RGB to grayscale (luminosity)

Background

Converting colour to grayscale isn't a plain average — human eyes are more sensitive to green than red or blue. The standard luminosity weights are:

$$Y = 0.299\,R + 0.587\,G + 0.114\,B$$

applied per pixel.

Problem statement

Implement rgb_to_grayscale(img) converting an RGB image to a grayscale matrix using the luminosity weights.

Input

• img — array-like of shape (H, W, 3): RGB intensities.

Output

Returns an np.ndarray of shape (H, W): the grayscale intensity per pixel.

Examples

Example 1 — white stays white

Input:  img = [[[255, 255, 255]]]
Output: [[255.]]

Explanation: $0.299+0.587+0.114 = 1.0$, so $255 \times 1.0 = 255$.

Example 2 — pure colors

Input:  img = [[[255, 0, 0], [0, 255, 0]]]
Output: [[76.245 149.685]]

Explanation: red → $0.299\times255=76.245$; green → $0.587\times255=149.685$.

Constraints

• Apply weights [0.299, 0.587, 0.114] along the channel axis.
• Return shape (H, W).

Notes

• Because green carries the most luminance weight, a pure-green pixel looks brighter in grayscale than a pure-red or pure-blue one of the same intensity.