Density Index: Extension of Shape Index in Describing Local Intensity Variations in a 3D Image

When applying to the quantifying intensity variation of the neighborhood of a voxel in a 3D image, shape index（SI） lacks an extended form and currently uses the combination of the three computed SI values based on three orthogonal sections of the neighborhood, which results in massive false detection. To cope with the problem, the extended form of SI was studied. First, in a spherical coordinates system, an unit sphere was chosen to remove the interference stemmed from the variation of intensity scale; Second, in the unit sphere, 6 equivalent regions were analyzed and one of them was selected as the representative region; Third, because the original calculation formula of SI is hard to extend, an equivalent formula of SI was deduced and it was extended to the case of describing the variation of intensity for a local region of a 3D image and the derived index is density index（DI）; Fourth, by analyzing the geometrical properties of the definition domain of DI, a curve with important qualities—inverse Z line was introduced and the intensity variation patterns of some typical points in it were studied. The simulation results show that the false detection rate of DI is much lower than SI for the typical cases of polyp detection in colon walls.