Modeling Human Vision with Differential Geometry

Ana Dodik

Keywords: vision, vision science, perception, differential geometry, exterior calculus, differential forms, discrete exterior calculus

TL;DR: This extended abstract frames a smooth geometric representation of impossible objects in the context of vision science.

Abstract: We describe recent efforts to tackle the problem of computationally representing impossible objects, i.e., shapes which have local geometry but cannot be globally assembled into 3D, in a manner reflective of how humans perceive them. We build off of the initial work describing a discrete representation of these objects [Dodik et al. 2025] toward a broader smooth mathematical theory independent of the parametric function class used to represent impossible objects on the computer, potentially opening doors to encoding them via, e.g., a neural network. We will also discuss implications of our work for human and machine vision research, including concrete testable hypotheses as well as some more speculative ideas.

Submission Number: 70