard, On being undigital with digital cameras: Extending dynamic range by combining differently exposed pictures, Proc. IS&T 46th Annual Conference (May 995), pp [4] T. Mitsunaga and S.K. ayer, Radiometric self calibration, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol., pp , June 999. [5] S.W. Hasinoff, F. Durand, and W.T. Freeman, oise-optimal capture for high dynamic range photography, 200 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp , June 200. [6] A. Akyuz and E. Reinhard, oise reduction in high dynamic range imaging, J. Visual Communication and Image Representation, vol.8, pp , [7] M. Granados, B. Ajdin, M. Wand, C. Theobalt, H.-P. Seidel, and H. Lensch, Optimal HDR reconstruction with linear digital cameras, 200 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp , June 200. [8] T. Jinno and M. Okuda, Motion blur free HDR image acquisition using multiple exposures, IEEE International Conference on Image Processing, pp , Oct [9] R.H. Chan, R.F. Chan, L. Shen, and Z. Shen, Wavelet algorithms for high-resolution image reconstruction, SIAM Journal on Scientific Computing, vol.24, pp , [0] T. Saito,. Fujii, and T. Komatsu, Iterative soft color-shrinkage for color-image denoising, IEEE International Conference on Image Processing, pp , ov [] M. Elad, Why simple shrinkage is still relevant for redundant representations?, IEEE Trans. Inf. Theory, vol.52, no.2, pp , Dec [2] D.L. Donoho, Denoising by soft thresholding, 29

12 204/3 Vol. J97 A o. 3 IEEE Trans. Inf. Theory, vol.4, no.3, pp , May 995. [3] T. Buades, Y. Lou, J.M. Morel, and Z. Tang, A note on multi-image denoising, International Workshop on Local and on-local Approximation in Image Processing, pp. 5, Aug [4] C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, Proc. IEEE 6th Inter. Conf. Computer Vision, pp , 988. [5] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image denoising by 3D transform-domain collaborative filtering, IEEE Trans. Image Process., vol.6, no.8, pp , Aug [6] G.J. Ward, H. Rushmeier, and C. Piatko, A visibility matching tone reproduction operator for high dynamic range scenes, IEEE Trans. Vis. Comput. Graphics, vol.3, no.4, pp , Dec [7] Z. Wang, A.C. Bovik, H.R. Sheikh, and E.P. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Trans. Image Process., vol.3, no.4, pp , [8] E. Reinhard, M. Stark, P. Shirley, and J. Ferwerda, Photographic tone reproduction for digital images, ACM Trans. Graphics, vol.2, no.3, pp , July 2002 (Proc. SIGGRAPH 2002). [9] K. Zuiderveld, Contrast limited adaptive histogram equalization, Graphic Gems IV, pp , Academic Press Professional, San Diego, 994. [20] R. Mantiuk K.J. Kim, A.G. Rempel, and W. Heidrich, HDR-VDP-2: A calibrated visual metric for visibility and quality predictions in all luminance conditions, ACM Trans. Graphics, vol.30, pp. 4, July 20. [2] S. Daly, The visible differences predictor: An algorithm for the assessment of image fidelity, in Digital Image and Human Vision, ed. A.B. Watson, pp , MIT Press, Cambridge, MA, 993. (4) (3) E(h) h =0 h 0 E(h) =+ λ (h l(n)) 2 (A ) n= h = n= l(n) (i) h =0 (ii) h = n= l(n) ( E(h) =+ λ l(k) n= k= ) 2 ( ) ) 2 l(k) l(n)+l(n) 2 k= ( ) 2 = λ l(n) + λ l(n) 2 n= n= (A 3) h ( ) 2 0, if λ h n= = l(n) >0. n= l(n), otherwise (A 4) E(0) = λ l(n) 2 n= (A 2) 220

4 4 2 RAW 4 4 4 (PCA) 4 4 4 4 RAW RAW [5] 4 RAW 4 Park [12] Park 2 RAW RAW 2 RAW y = Mx + n. (1) y RAW x RGB M CFA n.. R G B σr 2, σ2 G, σ2 B D n ( )

4 4 2 RAW 4 4 4 (PCA) 4 4 4 4 RAW RAW [5] 4 RAW 4 Park [12] Park 2 RAW RAW 2 RAW y = Mx + n. (1) y RAW x RGB M CFA n.. R G B σr 2, σ2 G, σ2 B D n ( ) RAW 4 E-mail: hakiyama@ok.ctrl.titech.ac.jp Abstract RAW RAW RAW RAW RAW 4 RAW RAW RAW 1 (CFA) CFA Bayer CFA [1] RAW CFA 1 2 [2, 3, 4, 5]. RAW RAW RAW RAW 3 [2, 3, 4, 5] (AWGN) [13, 14] RAW 2 RAW RAW RAW

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