Image segmentation using the student’s t-test on adjacent spherical populations of pixels

Abstract

We have developed a new framework for analyzing images called Shells and Spheres (SaS) based on a set of spheres with adjustable radii, with exactly one sphere centered at each image pixel. This set of spheres is considered optimized when each sphere reaches, but does not cross, the nearest boundary of an image object. Statistical calculations at varying scale are performed on populations of pixels within spheres, as well as populations of adjacent spheres, in order to determine the proper radius of each sphere. In the present work, we explore the use of a classical statistical method, the student's t-test, within the SaS framework, to compare adjacent spherical populations of pixels. We present results from various techniques based on this approach, including a comparison with classical gradient and variance measures at the boundary. A number of optimization strategies are proposed and tested based on pairs of adjacent spheres whose size are controlled in a methodical manner. A properly positioned sphere pair lies on opposite sides of an object boundary, yielding a direction function from the center of each sphere to the boundary point between them. Finally, we develop a method for extracting medial points based on the divergence of that direction function as it changes across medial ridges, reporting not only the presence of a medial point but also the angle between the directions from that medial point to the two respective boundary points that make it medial. Although demonstrated here only in 2D, these methods are all inherently n-dimensional.