# Tone mapping – Perceived brightness

Simplest function that modify luminance of the color: (0)

$$T(color) = \frac{color}{ 1 + \frac{luma}{range} }$$

• T – tone mapping function
• color – be tone mapped
• luma – luminance of color
• range -range to tone map into.
• inverse  would be 1 –

Luma – perceived brightness

Luminance standard – 0.2126*R + 0.7152*G + 0.0722*B (1)
Luminance po var 1 – 0.299*R + 0.587*G + 0.114*B (2)
Luminance po var 2 – sqrt( 0.299*R^2 + 0.587*G^2 + 0.1*B^2 ) : SLOW (3)

Approximation:

$$Y = \frac{(R + R + B + G + G + G)}{6}$$

$$Y = (R + R + R + B + G + G + G +G) >> 3$$

Reduce fireflies:

$$weight(s) = \frac{1}{ 1 + luma }$$

• s – samples

Average:

$$F(average)=\frac{sample * x}{weight(s)x}$$

• x – number of samples

Expensive function, better results –  more than color range linear best for us.

$$T(color) = \left\{ \begin{array}{l l} color & \quad \text{if luma \leq a}\\ \frac{color}{luma} \left( \frac{ a^2 – b*luma }{ 2a – b – luma } \right) & \quad \text{if luma \gt a} \end{array} \right.$$

$$T_{inverse}(color) = \left\{ \begin{array}{l l} color & \quad \text{if luma \leq a}\\ \frac{color}{luma} \left( \frac{ a^2 – ( 2a – b )luma }{ b – luma } \right) & \quad \text{if luma \gt a} \end{array} \right.$$

• 0 to a – linear
• a to b –  tone mapped
• if a = 0, b=range – will be the same as first two functions