Kabirian-based Optinalysis: Its Paradigm, Theorems, and Properties

The conceptual and theoretical backbones of symmetry/asymmetry detections or similarity/dissimilarity, and identity/unidentity study are automorphism or isomorphism respectively. However, the development of equations and methods for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures deviates from these backbones. In this article, an equation was proposed for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures, and proved that its isoreflective pairs-points are functionally bijective and inverse. The proposal, called Kabirian-based optinalysis, is based on the conceptual and theoretical frameworks of automorphism and isomorphism. The Kabirian-based optinalysis is also proven and characterized as invariant (robust) under translation (i.e., scaling and location shift), and rotation or reflection. Computing codes were written in python language for Kabirian-based optinalysis to serve as working codes for application and verification.