The concept of generalized scale (g-scale) was introduced previously to overcome the shape, topological, and anisotropic constraints imposed by previous local morphometric scale models. Roughly speaking, the g-scale of a voxel in a scene was defined as the largest set of all voxels associated with it, that satisfy some homogeneity criterion. g-scale was shown to have interesting theoretical properties, and its superiority to an existing image background inhomogeneity correction method was demonstrated. In this paper, we present a variant of g-scale that we refer to as gB-scale. The difference between g- and gB-scale is that, while for g-scale, individual voxels are included into the g-scale set one at a time, the gB-scale set is grown by including hyperballs, the hyperball corresponding to the local ball scale at every voxel (which, briefly, is the radius of the largest hyperball of homogeneous intensity centered at the voxel). The gB-scale model was found to be more resistant to severe levels of inhomogeneity and noise compared to g-scale. A methodology to perform image background inhomogeneity correction based on the idea of gB-scale was qualitatively and quantitatively compared on nearly 250 clinical and phantom datasets, with a ball-scale- and a g-scale-based correction methodology. For scenes containing inhomogeneity but no noise, the g-, and gB-scale methods performed comparably and were superior to the ball-scale method. For scenes containing both noise and inhomogeneity, the gB-scale-based method outperformed both the g- and ball-scale correction methods.