Comparison of the direct, empirical and model-predicted completeness maps, illustrated at G ~ 21. Top left: map of the direct completeness estimate, i.e. the ratio of source densities in Gaia and DECaPS in the magnitude range 20.9 < G < 21.1. Top right: map of the quantity M₁₀ used to predict the model completeness. Bottom left: completeness at G = 21 predicted from the M₁₀ map and the model of Eq. (1). Bottom right: map of the difference between the predicted and observed completenesses. We note that using more external information, the model-predicted completeness map (bottom left) is effectively a de-noised version of the empirical completeness map (top left).