Synthetic data construction used for controlled testing. Left: intrinsic filament density distribution (﹩{ \mathcal F }﹩) generated from analytically defined 3D spines. Second panel: turbulent background density field (﹩{ \mathcal B }﹩) generated using the fBm model with a power-law power spectrum. Third panel: projected column density map of the combined field ﹩{ \mathcal F }+{ \mathcal B }﹩. Right panel: higher-background realization ﹩{ \mathcal F }+2\times { \mathcal B }﹩ illustrating reduced contrast.