On the Foundations of Vision Modeling V. Noncommutative Monoids of Occlusive Preimages

A significant cue for visual perception is the occlusion pattern in 2-D images projected onto biological or digital retinas, which allows humans or robots to successfully sense and navigate the 3-D environments. There have been many works on modeling and studying the role of occlusion in image analysis and visual perception, mostly from analytical or statistical points of view. The current paper presents a new theory of occlusion based on simple topological definitions of preimages and a binary operation on them called “occlu.” We study many topological as well as algebraic structures of the resultant preimage monoids (a monoid is a semigroup with identity). The current paper is intended to foster the connection between mathematical ways of abstract thinking and realistic modeling of human and computer vision.