finite-difference approximation

Estimating a derivative by comparing a pixel to its neighbors instead of using calculus.

A finite-difference approximation stands in for a calculus derivative at a point where the function is only known at discrete samples, such as an image's integer pixel coordinates. It replaces $\partial f/\partial x$ with a comparison between nearby pixel values, computed by convolution with a small kernel (the Sobel and Prewitt kernels above) instead of by taking a limit.

Examples

One pixel minus its left neighbor is the simplest finite difference; Sobel and Prewitt combine several such differences in a $3\times3$ window to resist noise.