Morphologies for DECaLS Galaxies through a combination of non-parametric indices and machine learning methods: A comprehensive catalog using the Galaxy Morphology Extractor (galmex) code
Galaxy morphology encodes key information about formation and evolution. Large imaging surveys require automated, reproducible methods beyond visual inspection. Non--parametric indices provide an useful framework, but their performance must be quantitatively assessed. We present a homogeneous catalog of non--parametric 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 in the southern hemisphere. We developed galmex, a modular Python package for preprocessing images and measuring a variety of non--parametric 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 use the indices as input for a Light Gradient Boosted Machine (LightGBM) to obtain probabilistic classifications. Concentration is the most reliable parameter from the Concentratiom + Asymmetry + 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 (0/1) label for ellipticals/spirals, classifiers trained on non--parametric indices achieve high accuracy and well--calibrated probabilities, dominated by entropy, concentration, and Gini. We release the first public catalog of CA[A_S]S+MEGG indices for DECaLS, together with galmex. We combine the non-parametric indices with machine learning framework to derive spiral/elliptical separation for galaxies below z~0.15 through a probabilistic approach.