Abstract
The techniques of decomposing gray-scale structuring elements with emphasis on the additively separable structuring elements are presented. Based on the concept of additively separable, we proposed the square Euclidean distance as the measure in the distance transformation. Since the structuring element corresponding to square Euclidean distance is additively separable, the developed techniques can be applied to decompose the structuring element into successive dilation of small structuring elements with window size 3 × 3. © 1993.