A mathematical morphology approach to Euclidean distance transformation

A distance transformation technique for a binary digital image using a gray-scale mathematical morphology approach is presented. Applying well-developed decomposition properties of mathematical morphology, one can significantly reduce the tremendous cost of global operations to that of small neighborhood operations suitable for parallel pipelined computers. First, the distance transformation using mathematical morphology is developed. Then several approximations of the Euclidean distance are discussed. The decomposition of the Euclidean distance structuring element is presented. The decomposition technique employs a set of 3 by 3 gray scale morphological erosions with suitable weighted structuring elements and combines the outputs using the minimum operator. Real-valued distance transformations are considered during the processes and the result is approximated to the closest integer in the final output image.