Euclidean Distance Transformation by Parallel Operation

摘要

The diamond (city block), the square (chess-board) and the octagonal distances have been used for distance transformation of a digitized two-dimensional picture. However, they are all only approximations to Euclidean distance. Recently, a Euclidean distance propagation by a sequential operation using a vector having x and y components has been proposed. It is a very good approximation of Euclidean distance. In the report, proof is provided for a simple iterative local parallel operation that gives a complete Euclidean distance transformation without error. Skeletons for Euclidean distance and reverse transformations are also stated.