The survival of any animal depends on its ability to successfully interact with the objects in its environment, whether foraging for food, building a shelter, or identifying a conspecific. Thus, persistent objects, independently movable chunks of matter, constitute the fundamental unit of organization in an animal’s ecological universe. How does the brain come to represent such chunks as distinct, persistent wholes?

I will discuss a new mathematical theory of persistent surface representation (cf. https://arxiv.org/abs/2107.02036v1). The mathematical structure of light rays reflected from environment surfaces yields a natural representation of persistent surfaces, and this surface representation provides a solution to both the segmentation and tracking problems. I will describe how to generate this surface representation from continuous visual input, and present computational results showing how the approach can segment and invariantly track objects in the cluttered synthetic video despite severe appearance changes due to changes in viewpoint, occlusion, and object deformation, without requiring learning. Finally, I will speculate on where and how this surface representation might be implemented by the primate visual system.