An exploration of cross-arbitrary-modal image invariant feature extraction and matching is made, with a purely handcrafted full-chain algorithm, Homomorphism of Organized Major Orientation (HOMO), being proposed. Instead of using deep models to conduct data-driven black-box learning, we introduce a Major Orientation Map (MOM), effectively combating image modal differences. Considering rotation, scale, and texture diversities in cross-modal images, HOMO incorporates a novel, universally designed Generalized-Polar descriptor (GPolar) and a Multi-scale Strategy (MsS) to gain well-rounded capacity. HOMO achieves the best comprehensive performance in feature matching on a several generally cross-modal datasets, challenging compared with a set of state-of-the-art methods including 7 traditional algorithms and 10 deep network models. A dataset named General Cross-modal Zone (GCZ) is proposed, which shows practical values.