Demonstration of break-finding algorithm. Top: two idealized model Type III surface brightness profiles, with Poisson and simulated sky noise added. Both profiles use the same inner disk slope; the left profile contains a break with h_in/h_out = 0.5, while the right profile contains a break with h_in/h_out = 0.9. Red dashed lines mark the break radius. Middle: the local slope profiles of the model surface brightness profiles. The red dashed line in the left profile marks the break radius as determined by our break-finding algorithm. No significant break was found for the right profile. Bottom: cumulative sums, as defined in Eq. (2), with the break radius of the left profile again marked with a red dashed line. Gray dashed lines mark the locations of the maximum and minimum values of CS (in the text, max(CS) and min(CS)). We note that the minimum CS of the right profile occurs at the same location as the left profile; the break, however, was not found to be significant and is therefore not shown.