An efficient method for computing mathematical morphology for medical imaging

Abstract

Many medical imaging techniques use mathematical morphology (MM), with discs and spheres being the structuring elements (SE) of choice. Given the non-linear nature of the underlying comparison operations (min, max, AND, OR), MM optimization can be challenging. Many efficient methods have been proposed for various types of SE based on the ability to decompose the SE by way of separability or homotopy. Usually, these methods are only able to approximate disc and sphere SE rather than accomplish MM for the exact SE obtained by discretization of such shapes. We present a method that for efficiently computing MM for binary and gray scale image volumes using digitally convex and X-Y-Z symmetric flat SE, which includes discs and spheres. The computational cost is a function of the diameter of the SE and rather than its volume. Additional memory overhead, if any, is modest. We are able to compute MM on real medical image volumes with greatly reduced running times with increasing gains for larger SE. Our method is also robust to scale: it is applicable to ellipse and ellipsoid SE which may result from discretizing a disc or sphere on an anisotropic grid. In addition, it is easy to implement and can make use of existing image comparison operations. We present performance results on large medical chest CT datasets.