|
Adapting Luminance
|
$$L_o = \frac{Y_o E_o}{100 \pi}$$
|
|
Normalizing Luminance
|
$$L_o = \frac{Y_o E_{or}}{100 \pi}$$
|
|
$\xi$
|
$$\xi = \frac{0.48105 x_o + 0.78841 y_o - 0.08081}{y_o}$$
|
|
$\eta$
|
$$\eta = \frac{-0.272 x_o + 1.11962 y_o + 0.0457}{y_o}$$
|
|
$\zeta$
|
$$\zeta = \frac{0.91822 \left ( 1 - x_o - y_o \right )}{y_o}$$
|
|
Adapted cone response
|
$$\begin{vmatrix} R_o\\ G_o\\ B_o \end{vmatrix} = \frac{Y_o E_o}{100 \pi} \begin{vmatrix} \xi\\ \eta\\ \zeta \end{vmatrix}$$
|
|
$\beta_1$
|
$$\beta_1 \left ( x \right ) = \frac{6.469 + 6.362 x^{0.4495}}{6.469 + x^{0.4495}}$$
|
|
$\beta_2$
|
$$\beta_2 \left ( x \right ) = \frac{8.414 + 8.091 x^{0.5128}}{8.414 + x^{0.5128}}$$
|
|
Cone Response
|
$$\begin{vmatrix} R\\ G\\ B \end{vmatrix} = \begin{vmatrix} 0.40024 & 0.7076 & -0.08081\\ -0.2263 & 1.16532 & 0.0457\\ 0 & 0 & 0.91822 \end{vmatrix} \begin{vmatrix} X\\ Y\\ Z \end{vmatrix}$$
|
|
Scaling coefficient $e(R)$
|
$$e(R)= \left\{\begin{matrix} 1.758 & R \geq 20 \xi \\ 1 & R < 20 \xi \end{matrix}\right.$$
|
|
Scaling coefficient $e(G)$
|
$$e(G)= \left\{\begin{matrix} 1.758 & G \geq 20 \eta \\ 1 & G < 20 \eta \end{matrix}\right.$$
|
|
Achromatic Response
|
$$\begin{eqnarray} Q = \frac{41.69}{\beta_1(L_{or})}\left ( \frac{2}{3} \beta_1(R_o) e(R) \log_{10} \frac{R+n}{20 \xi + n} + \\
\frac{1}{3} \beta_1(G_o) e(G) \log_{10} \frac{G+n}{20 \eta + n}\right ) \end{eqnarray}$$
|
|
Red-Green Chromatic Response
|
$$\begin{eqnarray} t = \beta_1(R_o) \log_{10} \frac{R+n}{20 \xi + n} - \frac{12}{11}\beta_1(G_o) \log_{10}\frac{G+n}{20 \eta + n} + \\
\frac{1}{11} \beta_2(B_o) \log_{10}\frac{B+n}{20 \zeta + n} \end{eqnarray}$$
|
|
Yellow-Blue Chromatic Response
|
$$\begin{eqnarray} p = \frac{1}{9}\beta_1(R_o) \log_{10} \frac{R+n}{20 \xi + n} + \frac{1}{9}\beta_1(G_o) \log_{10}\frac{G+n}{20 \eta + n} - \\
\frac{2}{9} \beta_2(B_o) \log_{10}\frac{B+n}{20 \zeta + n} \end{eqnarray}$$
|
|
Hue Angle
|
$$\theta = \tan^{-1} \left ( \frac{p}{t} \right )$$
|
|
Brightness
|
$$B_r = Q + \frac{50}{\beta_1(L_{or})} \left ( \frac{2}{3} \beta_1(R_o) + \frac{1}{3} \beta_1(G_o)\right )$$
|
|
Reference White Brightness
|
$$\begin{eqnarray} B_{rw} = \frac{41.69}{\beta_1(L_{or})} \left ( \frac{2}{3} \beta_1(R_o) 1.758 \log_{10} \frac{100 \xi + n}{20 \xi + n} + \\
\frac{1}{3} \beta_1(G_o) 1.758 \log_{10} \frac{100 \eta + n}{20 \eta + n}\right ) + \frac{50}{\beta_1(L_{or})} \left ( \frac{2}{3} \beta_1(R_o) + \\
\frac{1}{3} \beta_1(G_o)\right ) \end{eqnarray}$$
|
|
Achromatic Lightness
|
$$L_p^* = Q + 50$$
|
|
Normalized Achromatic Lightness
|
$$L_n^* = \frac{100 B_r}{B_{rw}}$$
|
|
Red-Green Saturation
|
$$S_{RG} = \frac{488.93 E_s(\theta) t }{\beta_1(L_{or})}$$
|
|
Yellow-Blue Saturation
|
$$S_{YB} = \frac{488.93 E_s(\theta) p }{\beta_1(L_{or})}$$
|
|
Total Saturation
|
$$S = \sqrt{S_{RG}^2 + S_{YB}^2}$$
|
|
Red-Green Chroma
|
$$C_{RG} = \left ( \frac{L_p^*}{50} \right )^{0.7} S_{RG}$$
|
|
Yellow-Blue Chroma
|
$$C_{YB} = \left ( \frac{L_p^*}{50} \right )^{0.7} S_{YB}$$
|
|
Total Chroma
|
$$C = \left ( \frac{L_p^*}{50} \right )^{0.7} S$$
|
|
Red-Green Colorfulness
|
$$M_{RG} = \frac{C_{RG} B_{rw}}{100}$$
|
|
Yellow-Blue Colorfulness
|
$$M_{YB} = \frac{C_{YB} B_{rw}}{100}$$
|
|
Total Colorfulness
|
$$M = \frac{C B_{rw}}{100}$$
|