In both figures, all points represent objects that have passed the first 4 selection criteria. They are colour coded to represent their Galactic latitude b and therefore the interstellar reddening that affects their near-infrared J, H, and K magnitudes: black points correspond to objects with b > 2 deg, light blue ones are objects with deg (corresponding to average extinction of ⟨A_V⟩ ~ 2 mag), and purple ones are objects located close to the Galactic plane, with b < 1 deg (with ⟨A_V⟩ ~ 5 mag). The larger dots and stars represent known RCB and HdC stars with identical colour coding to Fig. 4. The dashed and solid red lines represent the selection cuts 5 (left) and 6 (right) used in the analysis. Left: J − H vs. H − K diagram. Right:  [4.6]  −  [12]  vs.  [12]  −  [22]  diagram. The black vertical lines correspond to the brightness correction that needs to be applied to bright RCBs in the [4.6] band due to the photometric bias (see Sect. 2.2.1).