Upper and lower left: simulated map of a 2D Gaussian source added on top of a variable background, extracted from a region centred on longitude l = 55° in the Galactic plane from the Hi-GAL survey at 160 μm. The source itself is masked in the centre to improve the polynomial fit to the background. Centre: background estimate adopting a first-order (plane) approximation (upper centre) and a fourth-order approximation (lower centre). Right: residual map assuming a first-order polynomial fit for the background estimation (upper right) or a fourth-order (lower right) polynomial fit. The high-order polynomial takes the complexity of the background into account.