双曲的色差公式

抄録

The expression for the color-difference line elements in a uniform color space in cylindrical co-ordinates as is the case of the Munsell system is modified to conform to the hyperbolic geometry as
Δs²=Δr²+(1+_??_)_??_Δθ²+Δz²
where r is the distance from the light source to the sample on the MacAdam (u, v) diagram, and for practical use it is rewritten as
ΔE={[10⁶_??_^1/2(_??_+_??_|_??_|²)]+[10Δ(v_Y)]²}^1/2
In spherical coodinates as is the case of the DIN color system, the above expression becomes
Δs²=Δr²+g₁(r)_??_Δθ²+g₁(r, θ)_??_sin²θΔφ²
For determination of the functional forms of g₁(r) and g₂(r, θ), psychophysical experimental data on the color-difference are lacking.