Gamut Matching ICS 280 Visual Perception Display Sensor Model E i u v h r i r x Q r u v x r yr h g ig x Q g u v x g y g h b ib x Q b u v x b y b B u v x B y B Slide 2 ICS 280 Visual Perception 1 Display Sensor Model E i E i h r i r x Q r x r yr h g ig x Q g x g y g h b ib x Q b x b y b B x B y B h r i r X r X B Y r Y B Z r Z B h g ig X g X B Y g Y B Z g Z B h b ib X b X B Y b Y B Z b Z B X B Y B Z B Slide 3 ICS 280 Visual Perception Display Sensor Model E i h r i r Xr XB Yr YB Zr ZB h g ig Xg XB Yg YB Zg ZB Xg Yg Zg h b ib Xb XB Yb YB Zb ZB X B Y B Z B XB YB ZB X r Y r Zr Xb Yb Zb Slide 4 ICS 280 Visual Perception 2 Display Sensor Model X g ZB Y g ZB Zg ZB X r ZB Y r ZB Zr ZB XB YB ZB X b ZB Y b ZB Zb ZB Slide 5 ICS 280 Visual Perception Display Sensor Model X g Y g Z g XB YB ZB X r Y r Z r X b Y b Z b Slide 6 ICS 280 Visual Perception 3 Display Sensor Model E i X g Y g Z g XB YB ZB h r i r X r Y r Z r h g ig X g Y g Z g h b ib X b Y b Z b X B Y B Z B X r Y r Z r X b Y b Z b X Y Z 1 X r X g X b X B h r i r Y r Y g Y b Y B h g i g Z r Z g Z b Z B h b i b 0 0 0 1 1 Slide 7 ICS 280 Visual Perception Linear Devices X Y Z 1 T M R G B 1 T Two devices X Y Z 1 T M1 R1 G1 B1 1 T X Y Z 1 T M2 R2 G2 B2 1 T R2 G2 B2 1 T M2 1 X Y Z 1 M2 1M1 R1 G1 B1 1 T Slide 8 ICS 280 Visual Perception 4 Display Sensor Model Slide 9 ICS 280 Visual Perception Display Sensor Model Slide 10 ICS 280 Visual Perception 5 Gamut Matching Find a common color gamut defined by Rc Gc Bc Find the common function Mc X Y Z 1 T Mc Rc Gc Bc 1 T For any device i Slide 11 Ri Gi Bi 1 T Mi 1Mc Rc Gc Bc 1 T ICS 280 Visual Perception Display Sensor Model Slide 12 ICS 280 Visual Perception 6 Three Four Primary Systems We dealt with only three primary systems Any n non parallel vector form a basis in ndimensional space Vectors will be linearly independent All other vectors can be expressed as a linear combination of the basis vectors Gamut will always be convex polytope The primaries form basis in 3D color space Slide 13 ICS 280 Visual Perception Three Four Primary Systems Four primaries Does not form a basis Non unique combinations for same color Disadvantages Slide 14 You have to know exactly how the combination is done The gamut depends on the method used for combination Gamut may not be a convex polytope ICS 280 Visual Perception 7 DLP Projectors Clear filter in addition to red green and blue filters Slide 15 ICS 280 Visual Perception Reconstruction of the gamut and function For three primaries Most of the time we do not know the method Just reconstruct the three primaries Sample the input space uniformly or nonuniformly Generate a 3D triangular mesh to generate the gamut Correspondence gives the M Slide 16 Is no longer a nice matrix ICS 280 Visual Perception 8 Finding the common gamut Find the intersection of the polytopes Since they are not convex This may give many disjoint polytopes Take the one with maximum volume The common color gamut should be a subset of this One on which a function Mc can be defined Slide 17 ICS 280 Visual Perception Finding the Common Function Start with M1 For all i Find Hi such that the distance between M1 and HiMi is minimum Find the average of all HiMi to generate the function M Find maximum Hs such that HsM spans the maximum volume within the common color gamut All are complex computational geometry problem Slide 18 ICS 280 Visual Perception 9
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