Shells and Spheres: A Framework for Variable Scale Statistical Image Analysis

Abstract

We have developed a framework for analyzing images, called Shells and Spheres, based on a set of spheres with adjustable radii, with exactly one sphere centered at each image pixel. This set of spheres, known as a sphere map, is considered optimized when each sphere reaches, but does not cross, the nearest boundary. Calculations denoted as Variable-Scale Statistics (VSS) are performed on populations of pixels within spheres, as well as populations of adjacent and overlapping spheres, in order to deduce the proper radius of each sphere. Spheres grow or shrink by adding or deleting an outer shell one pixel thick. Unlike conventional fixed-scale kernels, our spherical operators consider as many pixels as possible to differentiate between objects and accurately delineate boundaries. We use the word ?sphere? here for brevity, though the approach is not limited to 3D and is valid in n-dimensions. We illustrate our approach on synthetic images containing objects with uniform intensity. We then describe a particular algorithm using Shells and Spheres and demonstrate it by segmenting the aortic arch in a contrast-enhanced CT scan, both in 2D and 3D.