image gradient

An arrow at each pixel pointing toward the direction brightness increases fastest, sized by how fast it increases.

For an image treated as a function $f(x,y)$ of brightness, the gradient $\nabla f = (\partial f/\partial x,\ \partial f/\partial y)$ is a vector at each pixel: its direction points toward the steepest increase in brightness, and its magnitude $\|\nabla f\| = \sqrt{(\partial f/\partial x)^2+(\partial f/\partial y)^2}$ measures how steep that increase is. A large gradient magnitude marks an edge; the gradient's direction is what corner and keypoint detectors (Chapter 4) and gradient histograms (Section 4.3) build on.

Examples

Inside a flat, solid-colored region the gradient is nearly the zero vector everywhere; crossing a sharp light-to-dark boundary produces a large-magnitude gradient pointing across the boundary.