16 June 2004 2 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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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 1 2 2 15

16 June 2004 2 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 2 2 3 4 5 2. 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

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) 0 1 0 1 0 0 0 0 0 0 m R (i 1,i 2 ): 0 1 0 1 0 (8) 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 m G (i 1,i 2 ): 1 0 1 0 1 (9) 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 m B (i 1,i 2 ): 0 0 0 0 0 (10) 1 0 1 0 1 0 0 0 0 0 (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 3. 3.1 (12) ẑ

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 +0.587z G +0.114z B z Cb = 0.1687z R 0.3313z G +0.5z B z Cr =0.5z R 0.4187z G 0.0813z 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)

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 2 3.2 (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

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)

Vol. 45 No. SIG 8(CVIM 9) RAW 21 4. 4.1 7 (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) 2 1 7 (i)(j)(k) 7 (k) 8 2 (e)(h) (k) 8 2 (k) 1 7 (i)(j) 1 1 2 8 (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)

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) 8 2 8 1 00.250.50.751[] 10 0.25 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 3.2 11 (a) 1 4 11 (b)(c) demosaicking 2) 11 (d) 64 4.3 3CCD Bayer RAW 12 (1)(2) 12 (3) 2

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) 16 5. 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.317 339, JAI Press Inc, Greenwich (1984). 4) Irani, M. and Peleg, S.: Improving resolution by Image Registration, CVGIP: Graph. Models Image Process., Vol.53, pp.231 239 (Mar. 1991).

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.1621 1633 (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.169 172 (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.2169 2172 (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.90 97 (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.1239 1242 (W3B.4) (Jul. 2002). 13) Shimizu, M. and Okutomi, M.: Two-Dimensional Simultaneous Sub-Pixel Estimation on Area-Based Image Matching, Proc. Asian Con-

Vol. 45 No. SIG 8(CVIM 9) RAW 25 ference on Computer Vision (ACCV2004 ), pp.854 859 (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). ( 16 1 15 ) ( 16 3 4 ) 2001 2003 TLO 1981 1983 1987 1990 1994 2002 IEEE

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