Boundaries, shading, and border ownership: A cusp at their interaction.

The association of borders with "figure" rather than "background" provides a topological organizing principle for early vision. Such global influences have recently been shown to have local effects, with neuronal activity modulated by stimulus properties from well outside the classical receptive field. We extend the theoretical analysis of such phenomena by developing the geometry of interaction between shading, boundaries, and boundary ownership for smooth surfaces.

Cortical connections and early visual function: intra- and inter-columnar processing.

While it is widely assumed that the long-range horizontal connections in V1 are present to support contour integration, there has been only limited consideration of other possible relationships between anatomy and physiology (the horizontal connections) and visual function beyond contour integration. We introduce the possibility of other relationships directly from the perspective of computation and differential geometry by identifying orientation columns in visual physiology with the (unit) tangent bundle in differential geometry. This suggests abstracting early vision in a space that incorporates both position and orientation, from which we show that the physiology is capable of supporting a number of functional computations beyond contour integration, including texture-flow and shading-flow integration, as well as certain relationships between them.