Results of simulations comparing filaments with a linear or polynomial background component. (Top row): A simulated filament with a linear background. (Middle row): A simulated filament with a polynomial background. Both filaments also have random sky fluctuations with powerlaw index k = -2. Frame a/d: The simulated filament, m = 1.0. Frame b/e: Components of the filament at different values of m: the sky (dotted line), initial Plummer (dashed line), the initial background component (dash-dotted lines), and the median profile (solid line). Yellow corresponds to the flattest background component (m = 0.1), turquoise to m = 1.0, and purple to the strongest background component (m = 2.0). Frame c/f: Individual profiles (solid lines) and Plummer fits (dashed lines) to selected profiles in each map. Colors correspond to different strengths as in the previous frames. (Bottom row): R_flat (g), p (h), and FWHM (i) calculated for the profiles with a linear background (x-axis) and a polynomial background (y-axis). Colors are as in frame e. The vertical and horizontal dashed lines mark the initial parameter value.