Grayscale & Channel Normalization

The problem, from first principles

Two preprocessing steps appear in almost every vision pipeline. Converting color to grayscale collapses three channels into one brightness value, and it is not a plain average: the eye is most sensitive to green and least to blue, so the standard luma formula weights the channels 0.299, 0.587 and 0.114. Channel normalization then shifts and scales each channel to have roughly zero mean and unit variance across the dataset, which keeps the inputs of the first layer in a range where optimization is well behaved. The per-channel mean and standard deviation come from the training set, not from each image.

From theory to code

Implement to_grayscale and normalize_channels.

Constraints

• to_grayscale(img): img has shape (H, W, 3); return shape (H, W) equal to img @ [0.299, 0.587, 0.114].
• normalize_channels(img, mean, std): img has shape (H, W, C) and mean, std have shape (C,) with positive std; return (img - mean) / std.
• Neither function modifies its input.

Hints