Hands-On Image Processing with Python

Derivatives and gradients

The following diagram shows how to compute the partial derivatives of an image I (which is a function f(x, y)), using finite differences (with forward and central differences, the latter one being more accurate), which can be implemented using convolution with the kernels shown. The diagram also defines the gradient vector, its magnitude (which corresponds to the strength of an edge), and direction (perpendicular to an edge). Locations where the intensity (gray level value) changes sharply in an input image correspond to the locations where there are peaks/spikes (or valleys) in the intensity of the first-order derivative(s) of the image. In other words, the peaks in gradient magnitude mark the edge locations, and ...