Results of a log-normal fit for the singularity spectrum of the full Musca 250 μm map (also called PSW), edge-aware filtered (top image, λ = 0.7), and unfiltered (bottom image). In each image, the singularity spectrum h↦D(h) is shown in orange, and the log-normal parabola in blue. The values obtained for the coefficients of the fit (Eq. (9)) are given in each case. The differences between the two fits shows the importance of the edge-aware filtering for multifractal analysis of astronomical observational maps. It appears that the background noise “log -normalizes” the data, while the filtered version, which takes fine filamentary structures into account better, deviates from log -normality. We note in the filtered version the change in the orange curve around h = −0.2. This is an indication that different types of turbulent processes are present in the Musca cloud, in particular those processes inside the main filament and the surrounding cloud.