人間の視覚特性を考慮した投影画像の光学的補正 ... - 東京大学

「 画 像 の 認 識 ・ 理 解 シンポジウム(MIRU2006)」 2006 年 7 月
† †† † †
† 153–8505 4–6–1
†† 101–8430 2–1–2
E-mail: †{ashdownm,takahiro,ysato}@iis.u-tokyo.ac.jp, ††imarik@nii.ac.jp
,
Perceptual Photometric Compensation for Projected Images
Mark ASHDOWN † ,ImariSATO †† , Takahiro OKABE † , and Yoichi SATO †
† Institute of Industrial Science, The University of Tokyo Komaba 4–6–1, Meguro-ku, Tokyo, 153–8505 Japan
†† National Institue of Informatics Hitotsubashi 2–1–2, Chiyoda-ku, Tokyo, 101–8430 Japan
E-mail: †{ashdownm,takahiro,ysato}@iis.u-tokyo.ac.jp, ††imarik@nii.ac.jp
Abstract Digital projectors have been steadily becoming smaller and cheaper, and are now used to augment various surfaces
with digital information. However, in situations other than the ideal dark room with a perfect white screen we must contend
with ambient light and non-uniformity in surface colour, which will reduce the contrast of the output and introduce visible
irregularities. Here we present a method to compensate for the irregularities and simultaneously achieve contrast equal or similar
to that which would be obtained in the ideal situation. Rather than insisting on a photometrically perfect result we allow
some errors in the final output due to the limited projector range and spatial variations, but these are bounded by perceptual
limits derived from a model of the human visual system and the content of the image.
Key words projector, calibration, compensation, human vision, perception
1.
[1], [7]
()
()
()
Grossberg [4] Fujii [3]
RGB RGB
(, ) RGB
RGB
49

24 RGB 0
255
Grossberg
[4] Fujii [3]
Majumder [6] Wang
[10]
Majumder
Wang [10]
(Perceptually-based Threshold
Map, [8])
2. ·
()
.
,
·
.
2. 1
RGB Yxy
(Y ,xy 1 )
RGB
RGB ĩ .
Stone [9] 3×3
RGB XYZ (XYZ
) Grossberg
[4]
,
c = Mĩ + t (1)
c
XYZ , M 3 × 3 , t
.
M t 12
5. 1 .
c Yxy
Yxy Y XYZ Y xy
x = X+Y X
+Z , y = X+Y Y
+Z .
X = x Y y , Y = Y, Z =(1 − x − y) Y y .
2. 2
Yxy
1.
50

Y ,
e =(e x ,e y ) ⊤ . 2
1.
e [L, H] ( 1 )
L H .
2. e
() [L ′ , H ′ ].
3.
() .
[L ′′ , H ′′ ] .
4. Y [L ′′ , H ′′ ]
.
5. Y ′
(1) (
)
3.
3. 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) ⊤
(lh) .
e =(e x ,e y ) ⊤
e
3 e e
image minimum maximum
1 () ()
.
2
Y (cd/m 2 ) .
3
2
(a)
(b)
.
(a)
XYZ RGB (a) XYZ
d . (b)RGB
d .
( 2 (a)).
3. 2 e · [L, H]
e XYZ d =(e x ,e y ,1−e x −e y ) ⊤
sd, s > = 0 ,
e (1)
˜d = M −1 d˜t = M −1 t
(b)
sd = Mĩ+t. (2)
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
(
s L = max ,
d
˜tR˜
˜t G
, ˜t )
B
R d˜
G d˜
B
. (4)
(
s H 1 + ˜tR
= min , 1 + ˜t G
, 1 + ˜t )
B
. (5)
d˜
R d˜
G d˜
B
d L = s L dd H = s H d 2
L H
51

3. 3
() [LH]
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′ lh e
[L ′ ,H ′ ] [LH]
Wight
[11] .
3. 4
[L ′ , H ′ ]
Ramasubremanian (Perceptuallybased
Threshold map [8])
T . Threshold map
:
Threshold-versus-intensity function (TVI): TVI
80 cd/m 2
,
.
TVI
Contrast sensitivity function (CSF)
[2] CSF
Visual MaskingCSF
.
3 Visual masking
TVI CSF 2
r T =(Y +r)/Y
T T = 1.1
10%
3 T
L ′′ = L ′ /T, H ′′ = H ′ T (6)
3Weber’s law .
image
TVI component
CSF component
threshold map
4 Y TVI
CSF
T .
4.
4. 1
Y
[L ′′ ,H ′′ ]
Y ′
L = logL ′′ H = logH ′′ Y = logY
Y [0,1]
Y Y ′ = Y(Y h −Y l )+Y l
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
4. 1. 1 4. 1. 2
Y l Y h
52

5
1 Y
Y ′ , Y l = exp(Y l )
Y h = exp(Y h )
Original ε=0
6
Y ′
ε=0.9
ε=0.99
ε
5
[
Y ′ = exp Y(Y h − Y l )+Y l] (7)
4. 1. 1
HY Y l
Y h
H = Y(Y h − Y l )+Y l Y h
ε (0 < ε < = 1)
Y h
Y h ←
H − Yl
εY +(1 − ε) + Yl (8)
Y l
Y l ← L − εYYh
1 − εY
6 ε
ε = 0.9
4. 1. 2
Majumder [6]
(8) Y h
Y h (= logY h )
[
]
Y h i, j − Yh <
i ′ , j ′ = log 1 + δ
√(i−i ′ ) 2 +(j − j ′ ) 2 (10)
(9)
5 cycles per degree
1%
2m
1024 × 768 3m
δ =(180 × 5 × 0.01 × 2)/(π × 3 × 1024) ≈ 1/540
4. 2
Y ′ L < = Y ′ < = H
L < = Y ′ < = H
Case Luminance Final XYZ value
1 H ′ < = Y ′ d H′
2 H

(a)
(b)
(c)
(d)
(e)
8
3 4
RGB
XYZ
Ilie [5]
RGB XYZ
5. 2
8
9
10 (a) (b)
(c)
, 4 (d)
(e)
10 (c)
(f)
(g)
9 (a) (b)(d)
(c)(e) (f)(g) (d)(e)
(d) (e)
(d) (e) (e) (d)
Pentium 43.2 GHz PC
1024 × 768
Task
Time
Convert original image to XYZ 20 ms
Make L,H,L ′ ,H ′
550 ms
Threshold map
480 ms
Make L ′′ ,H ′′
10 ms
Iterative luminance fitting (3 rounds) 350 ms
Make final XYZ and convert to RGB 280 ms
TOTAL
1690 ms
4 [4] [3]
54

(a) (b) () (c) (d) (e) +
10
10 (a)
(b)
10 100
(a)94(b)4
2 (a)96(b)4
0
6.
[1] Oliver Bimber, Andreas Emmerling, and Thomas Klemmer. Embedded
Entertainment with Smart Projectors. IEEE Computer, 38(1):48–
55, 2005.
[2] Peter J. Burt and Edward H. Adelson. The Laplacian Pyramid as
a Compact Image Code. IEEE Transactions on Communications,
31(4):532–540, 1983.
[3] Kensaku Fujii, Michael D. Grossberg, and Shree K. Nayar. A
Projector-Camera System with Real-Time Photometric Adaptation
for Dynamic Environments. In Proceedings of CVPR 2005, pages
814–821, 2005.
[4] Michael D. Grossberg, Harish Peri, Shree K. Nayar, and Peter N.
Belhumeur. Making One Object Look Like Another: Controlling
Appearance Using a Projector-Camera System. In Proceedings of
CVPR 2004, pages 452–459, 2004.
[5] Adrian Ilie and Greg Welch. Ensuring Color Consistancy across
Multiple Cameras. In Proceedings of ICCV 2005, pages 1268–1275,
2005.
[6] Aditi Majumder and Rick Stevens. Perceptual Photometric Seamlessness
in Projection-Based Tiled Displays. ACM Transactions on
Graphics, 24(1):118–139, 2005.
[7] Claudio Pinhanez. The Everywhere Displays Projector: A Device to
Create Ubiquitous Graphical Interfaces. In Proceedings of Ubiquitous
Computing (UbiComp) 2001, pages 315–331, 2001.
[8] Mahesh Ramasubramanian, Sumanta N. Pattaniak, and Donald P.
Greenberg. A Perceptually Based Physical Error Metric for Realistic
Image Synthesis. In Proceedings of ACM SIGGRAPH 99, pages
73–82, 1999.
[9] Maureen C. Stone. Color and Brightness Appearance Issues in Tiles
Displays. IEEE Computer Graphics & Applications, 21(5):58–66,
2001.
[10] Dong Wang, Imari Sato, Takahiro Okabe, and Yoichi Sato. Radiometric
Compensation in a Projector-Camera System Based on the
Properties of Human Vision System. In Proceedings of IEEE International
Workshop on Projector-Camera Systems 2005, 2005.
[11] W. D. Wright. The Sensitivity of the Eye to Small Colour Differences.
Proceedings of the Physical Society, 53(2):93–112, 1941.
55