A framework for analyzing images, called emph{Shells and Spheres},has been developed based on a set of spheres with adjustable radii,with exactly one sphere centered at each image pixel. This set ofspheres, known as a emph{sphere map}, is considered optimized wheneach sphere reaches, but does not cross, the nearest boundary.Calculations denoted as emph{Variable-Scale Statistics} (VSS) areperformed on populations of pixels within spheres, as well aspopulations of adjacent and overlapping spheres, in order to deducethe proper radius of each sphere. Spheres grow or shrink by addingor deleting an outer shell one pixel thick . Unlike conventionalfixed-scale kernels, our spherical operators consider as many pixelsas possible to differentiate between objects and accuratelydelineate boundaries. The term ``sphere" is used for brevity, thoughthe approach is not limited to 3D and is valid in n-dimensions.The approach is illustrated using both real images and noiselesssynthetic images containing objects with uniform intensity, and moreclosely examined and validated using various synthetic images withadded white noise and multiple contrast enhanced CT scans of theaortic arch. A particular algorithm using Shells and Spheres isdescribed and demonstrated on segmentation of the aortic arch in acontrast-enhanced CT scan, both in 2D and 3D
