Good continuation in 3D: the neurogeometry of stereo vision

Abstract

Classical good continuation for image curves is based on $2D$ position and orientation. It is supported by the columnar organization of cortex, by psychophysical experiments, and by rich models of (differential) geometry. Here we extend good continuation to stereo. We introduce a neurogeometric model, in which the parametrizations involve both spatial and orientation disparities. Our model provides insight into the neurobiology, suggesting an implicit organization for neural interactions and a well-defined $3D$ association field. Our model sheds light on the computations underlying the correspondence problem, and illustrates how good continuation in the world generalizes good continuation in the plane.