Ridge detection

In image processing, ridge detection is the attempt, via software, to locate ridges in an image, defined as curves whose points are local maxima of the function, akin to geographical ridges. For a function of N variables, its ridges are a set of curves whose points are local maxima in N minus 1 dimensions, and valleys are defined in the same way with local minima. Ridge sets, valley sets and a related connector set together form the relative critical set of the function. The procedures were motivated by image analysis and computer vision, where they capture the interior of elongated objects. Because a computation at a single scale is noise sensitive, multi-scale ridges computed in scale space with Gaussian smoothing are used for a more robust representation. Typical applications are detecting roads in aerial images and blood vessels in retinal images or three-dimensional magnetic resonance images.