Color Seamlessness in Multi-Projector Displays using Constrained Gamut Morphing

Transcription

1 Coor Seamessness in Muti-Projector Dispays using Constrained Gamut Morphing IEEE Transactions on Visuaization and Computer Graphics, Vo. 15, No. 6, 2009 Behzad Sajadi, Maxim Lazarov, Aditi Majumder, and M. Gopi Presented by I-Su Park Schoo of Eectrica Engineering and Computer Science Kyungpook Nationa Univ.

2 Proposed method Abstract New constrained gamut morphing agorithm Remove spatia variation in 3D coor gamut Variation in chromaticity gamut across projector Vignetting effect of each projector Overap across adjacent projector Resuting in true coor seamessness Adjust intensities of ight from each pixe of each projector Achieve smooth morphing from one projector s gamut to others through overap region 2 / 31

3 Introduction Tied muti-projector dispay Reason of spatia coor variation in muti-projector dispay Spatia variation in coor gamut across dispay Cassify three different categories Intra-projector variation within singe projector Inter-projector variation across different projectors Overap variation 3 / 31

4 Previous method Gamut matching method Achieve coor baancing across projector Ignore intra-projector uminance and chrominance variation Reducing coor quaity and resoution of dispay Matching uminance transfer functions Achieve uminance baancing across projectors Ignore both inter and intra projector chrominance variations Bending or feathering technique Ramping intensity from each projector smoothy from 0 to 1 in overap region Ignore both intra and inter projector chrominance and uminance variation 4 / 31

5 Majumder and Stevens Addressing spatia variation of uminance» Achieve perceptuay smooth variation across dispay Not addressing spatia variation in chrominance Proposed method Address spatia variation in both uminance and chrominance in tied projection-based dispays Morph spatiay varying coor gamut of dispay in smoothy constrained manner Retaining white point Gamut morphing Smooth morphing of chrominance gamut Smoothing of uminance 5 / 31

6 Resuting image Fig. 1. This figure shows our resuts on two muti-projector dispays on a curved screen (eft) and a panar screen (right). Comparison of previous work Tabe 1. Comparison of previous work with our method in handing different types of uminance and chrominance variation in tied dispays. 6 / 31

7 CIE XYZ coor space Notation Coor in CIE XYZ coor space Defining 3D coordinate ( XYZ,, ) Y Luminance of coor Chrominance of coor Chromaticity coordinate X Y, =, X + Y + Z X + Y + Z ( xy) ( ) (,, ),,1 ( ) (1) X Y Z = xb yb x y B (2) where B= X + Y + Z which we ca the tristimuus brightness. 7 / 31

8 Scaing of coor A coors ying on vector where k is a scae factor. Addition of coors Addition of two coors, Y and B of new coor ( XYZ,, ) k( XYZ,, ) ( X, Y, Z ) ( X, Y, Z ) and ( X, Y, Z ) ( X X, Y Y, Z Z ) = (3) Y = Y + Y ; B = B + B (4) Chrominance of new coor ( x, y ), 3 3 xb + xb yb + yb = B1+ B2 B1+ B2 Barycentric coordinates of new chrominance B1 B2 and B + B B + B (5) 8 / 31

9 Definition Agorithm Dispay made of M projectors Each denoted by Pj,1 j M Reating dispay coordinate (, ) to coordinate pj, qj of projector P j ( st, ) = Gj( pj, qj) Coor formed by channe input ( X, Y, Z ) B = X + Y + Z Assuming inear dispays i Changing from 0 to 1 i ( X, Y, Z ) st ( ) i = 1 9 / 31

10 Remaining chrominance Scaing 3D coor gamut of dispay B 2D chrominance gamut Given by triange T given by Tristimuus brightness of white Chrominance of white B = X + Y + Z = B W B = (6) ( x, y ) ( x, y ) W W BW ( x, y ) 10 / 31

11 Singe projector dispay Vignetting effect Spatia fa off of brightness from around center to fringes of projector Channe independent effect B Affecting of a different channes in same manner (, ) (, ) B pq = V pq B (7) V( pq, ) ( pq, ) Spatiay varying tristimuus brightness of white B ( pq, ) V( pq, ) B where is the vignetting of the projector at pixe. W = (8) 11 / 31

12 Muti-projector dispay Overap of N projectors and coordinate B for each channe Spatia variation in (, ) (, ) j j j j j N B W Spatiay varying chrominance gamut Defining three primaries ( st, ) B st = V p q B (9) BW ( st, ) = Vj( pj, qj) B j j N (10) ( ( ) ( )) ( st, ) ( ) ( ) j j st, T( st, ) B x st,, y st, = x, y B (11) j W 12 / 31

13 Per projector white point baancing Desired white point αb( x, y) αb Procedure Fix Sove two inear equations = ( x, y ) where α is a per-channe scae factor, 0 1. α = 1 r D α D (12) 13 / 31

14 Per pixe chrominance gamut morphing Morphing two-dimensiona chrominance gamut Chrominance of primaries r ( 1 τ) R1 τr2 Scae factor and between 0 and 1 Ruin white point baancing k k = + (13) ( 1 τ) 1 τ 2 g = G + G (14) k ( 1 τ) 1 τ 2 b = B + B (15) where 1 τ is given by the proportions of the is a per-channe scae B of the channe. β 1 β 2 β B β B β B + β B β B β B = 1 τ (16) = τ (17) 14 / 31

15 Retain white point by computing one common factor β β1 2 Seeking and β B β B Transition from to T through n steps 1 W 1 + β B 1 W 2 β B W 1 2 β B W 2 T1 2 + β B W 1 2 T t t... t n T = 1 τ (18) = τ (19) ( RR 1 2 GG 1 2 BB 1 2 ) max,, n = (20) δ 15 / 31

16 Fig. 2. The morphing of the chrominance gamut in the horizonta and vertica direction in a dispay made of rectanguar projectors and overaps. Fig. 3. The chrominance gamut morphs with 2 intermediate steps (across 2 overapping pixes) 16 / 31

17 Chrominance gamut morphing step Generate two attenuation maps for each projector Fina attenuation map New B W (, ) H V p q = ( p, q ) ( p, q ) β β β j j j j j j j j j Foowing appication of attenuation map P j BW ( s, t) = (, ) (, ) C β j pj qj BV j j pj qj j N (21) where is the set of projectors that overap at pixe st, (Figure 4). N ( ) 17 / 31

18 Per pixe perceptua brightness constraining Appying perception based gradient constraint to ( st, ) B W ( st, ) ( st, ) ζ = E (22) B W C BW C ( st, ) Per pixe bezier based brightness smoothing 1 Assuring C continuity Fit higher order 1 C B ( st, ) continuous 2D Bezier surface to ( st, ) B W ( st, ) ( st, ) η = S (23) B W E W E 18 / 31

19 Fig. 4. The compete fowchart of our agorithm. We show the spatia variation in brightness (bue), the x (red) and y (green) of the red primary of the entire dispay after every step of our agorithm. Note how a of these are smoothened during the course of our method. On the eft, we show the attenuation map for a singe projector after every step. 19 / 31

20 Image correction Linearize image ( pq, ) Using gamma function of 2 Mutipy different attenuation map Creating fina attenuation map Aj( pq, ) = β j( pq, ) ζ j( pq, ) ηj( pq, ) Mutipy I with attenuation map Achieving coor correction S I (, ) = (, ) (, ) I pq I pq A pq j Aj 20 / 31

21 Appy channe dependent white point correction Generating white point corrected image { } where rgb,,. Fina correction Appying inverse of h to Achieve desired changes in non-inear device { } where rgb,,. (, ) = α (, ) I pq I pq W S I W ( ) 1 (, ) = (, ) I pq h I pq C W 21 / 31

22 Impementation Impementation of proposed method on two dispays Panar rear projected dispay of 3x3 array of nine very ow-end projectors Cyindrica front projected dispay of 2x4 array of eight reativey higher-end projectors Reconstruct spatiay varying coor gamut Using srgb camera as sensor 22 / 31

23 Resuts Comparison of proposed method with existing work Fig. 5. Comparison of our method with existing work on the most difficut case of white on the panar dispay. Before any correction; After simpe RGB bending; After appying Majumder and Stevens 2005 photometric seamessness agorithm; after our gamut morphing agorithm. 23 / 31

24 Resut on curved dispay Fig. 6. Comparison of our method with existing work on the most difficut case of white on the curved dispay made of 2 4 array of eight dispays. In scanine order: Before any correction; After simpe RGB bending; After appying Majumder and Stevens 2005 photometric seamessness agorithm; after our gamut morphing agorithm 24 / 31

25 Resut of proposed agorithm on different images Fig. 7. arge variety of images corrected using our method on our 9 projector panar (top) and eight projector curved dispay (bottom). Note that the number of projectors are not visibe in any of them. 25 / 31

26 Different steps of proposed method Fig. 8. The resuts from the different steps of our method iustrated on the panar dispay of 9 projectors. In scanine order from top eft: Before correction; after white point baancing; After chrominance gamut morphing in the horizonta direction; After chrominance gamut morphing in the vertica direction; after perceptua uminance constraining; fina resut after Bezier based smoothing. 26 / 31

27 Discussion Minimum size of the overap and Maximum LAB distance between adjacent pixes in overap region δ Fig. 9. Left: The pot of the size of the overap region vs the maximum LAB distance between the chrominance of the primaries of adjacent pixes. Right: Comparison of change in chromaticity coordinates across an overap region achieved by RGB bending with our chrominance morphing. 27 / 31

28 Difference from the traditiona RGB bending Traditiona bending methods Feather RGB input of projectors in inear or cosine manner in overap region Proposed chrominance morphing Constrain change in chrominance easiy to be within human toerance Retaining more of brightness of dispay 28 / 31

29 Effect on the Dispay Quaity Impose some constraints on spatia coor variation Reduction in brightness of dispay Tabe 2. Evauation of the percentage reduction in dynamic range(dr) and the uniformity achieved (measured by the standard deviation of the variation in brightness and chrominance from the mean across the dispay) by different steps of our method and other existing methods. 29 / 31

30 Is the perceptua brightness constraining required? Bezier based smoothing Way to fit smooth function to spatiay varying brightness Fig. 10. The comparison of our method with (eft) and without (right) appying the perceptua brightness constraining. Note that not appying perceptua brightness constraining cannot yied the desired smoothness. 30 / 31

31 Concusion Coor morphing agorithm for muti-projector dispays Smoothing both chrominance and brightness across entire dispay resuting in true coor seamessness Morphing of 2D chrominance gamut in overap region Brightness smoothing across entire dispay Achieving seamessness even for difficut case of fat coors 31 / 31

32 Method to find rectanguar projections and overaps Fig. 11. Method to find rectanguar projections and overaps from a set of overapping keystoned projectors. 32 / 31

33 Order of continuity C 1 : curves incude discontinuities 0 C : curves are joined 1 C : first derivatives are equa n C th : first through n derivatives are equa 33 / 31

34 Perceptua uniformity constraint [ ][ ] [ ][ ] W u v W u v 2 2 u u + v v λ W 1 W x λ where λ is the smoothing parameter and W x is the gradient of W, aong any direction x. 1 W u v, uvu,,, v [ ][ ] 34 / 31

35 Bezier curve Linear Bezier curves ( ) = + ( ) = ( 1 ) +, [ 0,1] B t P t P P t P tp t Quadratic Bezier curves 2 2 ( ) = ( 1 ) 0 + 2( 1 ) 1+ 2, [ 0,1] ( ) = ( 1 )(( 1 ) 0 + 1) + (( 1 ) 1+ 2), [ 0,1] B t t P t tp t P t B t t t P tp t t P tp t Linear Bezier curves Quadratic Bezier curves 35 / 31