SLIDE 12 Multimedia & Mathematics July 23-28, 2005 Banff, Alberta
Spectral model (SM) Spectral model (SM)
- considers spectral & spatial characteristics of neighboring color pixels
Modelling assumption in the existing SMs:
( , ) ( , ) ( , )2 ( , )2
/ / ; 1 or 3
p q k i j k p q i j
x x x x k k = = =
- color ratio model (uniform hue modelling assumption)
( , ) ( , )1 ( , )2 ( , )3
[ , , ]
p q p q p q p q
x x x = x
( , ) ( , )1 ( , )2 ( , )3
[ , , ]
i j i j i j i j
x x x = x
pixel occupying location to be interpolated pixel occupying neighboring location
( , ) ( , ) ( , )2 ( , )2
( ) /( ) ( ) /( )
p q k i j k p q i j
x x x x γ γ γ γ + + = + +
- normalized color ratio model (hue constancy is enforced in both in edge
transitions and uniform image areas)
( , ) ( , ) ( , )2 ( , )2 p q k i j k p q i j
x x x x − = −
- color difference model (constrained component-wise magnitude
difference)
Modelling assumption
- two neighboring vectors should have identical color chromaticity
properties (directional characteristics)
- two spatially neighboring vectors should be collinear in the RGB
(vector) color space
Computational approach
( )
( , ) ( , ) ( , ) ( , ) ( , ) ( , )
. cos ,
p q i j p q i j p q i j
= x x x x x x
3 ( , ) ( , ) 1 ( , ) ( , ) 3 3 2 2 ( , ) ( , ) 1 1
, 1
p q k i j k k p q i j p q k i j k k k
x x x x
= = =
= ⇔ =
∑ ∑ ∑
x x
- any color component can be determined from the expression above by
solving the quadratic equation expression
- y denotes the component to be determined, e.g.
Vector SM Vector SM
2
ay by c + + =
( , )2 p q
y x =
