A Fast Algorithm to Euclidean Distance Transformation by Modeling Ripple Effect

Abstract

A noval approach to accurate Euclidean distance transformation (EDT) is presented in this paper. Distance transformation (DT) is an operation of converting a binary image, consisting of object and non-object pixels into distance map (or image) where the value of each pixel represents the minimum distance from the corresponding pixel to the object surface in the input image. DT has a wide variety of applications in digital image processing. Most of the existing methods of EDT are based on mathematical morphology, which, in nature, is not approprite to perform the task with enough accuracy. To overcome this difficultly, the rippling model, which simulates the ripple effect in the real world, is proposed. Based on this model, accurate EDT can be achieved efficiently as the corresponding Voronoi diagram of the input image is formed. That is, all the points that have the minimum distances to one of the predefined points are, bounded by the boundary defined by Vornoi diagram, in the same region. The minimum distance at each pixel with respect to the uniquely defined surface points is thus encoded as the exact Euclidean distance. We have shown that the digital Voronoi diagram as well as the Enclidean distance map can be obtained by using the proposed algorithm.