Arturo Tozzi

Center for Nonlinear Science, University of North Texas

1155 Union Circle, #311427

Denton, TX 76203-5017 USA


James F. Peters

Department of Electrical and Computer Engineering, University of Manitoba

75A Chancellor’s Circle

Winnipeg, MB R3T 5V6 Canada


Sheela Ramanna

Department of Applied Computer Science, University of Winnipeg

Winnipeg, Manitoba R3B 2E9, Canada



DOI: 10.13140/RG.2.1.2399.0167




During the exploration of the surrounding environment, the brain links together external inputs in a complex of sensations, giving rise to the perception of a persistent object.  Here, Borsuk’s theory of shape and the Borsuk-Ulam theorem provide a mathematical foundation for Gibson’s notion of persistence perception.  We show how the latter   can be viewed as signals matching, e.g., real-scene visual signals that are collectively the umbra of physical shapes impinging on the optic nerves, which we map to similar shape representations.  We show how Gibson’s ecological theory of perception accounts for our knowledge of world objects by borrowing a concept of invariance in topology:  a series of transformations can be endlessly and gradually applied to a pattern, in particular the shape of an object, without affecting its invariant properties. In sum, high-level representations of objects in our environment are mapped to simplified views (our interpretations) of the objects, in order to construct a symbolic representation of the environment.  The fact that our perception of an object continues, even when it is out of sight, can be explained by viewing regions on the surface of a hypersphere as multiple representations of object shapes that can be projected continuously to an ecological object that have seen and continue to see, thanks to the mapping from shapes in our memory to shapes in Euclidean space.  





NOVEL VERSION: Tozzi A, Peters JF, Ramanna S. 2016. A topological/ecological approach to perception. BiorXiv,