Radial Decomposition of Disks and Spheres

For people engaged in image analysis without the advantage of parallel processors or specialized hardware, the computational cost of greyscale morphological operations is a major issue. A method known as radial decomposition is presented here which enables dilations or erosions by discs or spheres to be approximated by a series of dilations or erosions by elements defined on line segments. This achieves a reduction in the number of computations involved which is of the order of the radius of the element, thus speeding up such operations as the top hat and rolling ball transformations. The method has been tested successfully and a lookup table is included in this paper enabling a user to incorporate it into an image processing package.