RGB to Lab Color Space Conversion: A Comprehensive Guide

To convert RGB color space to Lab color space, you need to use the following formulas:

1. Normalize RGB values: Divide each RGB value by 255 to obtain values in the range [0, 1].

2. Convert normalized RGB to linear RGB: Apply gamma correction to each normalized RGB value to get linear RGB values. The gamma correction formula is:

R' = R / 12.92 (R <= 0.04045) R' = ((R + 0.055) / 1.055) ^ 2.4 (R > 0.04045)

G' and B' are calculated similarly.

3. Calculate XYZ values from linear RGB: Use the following matrix for conversion:

[0.4124 0.3576 0.1805] [0.2126 0.7152 0.0722] [0.0193 0.1192 0.9505]

where the first row represents the coefficients for X, the second row for Y, and the third row for Z. Matrix multiplication can be performed as follows:

[X Y Z] = [R' G' B'] * M

4. Convert XYZ to Lab values: Use the following formulas:

Xn = 95.047 Yn = 100 Zn = 108.883

xn = X / Xn yn = Y / Yn zn = Z / Zn

f(t) = (t^(1/3)) (t > 0.008856) f(t) = 7.787 t + 16/116 (t <= 0.008856)

L* = 116 f(yn) - 16 a* = 500 (f(xn) - f(yn)) b* = 200 (f(yn) - f(zn))

The final result is L*, a*, b*.