Images as matrices

A colour image is a matrix of matrices: for every pixel, three numbers 0–255 (red, green, blue).

In code the image has a shape (height, width, channels). An image of 32 × 32 pixels in colour has the shape (32, 32, 3) and contains 3 072 numbers.

Doing things to the image means doing arithmetic on the numbers:

• Brighter: add 40 to every value (but clip at 255).
• Greyscale: merge the three channels into one value.
• Crop: take a rectangular cut-out of the matrix.
• Mirror: read the columns backwards.

import numpy as np

image = np.zeros((4, 6, 3), dtype=np.uint8)   # a black image, 4 rows × 6 columns
image[:, 3:, 0] = 255                          # the right half red
print(image.shape, image.size)                 # (4, 6, 3) 72

grey = image.mean(axis=2)                      # merge the channels → (4, 6)
print(grey.shape, grey[0, 0], round(float(grey[0, 4]), 1))   # (4, 6) 0.0 85.0

brighter = np.clip(image.astype(int) + 40, 0, 255).astype(np.uint8)
cutout = image[1:3, 2:5]                       # rows 1–2, columns 2–4
mirrored = image[:, ::-1]                      # flip left/right
print(cutout.shape, mirrored.shape)            # (2, 3, 3) (4, 6, 3)

A CNN does fundamentally the same thing: it slides a small filter across the matrix and does the arithmetic. The difference is that the filter's numbers are learnt instead of chosen by you.