luma.md

Background

Much image data is encoded with the ‘RGB colour model’ which measures the presence of the three colours red, green and blue (hence RGB) in a light source.

Compression formats like JPEG use 'transform coding' part of which involves a 'colour space transformation', converting images from RGB into a different colour space called $Y'$$C_B$$C_R$. (a.k.a., 'YCbCr').

This has three components:

• The $Y$ component represents the 'brightness' of a pixel
• $C_B$, & $C_R$ represent the 'chrominance' (split into blue and red components).

If $R$, $G$, and $B$, are the red, green and blue signals, each with a value between 0 and 1, then our the components of our new colour space are defined by

$$ \begin{align*} Y' &= K_R R + K_G G + K_B B,\\ C_B &= \frac {1}{2} \frac {B-Y'}{1-K_B},\\ C_R &=\frac {1}{2} \frac {R-Y'}{1-K_R}, \end{align*} $$ where $K_R$, $K_G$, and $K_B$ are constants that satisfy $K_R + K_G +K_B = 1$. For instance, $$ \begin{align*} K_R &= 0.299,\\ K_G &= 0.587,\\ K_B &=0.114. \end{align*} $$

Task

• Type: Implementation
• Task: Implement $Y'$, $C_B$, & $C_R$ using the constants given as default arguments.
• Bonus:
  • Experiment with alternative weightings,
  • Import a real image (e.g., from scikit), take a 16x16 array and apply this transform. Return both luminance values (a 16x16 array) and two 8×8 blocks of chrominance samples (sampling every other value).
• Reference implementation: luma.brightness, luma.c_b, luma.c_r, luma.mb_to_luma_cb_cr