Modeling Human Vision with Differential Geometry

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.