The signed Euclidean distance transform and its applications

The signed Euclidean distance transform described is a modified version of P.E. Danielsson's Euclidean distance transform (1980). The distance transform produces a distance map in which each pixel is a vector of two integer components. If a distance map is created inside the objects, the two integer values of a pixel in the distance map represent the displacements of the pixel from the nearest background point in the x and y directions, respectively. The unique feature of this distance transform, that a vector in the distance map is always pointing to the nearest background point, is exploited in several applications, such as the detection of dominant point in digital curves, curve smoothing, computing Dirichlet tessellations and finding convex hulls.>