Calibration of the antenna temperature of the HFI 857 GHz map in N_HI units. Left panel: HFI 857 GHz map intensity observable within a dust-gas correlation region, characterised by low N_HI values, a low contribution of intermediate- or high-velocity clouds (IVC and HVC) to the N_HI values, and a low contamination from thermal SZ sources (see details in Sect. 3). Right panel: pixel-to-pixel correlation and linear regression between the HFI 857 GHz and HI4PI N_HI maps in the sky region visible in the left panel.