Morphologies for DECaLS galaxies through a combination of nonparametric indices and machine learning methods

Context. Galaxy morphology encodes key information about formation and evolution. Large imaging surveys require automated, reproducible methods beyond visual inspection. Nonparametric indices provide a useful framework, but their performance must be quantitatively assessed. Aims. We present a homogeneous catalog of nonparametric morphological indices for DECaLS galaxies with effective radii larger than 2 arcsec. Our goal is to evaluate the reliability of indices in separating spirals and ellipticals, test their consistency with existing classification schemes, and establish their applicability for the upcoming surveys focused on the southern hemisphere. Methods. We developed galmex, a modular Python package for preprocessing images and measuring a variety of nonparametric indices. Using bona fide spirals and ellipticals as control samples, we assessed the discriminatory power of each index, and compared them with CNN-based T-Types and Galaxy Zoo DECaLS labels. We used the indices as input for a light gradient boosting machine (LightGBM) to obtain probabilistic classifications. Results. Concentration is the most reliable parameter from the concentration and asymmetry and smoothness system (CAS), while asymmetry-based indices (A and S) are limited to detecting disturbed morphologies. MEGG indices (M20, Entropy, Gini, G2) provide stronger separation and trace a gradient with T-Type. By using a simple binary (0 or 1) label for ellipticals and spirals, classifiers trained on nonparametric indices achieve high accuracy and well-calibrated probabilities, dominated by entropy, concentration, and Gini. Conclusions. We release the first public catalog of CA[As]S+MEGG indices for DECaLS, together with galmex. We combine the nonparametric indices with machine learning framework to derive spiral and elliptical separation for galaxies below z ~ 0.15 through a probabilistic approach.