Separating the blue cloud and the red sequence using Otsu's method for image segmentation

The observed colour bimodality allows a classification of the galaxies into two distinct classes: the `blue cloud' and the `red sequence'. Such classification is often carried out using empirical cuts in colour and other galaxy properties that lack solid mathematical justifications. We propose a method for separating the galaxies in the `blue cloud' and the `red sequence' using Otsu's thresholding technique for image segmentation. We show that this technique is insensitive to the choice of binning. It provides a robust and parameter-free method for the classification of the red and blue galaxies based on the minimization of the intra-class variance and maximization of the inter-class variance. We also apply an iterative triclass thresholding technique based on Otsu's method to improve the classification. The galaxy colour is known to depend on the stellar mass and the luminosity of galaxies. We obtain the dividing lines between the two populations in the colour-stellar mass plane and the colour-absolute magnitude plane by employing these methods in a number of independent stellar mass bins and absolute magnitude bins.