A single coordinate framework for optic flow and binocular disparity

TL;DR

This paper proposes a unified coordinate framework for analyzing optic flow and binocular disparity, emphasizing the geometric relationships and practical advantages of decomposing flow patterns during fixation.

Contribution

It introduces a single coordinate system that unifies optic flow and disparity analysis, clarifying their geometric relationship and simplifying understanding of flow patterns during fixation.

Findings

Decomposition of flow into 'towards', 'sideways', 'vergence', and 'cyclovergence' components.

Unified framework clarifies the relationship between optic flow and disparity.

Practical benefits for surface perception and action control.

Abstract

Optic flow is two dimensional, but no special qualities are attached to one or other of these dimensions. For binocular disparity, on the other hand, the terms 'horizontal' and 'vertical' disparities are commonly used. This is odd, since binocular disparity and optic flow describe essentially the same thing. The difference is that, generally, people tend to fixate relatively close to the direction of heading as they move, meaning that fixation is close to the optic flow epipole, whereas, for binocular vision, fixation is close to the head-centric midline, i.e. approximately 90 degrees from the binocular epipole. For fixating animals, some separations of flow may lead to simple algorithms for the judgement of surface structure and the control of action. We consider the following canonical flow patterns that sum to produce overall flow: (i) 'towards' flow, the component of translational flow produced by approaching (or retreating from) the fixated object, which produces pure radial flow on the retina; (ii) 'sideways' flow, the remaining component of translational flow, which is produced by translation of the optic centre orthogonal to the cyclopean line of sight and (iii) 'vergence' flow, rotational flow produced by a counter-rotation of the eye in order to maintain fixation. A general flow pattern could also include (iv) 'cyclovergence' flow, produced by rotation of one eye relative to the other about the line of sight. We consider some practical advantages of dividing up flow in this way when an observer fixates as they move. As in some previous treatments, we suggest that there are certain tasks for which it is sensible to consider 'towards' flow as one component and 'sideways' + 'vergence' flow as another.