2007/8 Vol. J90 D No RGB Grossberg [5] Grossberg [5] Fujii [4] Majumder [8] Wang [12] Majumder Wang [12] Perceptually-based Threshold Map

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1 Perceptual Photometric Compensation for Projected Images Mark ASHDOWN,ImariSATO, Takahiro OKABE, and Yoichi SATO 1. [1], [9] Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 0213, USA National Institue of Informatics, Hitotsubashi, Chiyoda-ku, Tokyo, Japan Institute of Industrial Science, The University of Tokyo, Komaba, Meguro-ku, Tokyo, Japan [3], [7], [14] Grossberg [5] Fujii [4] RGB RGB RGB RGB D Vol. J90 D No. 8 pp c

2 2007/8 Vol. J90 D No RGB Grossberg [5] Grossberg [5] Fujii [4] Majumder [8] Wang [12] Majumder Wang [12] Perceptually-based Threshold Map [10]

3 2. 1 RGB Yxy Y xy 1 [8] 1 2 RGB RGB ĩ Stone [11] 3 3 RGB XYZ XYZ Grossberg [5] c = Mĩ + t (1) c XYZ M 3 3 t RGB XYZ Ilie [6] RGB XYZ c Yxy Yxy Y XYZ X Y xy x = y = Y X+Y +Z X+Y +Z X = x Y Y = Y y Z =(1 x y) Y y (1) M t Yxy Y e =(e x,e y) 3 1 e [L, H] 10 L H Fig. 1 1 Projector response functions for the projector s red, green, and blue channels, measured using a colorimeter Y cd/m

4 2007/8 Vol. J90 D No. 8 2 e [L,H ] 3 [L,H ] 4 Y [L,H ] 5 Y (1) e (1) XYZ Yxy RGB ĩ XYZ Yxy RGB ĩ =(1, 0, 0) (0, 1, 0) (0, 0, 1) Yxy xy 3 (r, g, b) 2(a) RGB ĩ =(0, 0, 0) (1, 1, 1) l h e =(e x,e y) e 3 e e 2(a) 3. 2 e [L, H] e XYZ d =(e x,e y, (a) (b) 2 Fig. 2 Chrominance clipping and chrominance threshold. (a) (b) 3 YZ RGB (a) XYZ d (b) RGB d Fig. 3 Gamut in XYZ and RGB color spaces. (a) Any multiple of d in XYZ space will have the desired chrominance. (b) We perform the intersection between line and projector gamut in RGB space. 1 e x e y) sd s 0 e (1) sd = Mĩ + t. (2) d = M 1 d t = M 1 t ĩ = s d t. (3) RGB d (s L,s H ) RGB ĩ e ĩ R =0 ĩ G =0 ĩ B =0 d 3(b) s s R = t R/ d R s G = t G/ d G s B = t B/ d B t e ( ) t s L R t G t B =max,, (4) d R d G d B 2118

4 [L,H ] Ramasubremanian Perceptually-based Threshold map [10] T Threshold map 3 Threshold-versus-intensity function TVI TVI 1 80 cd/m 2 TVI image TVI component CSF component threshold map 4 Y TVI

5 ( s H 1+ t R =min, 1+ t G, 1+ t ) B (5) d R d G d B d L = s L d d H = s H d 2 L H 3. 3 [L, H] 2(b) xy l h e e L e H e e L e H e e L L e H H e L e H l h e [L,H ] [L, H] Wright [13] d L d H e L e H XYZ d L d H 3. 4 [L,H ] Ramasubremanian Perceptually-based Threshold map [10] T Threshold map 3 Threshold-versus-intensity function TVI TVI 1 80 cd/m 2 TVI image TVI component CSF component threshold map 4 Y TVI CSF T Fig. 4 The threshold map for an image determines how much error in luminance can be tolerated at each pixel. The luminance channel Y of the original image is used to compute TVI and CSF components which are multiplied to create the final threshold map. Contrast sensitivity function CSF [2] CSF Visual Masking CSF 3 Visual masking TVI CSF r T =(Y + r)/y 4 TVI CSF T T =1.1 10% 4 T L = L /T, H = H T (6) 4 Weber s law 2119

6 2007/8 Vol. J90 D No RGB l h 2(b) [L, H] Wright [13] Threshold-versus-intensity function TVI 80 cd/m 2 80 cd/m 2 80 cd/m 2 5 [L, H] Y l Y h Y l Y h Y L Y(Y h Y l )+Y l H Y l Y h δ Y l Y h Y l =0 Y h Y l Y l Y h Y [ Y =exp Y(Y h Y l )+Y l] (7) H Y Y l Y h Y [L,H ] Y L =logl H =logh Y =logy Y [0, 1] Y Y = Y(Y h Y l )+Y l 5 Y Y Y l =exp(y l ) Y h =exp(y h ) Fig. 5 Illustration of the luminance fitting algorithm in a single dimension. The initial luminance values Y (left) are fit into into the the low Y l =exp(y l ) and high Y h =exp(y h )luminance range (right)

7 Fig. 6 6 ɛ The parameter ɛ is used to control the stretching applied to the original image. H = Y(Y h Y l )+Y l Y h ɛ (0 <ɛ 1) Y h Y h H Yl ɛy +(1 ɛ) + Yl (8) Y l Y l L ɛyyh 1 ɛy (9) 6 ɛ ɛ = Majumder [8] (8) Y h Y h (= log Y h ) Y h i,j Y h i,j log [1+δ ] (i i ) 2 +(j j ) 2 (10) i {i 1,i,i+1}, j {j 1,j,j+1} Y h Y l (9) 5 cycles per degree 1% 2m m δ = ( )/(π ) 1/ Y L Y H L Y H Case Luminance Final XYZ value 1 H Y d H 2 H <Y <H interpolate between d H and d H 3 L Y H interpolate between d L and d H 4 L <Y <L interpolate between d L and d L 5 Y L d L XYZ (1) RGB

8 2007/8 Vol. J90 D No (a) (b) (c) (d) (e) [4], [5] 7(c) 7(c) (d) (e) (c) (d) (e) (d) (e) (e) (d) Pentium GHz CPU Task Convert original image to XYZ Make L, H, L,H Threshold map Make L,H Iterative luminance fitting (3 rounds) Make final XYZ and convert to RGB TOTAL Time 20 ms 550 ms 480 ms 10 ms 350 ms 280 ms 1690 ms 10 (a) (b) (a) 94 (b) 4 2 (a) 96 (b)

9 (a) (b) (c) (d) (e) + Fig. 7 7 Compensation results with and without perceptual thresholds using uniform or non-uniform fitting. 8 Fig. 8 Compensation results (a) (b) (c) (d)(e) (b)(c) Fig. 9 Compensation results. (a) A surface used for displaying projected images, (b) when an imageis projected, variations in surface reflectivity, lighting, and projector brightness are apparent in the final output, (c) we alter the input to the projector to compensate for the irregularities. (d)(e) shows an enlarged version of the cat image above. image minimum maximum 10 Fig. 10 Two colours are calculated for each pixel that have the same chrominance as the original image, but minimal and maximam luminance based on the projector capability. 2123

2007/8 Vol. J90 D No. 8 PRESTO [1] O. Bimber, A. Emmerling, and T. Klemmer, Embedded entertainment with smart projectors, IEEE Comput., vol.38, no.1, pp.48 55, 2005. [2] P.J. Burt and E.H.

10 2007/8 Vol. J90 D No. 8 PRESTO [1] O. Bimber, A. Emmerling, and T. Klemmer, Embedded entertainment with smart projectors, IEEE Comput., vol.38, no.1, pp.48 55, [2] P.J. Burt and E.H. Adelson, The Laplacian pyramid as a compact image code, IEEE Trans. Commun., vol.31, no.4, pp , [3] top.html [4] K. Fujii, M.D. Grossberg, and S.K. Nayar, A projector-camera system with real-time photometric adaptation for dynamic environments, Proc. CVPR 2005, pp , [5] M.D. Grossberg, H. Peri, S.K. Nayar, and P.N. Belhumeur, Making one object look like another: Controlling appearance using a projector-camera system, Proc. CVPR 2004, pp , [6] A. Ilie and G. Welch, Ensuring color consistancy across multiple cameras, Proc. ICCV 2005, pp , [7] digitalcinema.html [8] A. Majumder and R. Stevens, Perceptual photometric seamlessness in projection-based tiled displays, ACM Trans. Graphics, vol.24, no.1, pp , [9] C. Pinhanez, The everywhere displays projector: A device to create ubiquitous graphical interfaces, Proc. Ubiquitous Computing (UbiComp) 2001, pp , [10] M. Ramasubramanian, S.N. Pattaniak, and D.P. Greenberg, A perceptually based physical error metric for realistic image synthesis, Proc. ACM SIG- GRAPH 99, pp.73 82, [11] M.C. Stone, Color and brightness appearance issues in tiles displays, IEEE Comput. Graph. Appl., vol.21, no.5, pp.58 66, [12] D. Wang, I. Sato, T. Okabe, and Y. Sato, Radiometric compensation in a projector-camera system based on the properties of human vision system, Proc. IEEE International Workshop on Projector-Camera Systems 2005, [13] W.D. Wright, The sensitivity of the eye to small colour differences, Proc. Physical Society, vol.53, no.2, pp , [14] vol.59, no.2, pp , Mark Ashdown received a B.A. and Ph.D. in Computer Science from the University of Cambridge, UK. He spent two years as a postdoctoral fellow at the University of Tokyo, Japan, and is currently a research scientist at the Massachusetts Institute of Technology in the US. His research interests span computer vision, human-computer interaction, and computer -supported co-operative work. His work has included geometric and photometric projector calibration and compensation, personal projected desk displays, and the use of such displays for remote collaboration in conventional meetings and in time-sensitive decision making. 2124

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Fundamentals of Projector-Camera Systems and Their Calibration Methods Takayuki OKATANI To make the images projected by projector s appear as desired, it is e ective and sometimes an only choice to capture