Same Photo, Different Light

Colour jitter is one of the four standard augmentations: every time a training photo is used, its lighting is nudged a little, so the model can't depend on one exact exposure. For a grayscale photo, two dials do the work.

• Contrast $c$ scales how far each pixel sits from the photo's average pixel value $m$. With $c = 2$ every pixel ends up twice as far from the average as before; with $c = 0.5$, half as far; with $c = 0$ the whole photo becomes one flat grey at the average. $c = 1$ changes nothing.
• Brightness $b$ is then added to every pixel. A positive $b$ lightens the photo; a negative one darkens it.

For example, in a photo whose average is $100$, a pixel at $130$ sits $30$ above the average. With $c = 2$ and $b = -10$ it becomes $100 + 2 \times 30 - 10 = 150$.

The result must still be a valid 8-bit photo. Round each new value to the nearest whole number. Then any value below $0$ becomes $0$, and any value above $255$ becomes $255$.

Task: write colour_jitter(image, brightness, contrast).

• image is a list of rows of whole-number pixel values from 0 to 255.
• $m$ is the average of all the pixels in the original photo, worked out once before anything changes.
• Return a new grid of the same shape holding whole numbers.

No test produces a value exactly halfway between two whole numbers, so any ordinary rounding works.