A long-standing problem in the characterization of multi-layered ICF capsules is the determination of the position of surfaces and interfaces from x-radiographic images. The accepted procedure for analyzing such images is to calculate the radial second derivative of x-ray absorption through a shell to locate the points of inflection in the absorption vs. radius plot which denote the layer interfaces. The computer routine developed in 1994 as an addition to NIH Image to perform this analysis was subject to unnecessary noise caused by calculating the radial finite second derivative (Δ2z/Δr2) from the interpolated radial points. Our most recent algorithm update solves this problem by directly determining the radial infinitesimal second derivative (d2z/dr2) of a cubic interpolation of surrounding pixels. This new procedure allows us to make reliable measurements of wall thickness vs. angle and layer uniformity, an improvement over the original method which only yielded layer thickness values averaged over all 360° of the shell.