Researching | The von Kries chromatic adaptation transform and its generalization

Journals >Chinese Optics Letters >Volume 18 >Issue 3 >Page 033301 > Article

Chinese Optics Letters
Vol. 18, Issue 3, 033301 (2020)

The von Kries chromatic adaptation transform and its generalization

Cheng Gao^1、2, Zhifeng Wang², Yang Xu², Manuel Melgosa³, Kaida Xiao⁴, Michael H. Brill⁵, and Changjun Li^2、*

Author Affiliations

¹School of Electronics and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China

²School of Computer and Software Engineering, University of Science and Technology Liaoning, Anshan 114051, China

³Department of Optics, Faculty of Sciences, University of Granada, Granada 18071, Spain

⁴School of Design, University of Leeds, Leeds LS2 9JT, UK

⁵Datacolor, Lawrenceville, NJ 08648, USA

show less

DOI: 10.3788/COL202018.033301 Cite this Article Set citation alerts

Cheng Gao, Zhifeng Wang, Yang Xu, Manuel Melgosa, Kaida Xiao, Michael H. Brill, Changjun Li. The von Kries chromatic adaptation transform and its generalization[J]. Chinese Optics Letters, 2020, 18(3): 033301 Copy Citation Text

show less

Abstract

Most viable modern chromatic adaptation transforms (CATs), such as CAT16 and CAT02, can trace their roots both conceptually and mathematically to a simple model formulated from the hypotheses of Johannes von Kries in 1902, known as the von Kries transform/model. However, while the von Kries transform satisfies the properties of symmetry and transitivity, most modern CATs do not satisfy these two important properties. In this Letter, we propose a generalized von Kries transform, which satisfies the symmetry and transitivity properties in addition to improving the fit to most available experimental visual datasets on corresponding colors.

Keywords

CAT02 CAT16 chromatic adaptation transforms corresponding colors von Kries transform

(\begin{matrix} R_{β} \\ G_{β} \\ B_{β} \end{matrix}) = M (\begin{matrix} X_{β} \\ Y_{β} \\ Z_{β} \end{matrix}),

(1)

View in Article

(\begin{matrix} R_{a, β} \\ G_{a, β} \\ B_{a, β} \end{matrix}) = (\begin{matrix} k_{R, β} R_{β} \\ k_{G, β} G_{β} \\ k_{B, β} B_{β} \end{matrix}),

(2)

View in Article

k_{R, β} = \frac{1}{R_{w, β}}, k_{G, β} = \frac{1}{G_{w, β}}, k_{B, β} = \frac{1}{B_{w, β}},

(3)

View in Article

(\begin{matrix} R_{w, β} \\ G_{w, β} \\ B_{w, β} \end{matrix}) = M (\begin{matrix} X_{w, β} \\ Y_{w, β} \\ Z_{w, β} \end{matrix}),

(4)

View in Article

(\begin{matrix} R_{a, β} \\ G_{a, β} \\ B_{a, β} \end{matrix}) = (\begin{matrix} R_{a, δ} \\ G_{a, δ} \\ B_{a, δ} \end{matrix}) or (\begin{matrix} k_{R, β} R_{β} \\ k_{G, β} G_{β} \\ k_{B, β} B_{β} \end{matrix}) = (\begin{matrix} k_{R, δ} R_{δ} \\ k_{G, δ} G_{δ} \\ k_{B, δ} B_{δ} \end{matrix}) .

(5)

View in Article

Γ_{δ, β} = diag (\begin{matrix} \frac{k_{R, β}}{k_{R, δ}} & \frac{k_{G, β}}{k_{G, δ}} & \frac{k_{B, β}}{k_{B, δ}} \end{matrix}),

(6)

View in Article

s_{RGB, δ} = Γ_{δ, β} s_{RGB, β} or s_{XYZ, δ} = M^{- 1} Γ_{δ, β} {Ms}_{XYZ, β} .

(7)

View in Article

Γ_{δ, β} Γ_{β, δ} = I_{3},

(8)

View in Article

Γ_{γ, δ} Γ_{δ, β} = Γ_{γ, β} .

(9)

View in Article

k_{R, β}^{'} = k_{R, β} q_{R, β}, k_{G, β}^{'} = k_{G, β} q_{G, β}, k_{B, β}^{'} = k_{B, β} q_{B, β} .

(10)

View in Article

Γ_{δ, β}^{'} = diag (\begin{matrix} \frac{k_{R, β}^{'}}{k_{R, δ}^{'}} & \frac{k_{G, β}^{'}}{k_{G, δ}^{'}} & \frac{k_{B, β}^{'}}{k_{B, δ}^{'}} \end{matrix}) .

(11)

View in Article

q_{R, β} = p_{R, β},

(12)

View in Article

p_{R, β} = \frac{1 + {(L_{β})}^{1 / 3} + r_{E, β}}{1 + {(L_{β})}^{1 / 3} + 1 / r_{E, β}},

(13)

View in Article

r_{E, β} = \frac{3 R_{w, β} / R_{E}}{R_{w, β} / R_{E} + G_{w, β} / G_{E} + B_{w, β} / B_{E}};

(14)

View in Article

q_{R, β} = q_{G, β} = q_{B, β} = Y_{w, β};

(15)

View in Article

q_{R, β} = R_{E}, q_{G, β} = G_{E}, q_{B, β} = B_{E} .

(16)

View in Article

\frac{q_{R, β}}{q_{R, δ}} = \frac{q_{G, β}}{q_{G, δ}} = \frac{q_{B, β}}{q_{B, δ}} = c;

(17)

View in Article

Γ_{δ, β}^{'} = c \cdot diag (\begin{matrix} \frac{R_{w, δ}}{R_{w, β}} & \frac{G_{w, δ}}{G_{w, β}} & \frac{B_{w, δ}}{B_{w, β}} \end{matrix}) = c Γ_{δ, β} .

(18)

View in Article

s_{XYZ, δ} = M^{- 1} Γ_{δ, β}^{'} M s_{XYZW, β} = c s_{XYZW, δ} .

(19)

View in Article

\frac{q_{R, β}}{q_{R, δ}} = \frac{q_{G, β}}{q_{G, δ}} = \frac{q_{B, β}}{q_{B, δ}} = c = 1 .

(20)

View in Article

Γ_{δ, β, CATxx} = D_{xx} Γ_{δ, β}^{'} + (1 - D_{xx}) I_{3},

(21)

View in Article

Π_{δ, β, 2 Step} = {(Γ_{E, δ, CATxx})}^{- 1} Γ_{E, β, CATxx} .

(22)

View in Article

k_{R, β}^{″} = D_{β} k_{R, β}^{'} + (1 - D_{β}), k_{G, β}^{″} = D_{β} k_{G, β}^{'} + (1 - D_{β}), k_{B, β}^{″} = D_{β} k_{B, β}^{'} + (1 - D_{β}) .

(23)

View in Article

Γ_{δ, β}^{″} = diag (\begin{matrix} \frac{k_{R, β}^{″}}{k_{R, δ}^{″}} & \frac{k_{G, β}^{″}}{k_{G, δ}^{″}} & \frac{k_{B, β}^{″}}{k_{B, δ}^{″}} \end{matrix}) .

(24)

View in Article

q_{R, β} = q_{G, β} = q_{B, β} = c_{2} .

(25)

View in Article

R_{w, E} = G_{w, E} = B_{w, E} = X_{w, E} = Y_{w, E} = Z_{w, E} = 100 .

(26)

View in Article

k_{R, E}^{'} = k_{G, E}^{'} = k_{B, E}^{'} = k_{R, E}^{″} = k_{G, E}^{″} = k_{B, E}^{″} = 1 .

(27)

View in Article

Γ_{E, β}^{″} = Γ_{E, β, CATxx} .

(28)

View in Article

Γ_{δ, E}^{″} = {(Γ_{E, δ, CATxx})}^{- 1} .

(29)

View in Article

Figures&Tables (1)

References (28)

Copy Citation Text

Cheng Gao, Zhifeng Wang, Yang Xu, Manuel Melgosa, Kaida Xiao, Michael H. Brill, Changjun Li. The von Kries chromatic adaptation transform and its generalization[J]. Chinese Optics Letters, 2020, 18(3): 033301

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address