TSL color space

TSL (Tint, Saturation, and Luminance) is a color space due to (Terrillon & Akamatsu 2000) that is used in face detection and based on hue (“teint” in French), saturation and luma.

The transformation from RGB to TSL is:

$T = \begin{cases} \frac{1}{2\pi} \arctan{\frac{r'}{g'}} + \frac{1}{4}, & \mbox{if}~g'>0 \\ \frac{1}{2\pi} \arctan{\frac{r'}{g'}} + \frac{3}{4}, & \mbox{if}~g'<0 \\ 0, & \mbox{if}~g'=0 \\ \end{cases}$

$S = \sqrt{\frac{9}{5}\left( r'^2 + g'^2 \right)}$

$L = 0.299R + 0.587G + 0.114B$

where:

$r' = r - \tfrac{1}{3}$

$g' = g - \tfrac{1}{3}$

$r = \tfrac{R}{R+G+B}$

$g = \tfrac{G}{R+G+B}$

The reverse transformation from TSL to RGB is:

$R = k \cdot r$

$G = k \cdot g$

$B = k \cdot (1-r-g)$

where:

$r = \begin{cases} \frac{\sqrt{5}}{3} S, & \mbox{if}~T=0 \\ x \cdot g + \frac{1}{3}, & \mbox{if}~T \ne 0 \\ \end{cases}$

$g = \begin{cases} - \sqrt{\frac{5}{9(x^2+1)}} \cdot S, & \mbox{if}~T>\frac{1}{2} \\ \sqrt{\frac{5}{9(x^2+1)}} \cdot S, & \mbox{if}~T<\frac{1}{2} \\ 0, & \mbox{if}~T=0 \\ \end{cases}$

$k = \frac{1}{0.185r + 0.473g + 0.114}$

$x = - \cot ({2\pi \cdot T})$

See also

• HSL and HSV

References

• Terrillon, Jean-Christophe; Akamatsu, Shigeru (2000), Comparative Performance of Different Chrominance Spaces for Color Segmentation, International Conference on Face and Gesture Recognition, pp. 54–61, http://citeseer.ist.psu.edu/terrillon00comparative.html, retrieved 2008-02-10