16 June RAW Fig. 2 High resolution color image reconstruction from RAW data. u(i 1,i 2 )= p(i 1 x, i 2 y)i(x, y)dxdy (1) 1 demosaicking Fig. 1
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1 Vol. 45 No. SIG 8(CVIM 9) June 2004 RAW, RAW demosaicking High Resolution Color Image Reconstruction Using Raw Data of a Single Imaging Chip Tomomasa Gotoh, and Masatoshi Okutomi The limited resolution of image sensors has motivated the enhancement of image resolution. Super-resolution has been applied mainly to grayscale images, but producing a high-resolution color image using a single-chip imaging device has not been investigated thoroughly. This work aims at producing a high-resolution color image directly from raw data obtained by a single imaging chip employing a color filter array. This method is based on a generalized formulation of super-resolution that simultaneously performs both resolution enhancement and demosaicing. The proposed method is verified through experiments using synthetic and real images. 1. CFA: Color Filter Array RAW demosaicking demosaicking demosaicking 1),2) demosaicking Graduate School, Tokyo Institute of Technology Presently with Sony Corporation 3) 7) RAW RAW demosaicking
2 16 June RAW Fig. 2 High resolution color image reconstruction from RAW data. u(i 1,i 2 )= p(i 1 x, i 2 y)i(x, y)dxdy (1) 1 demosaicking Fig. 1 Demosaicking and super-resolution. RAW u(i 1,i 2 ) I(x, y) p(x, y) CCD 2 3 (x, y) (ξ, η) (x, y) =s(ξ, η) (2) (1) u(i 1,i 2 )= p((i 1,i 2 ) s(ξ, η))i(x, y) s (ξ, η) dξdη (3) s (ξ, η) (j 1,j 2 ) [j 1 1/2,j 1 +1/2] [j 2 1/2,j 2 +1/2] I(x, y) z(j 1,j 2 ) (3) u(i 1,i 2 )= z(j 1,j 2 )h(i 1,i 2,j 1,j 2 ; s)(4) j 1 j 2
3 Vol. 45 No. SIG 8(CVIM 9) RAW 17 3 Fig. 3 Definition of the coordinate system. j1 +1/2 j2 +1/2 h(i 1,i 2,j 1,j 2 ; s) = j 1 1/2 j 2 1/2 s p((i 1,i 2 ) s(ξ, η)) (ξ, η) dξdη (5) c {R, G, B} c (4) u c (i 1,i 2 )= z c (j 1,j 2 )h(i 1,i 2,j 1,j 2 ; s) j 1 j 2 (6) CFA (i 1,i 2 ) 1 c y c (i 1,i 2 ) y c (i 1,i 2 )=m c (i 1,i 2 )u c (i 1,i 2 ) = m c (i 1,i 2 ) z c (j 1,j 2 )h(i 1,i 2,j 1,j 2 ; s) j 1 j 2 (7) m c (i 1,i 2 ) (i 1,i 2 ) c m c (i 1,i 2 )=1 m c (i 1,i 2 )=0 5 5 Bayer 10) m R (i 1,i 2 ): (8) m G (i 1,i 2 ): (9) m B (i 1,i 2 ): (10) (7) M y c,k (i 1,i 2 )k =1,...M s k k =1,...M y c,k (i 1,i 2 )= m c (i 1,i 2 ) z c (j 1,j 2 )h(i 1,i 2,j 1,j 2 ; s k ) j 1 j 2 (11) y k = A k z (12) y k y R,k (i 1,i 2 )y G,k (i 1,i 2 )y B,k (i 1,i 2 ) m c (i 1,i 2 )=1 z = [ z T R, z T G, zb] T T zr (j 1,j 2 )z G (j 1,j 2 ) z B (j 1,j 2 ) A k h(i 1,i 2,j 1,j 2 ; s k ) m c (i 1,i 2 ) (12) z RAW k y k (12) ẑ
4 18 June 2004 (a) (b) 4 (a) RAW (b) Fig. 4 Artifact in reconstructed image. High resolution reference image (a) is used to simulate raw data. Image reconstruction with independent regularization gives (b). ẑ = arg min{f 1 (z)+f p (z)} (13) z 1 M f 1 (z) = y k A k z 2 (14) k=1 2 RGB f p (z) RGB 4 (b) demosaicking RGB RAW (14) y 1,..., y M, (M >2) (14) overdetermined (14) over-determined s k RGB f p (z) RGB YCbCr z Y =0.299z R z G z B z Cb = z R z G +0.5z B z Cr =0.5z R z G z B (15) f p (z) =f 2 (z Y )+f 3 (z Cb, z Cr ) (16) 8) D : { 2 } P d,d D f 2 (z Y )= Λ d P d z Y 2 (17) d D Λ d z Y d (14) under-determined H f 3 (z Cb, z Cr )=λ c ( Hz Cb 2 + Hz Cr 2 ) (18)
5 Vol. 45 No. SIG 8(CVIM 9) RAW 19 5 R G B Fig. 5 Edge model for red (solid line), green (dashed line), and blue (dotted line) signals. λ c (14) over-determined H (14) over-determined H RGB 2 1 RGB z R (j) =erf(j)+2, z G (j) =a 1 z R (j Dg)+b 1, z B (j) =a 2 z R (j Db)+b 2 (19) erf( ) a 1 a 2 b 1 b 2 DgDb R G B 5RGB Dg = Db =0 2 H(u, v) =1 exp( (u 2 + v 2 )/2σc 2 ) erf(ξ) = 2 π ξ 0 exp( t2 )dt 6 Fig. 6 Chrominance energy function characteristic. Dg 0Db 0 (19) DgDb f 3 (z Cb, z Cr ) 6 (a 1,a 2,b 1,b 2 )=(1.2, 0.8, 0.1, 0.1) 6 a 1 a 2 > 0 a 1 a 2 b 1 b (13) s k k =1,...M 9) 2 y k z f [ ] [ s k (ξ, η) = 1 ξ + f η d xk d yk ] (20) d k = RGB
6 20 June 2004 [d xk,d yk ] T RAW y 1,..., y M demosaickingrg B 11) 13) 1 y 1 d 1 =[0, 0] T de-aliasing Bayer 2 [d x1,d y1 ] T,..., [d xm,d ym ] T A = [ A T 1,...AM] T T [dx1 + 2K 1,d y1 +2L 1 ] T,..., [d xm +2K M,d ym +2L M ] T K k, L k (k =1,..., M) A A 2 mod(d 1, 2), mod(d 2, 2),..., mod(d M, 2) (21) z [0, 2) [0, 2) A (12) RAW RAW-to-RAW registration 15) 3.3 (1) RAW y 1,..., y M (2) CFA m c (i 1,i 2 ) RG B (3) RAW demosaicking d k =[d xk,d yk ] T (4) f (13) (5) n =0 1 z (0) (6) z (n) 8) f 2 (z Y ) Λ d (7) z (n) [ ] z (n+1) = z (n) 3 α f m (z) (22) z m=1 z=z (n) f 1 (z) M = A T k (A k z (n) y k ) (23) z z=z (n) f 2 (z Y ) z z=z (n) = f 3 (z Cb, z Cr ) z k=1 T T Y P T d Λ T d Λ d P d T Y z (n) d D z=z (n) = λ c C {Cb,Cr} (24) T T CH T HT C z (n) (25) α T T T Cb T Cr RGB Y CbCr (8) n = n +1(6) (9)
![.., y M (2) CFA m c (i 1,i 2 ) RG B (3) RAW demosaicking d k =[d xk,d yk ] T (4) f (13) (5) n =0 1 z (0) (6) z (n) 8) f 2 (z Y ) Λ d (7) z (n) [ ] z (n+1) = z (n) 3 α f m (z) (22) z m=1 z=z (n) f 1](/docs-images/45/20574708/images/page_6.jpg "(z) M = A T k (A k z (n) y k ) (23) z z=z (n) f 2 (z Y ) z z=z (n) = f 3 (z Cb, z Cr ) z k=1 T T Y P T d Λ T d Λ d P d T Y z (n) d D z=z (n) = λ c C {Cb,Cr} (24) T T CH T HT C z (n) (25) α T T T Cb T")
7 Vol. 45 No. SIG 8(CVIM 9) RAW (a) 7 (b) (a) s k 7 (c) 1 demosaicking (d) (c) (e) 8 demosaicking 5) 1 (f) 1 demosaicking 2) (g) (f) (h) 8 demosaicking 2) 5) (d)(e)(g)(h) 2 (d)(g) RAW (e)(h) (i)(j)(k) 7 (k) 8 2 (e)(h) (k) 8 2 (k) 1 7 (i)(j) (a)(b)(c) 8 (a) (b) (c) (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) 7 (a) (b) (c) demosaicking(d) demosaicking (e) demosaicking 5) (f) Demosaicking 2) (g) Demosaicking 2) (h) Demosaicking 2) 5) (i) f =1M =1(j) f =2M =1(k) f =2M =8 Fig. 7 Reconstructed images. (a) Reference. (b) Input. (c) Linear demosaicking. (d) Linear demosaicking and interpolation. (e) Linear demosaicking and conventional super-resolution 5). (f) Demosaicking 2). (g) Demosaicking 2) and bi-cubic interpolation. (h) Demosaicking 2) and conventional super-resolution 5). (i) Proposed, f = 1, M = 1. (j) Proposed, f = 2, M = 1. (k) Proposed, f =2,M =8. (d) (a)(b)(c) (d) Root Mean Square: RMS 9 RMS 1 2 demosaicking 2) 5)
8 22 June 2004 (a) (c) 8 (a) (b) (c) (d) f =2M =8 Fig. 8 Reconstructed images. (a) Nearest neighbor interpolation (multi-frame). (b) Linear interpolation (multi-frame). (c) Cubic interpolation (multiframe). (d) Proposed, f =2, M =8. (b) (d) 9 RMS 5) demosaicking 2) 5) Fig. 9 RMS error. Dotted line: linear interpolation, dashed line: demosaicking 2) and bi-cubic interpolation, solid line: proposed. RMS 7 (k) [] Pentium MHz PC CPU sec sec Demosaicking 2) sec sec Point Grey Research Dragonfly CFA Bayer (a) (b)(c) demosaicking 2) 11 (d) CCD Bayer RAW 12 (1)(2) 12 (3) 2
![Dotted line: linear interpolation, dashed line: demosaicking 2) and bi-cubic interpolation, solid line: proposed. RMS 7 (k) 8 2 8 1 00.250.50.751[] 10 0.](/docs-images/45/20574708/images/page_8.jpg "25 Pentium 3 933 MHz PC 30 30 2 CPU 8 2.10 sec 1 0.79 sec Demosaicking 2) 1 0.31 sec 1 0.13 sec 1 4.2 Point Grey Research Dragonfly CFA Bayer 3.")
9 Vol. 45 No. SIG 8(CVIM 9) RAW 23 (a) (b) (c) (d) (e) 10 (a) 0 (b) 0.25 (c) 0.5 (d) 0.75 (e) 1 Fig. 10 Motion estimation error affecting the image estimate. (a) 0 pixels, (b) 0.25 pixels, (c) 0.5 pixels, (d) 0.75 pixels, (e) 1 pixels. (a) (b) (c) (d) 11 (a) (b) demosaicking (c) Demosaicking 2) (d) f =4M =64 Fig. 11 Reconstructed high-resolution images. (a) Observed color mosaic. (b) Linear demosaicking and interpolation. (c) Demosaicking 2) and bi-cubic interpolation. (d) Proposed, f =4, M = 64. mod(d 1, 2), mod(d 2, 2),..., mod(d M, 2) [0, 2) [0, 2) SSDSAD 12 (1)(2) 4 12 (3) 2 12 (b) (c) demosaicking 2) (d) (1)(2) 64 (3) RAW CFA Bayer RAW 1) Cok, D.R.: Signal processing method and apparatus for producing interpolated chrominance values in a sampled color image signal, United States Patent 4,642,678 (1987). 2) Laroche, C.A, and Prescott, M.A.: Apparatus and method for adaptively interpolating a full color image utilizing chrominance gradients, United States Patent 5,373,322 (1994). 3) Huang, T.S. and Tsay, R.Y.: Multiple frame image restoration and registration, Advances in Computer Vision and Image Processing, Vol.1, Huang, T.S. (Ed)., pp , JAI Press Inc, Greenwich (1984). 4) Irani, M. and Peleg, S.: Improving resolution by Image Registration, CVGIP: Graph. Models Image Process., Vol.53, pp (Mar. 1991).
10 24 June 2004 (1) (2) (3) (a) (b) (c) (d) 12 (a) (b) demosaicking (c) Demosaicking 2) (d) (1)f =4M =64(2)f =4M =64 (3)f =2M =16 Fig. 12 Reconstructed high-resolution images. (a) Observed color mosaic. (b) Linear demosaicking and interpolation. (c) Demosaicking 2) and bi-cubic interpolation. (d) Proposed ((1): f = 4, M = 64, (2): f =4,M = 64, (3): f =2,M =16). 5) Hardie, R.C., Barnard, K.J. and Amstrong, E.E.: Joint MAP Registration and High- Resolution Image Estimation using a Sequence of Undersampled Images, IEEE Trans. Image Processing, Vol.6, pp (1997). 6) Tekalp, A.M., Ozkan, M.K. and Sezan, M.I.: High-resolution image reconstruction from lower-resolution image sequences and space varying image restoration, IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), San Francisco, CA., Vol.III, pp (Mar. 1992). 7) Schultz, R.R. and Stevenson, R.L.: Improved definition video frame enhancement, IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Detroit, MI., Vol.IV, pp (May 1995). 8) Shin, J., Paik, J., Price, J.R. and Abidi, M.A.: Adaptive regularized image interpolation using data fusion and steerable constraints, SPIE Visual Communications and Image Processing, Vol.4310 (Jan. 2001). 9) Capel, D. and Zisserman, A.: Automated Mosaicing with Super-resolution Zoom, Proc. IEEE Conference on Computer Vision and Pattern Recognition (1998). 10) Bayer, B.E.: Color Imaging Array, United States Patent 3,971,065 (1976). 11) Shimizu, M. and Okutomi, M.: Precise subpixel estimation on area-based matching, Proc. 8th International Conference on Computer Vision, pp (Jul. 2001). 12) Shimizu, M. and Okutomi, M.: An Analysis of Sub-Pixel Estimation Error on Area-Based Image Matching, Proc. 14th International Conference on Digital Signal Processing (DSP2002), Vol.II, pp (W3B.4) (Jul. 2002). 13) Shimizu, M. and Okutomi, M.: Two-Dimensional Simultaneous Sub-Pixel Estimation on Area-Based Image Matching, Proc. Asian Con-
11 Vol. 45 No. SIG 8(CVIM 9) RAW 25 ference on Computer Vision (ACCV2004 ), pp (P-93) (Jan. 2004). 14) Gotoh, T. and Okutomi, M.: Color Super Resolution from a Single-CCD, CD-ROM Proc. IEEE Workshop on Color and Photometric Method in Computer Vision (CPMCV, in conjunction with ICCV ) (Oct. 2003). 15) Gotoh, T. and Okutomi, M.: Direct Super- Resolution and Registration Using Raw CFA Images, Proc. IEEE International Conference on Computer Vision and Pattern Recognition (CVPR2004) (Jun. 2004). ( ) ( ) TLO IEEE
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 ( )](/thumbs/40/20574692.jpg "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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![1 Kinect for Windows M = [X Y Z] T M = [X Y Z ] T f (u,v) w 3.2 [11] [7] u = f X +u Z 0 δ u (X,Y,Z ) (5) v = f Y Z +v 0 δ v (X,Y,Z ) (6) w = Z +](/thumbs/81/83701592.jpg "1 Kinect for Windows M = [X Y Z] T M = [X Y Z ] T f (u,v) w 3.2 [11] [7] u = f X +u Z 0 δ u (X,Y,Z ) (5) v = f Y Z +v 0 δ v (X,Y,Z ) (6) w = Z +")
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![2.2 (a) = 1, M = 9, p i 1 = p i = p i+1 = 0 (b) = 1, M = 9, p i 1 = 0, p i = 1, p i+1 = 1 1: M 2 M 2 w i [j] w i [j] = 1 j= w i w i = (w i [ ],, w i [](/thumbs/93/111684107.jpg "2.2 (a) = 1, M = 9, p i 1 = p i = p i+1 = 0 (b) = 1, M = 9, p i 1 = 0, p i = 1, p i+1 = 1 1: M 2 M 2 w i [j] w i [j] = 1 j= w i w i = (w i [ ],, w i [")
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