digital image

A digital image is a grid of numbers that stands in for a picture. Where a photograph on film is a continuous smear of silver grains, a digital image has been discretized twice: in space (the scene is chopped into a finite array of pixel locations) and in value (each pixel's measured light is rounded to a finite set of levels). The result is a table you can store, copy and compute on exactly, with no further loss from handling.

Formally, a grayscale digital image is a function I(x, y) defined on a finite integer grid, mapping each pixel coordinate to an intensity — a 2D matrix of numbers. A color image is a stack of such matrices, one per channel, so it is naturally a 3D array (height x width x channels), often called a tensor in modern vision code. A video adds a time axis, giving height x width x channels x frames. The two ingredients of any digital image are therefore the spatial coordinates (where a sample sits) and the stored value at that location (how much light, and of what color).

This array-of-numbers view is what makes computer vision possible: every operation, from blurring to edge detection to running a convolutional network or a Vision Transformer, is arithmetic on these numbers. A ResNet does not see a cat; it multiplies and adds pixel values through learned filters. Keeping the abstraction crisp — image as a sampled, quantized function on a grid — clarifies why sampling rate, bit depth and color space all change what the downstream algorithm can possibly recover.