The spiral arm mask overlaid on the column density of the disc galaxy. The first two panels show the spiral arm mask we used in the (lnR, θ) plane and in the (x, y) plane, respectively. The first panel also shows the unit vectors $({\widehat{e}}_{\xi },{\widehat{e}}_{\eta })$. The third panel shows the binned relative projected density Σ/Σ₀ − 1 along the arm. We can see the clumps as peaks in relative density in the third panel.