Spherical retinal flow for a fixating observer

When a human observer moves, the eye continually fixates on targets in the world. Although fixation is a common process in human vision, its role has not yet been established for computational purposes. The main contribution of this paper is to formalize the retinal flow for a fixating observer. A further contribution- a potentially more practical one- is to explore the role of the periphery in predicting collision. Utilizing fixation is expected to turn out to be especially fruitful in light of recent advances in computer vision for constructing active head/eye systems. In this work we make the following assumptions: (i) the observer moves with respect to the world and fixates on a target; (ii) the world is rigid, with no independently moving elements; and (iii) the possible rotation axes of the eye lie on a plane (comparable to Listing's Plane). Assumptions (ii) and (iii) make the problem of determining retinal flow tractable. We first define retinal flow for a 2D universe and then extend it to the full 3D will be decomposed into longitudinal and latitudinal flow; the behavior of longitudinal flow along the retinal periphery will be further analyzed for interesting properties. Finally the results of a simulated experiment on retinal flow at th