Good continuation in 3D: the neurogeometry of stereo vision

TL;DR

This paper extends the concept of good continuation from 2D image curves to 3D stereo vision by introducing a neurogeometric model that incorporates spatial and orientation disparities, offering insights into neural organization and the correspondence problem.

Contribution

It presents a novel neurogeometric model for 3D good continuation that integrates spatial and orientation disparities, advancing understanding of stereo vision processing.

Findings

Proposes a neurogeometric model for 3D good continuation.

Provides a neural organization framework for stereo correspondence.

Illustrates how 2D continuation principles generalize to 3D.

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.