Latitude and longitude vertical disparities

Abstract

The literature on vertical disparity is complicated by the fact that several different definitions of the term "vertical disparity" are in common use, often without a clear statement about which is intended or a widespread appreciation of the properties of the different definitions. Here, we examine two definitions of retinal vertical disparity: elevation-latitude and elevation-longitude disparities. Near the fixation point, these definitions become equivalent, but in general, they have quite different dependences on object distance and binocular eye posture, which have not previously been spelt out. We present analytical approximations for each type of vertical disparity, valid for more general conditions than previous derivations in the literature: we do not restrict ourselves to objects near the fixation point or near the plane of regard, and we allow for non-zero torsion, cyclovergence, and vertical misalignments of the eyes. We use these expressions to derive estimates of the latitude and longitude vertical disparities expected at each point in the visual field, averaged over all natural viewing. Finally, we present analytical expressions showing how binocular eye position-gaze direction, convergence, torsion, cyclovergence, and vertical misalignment-can be derived from the vertical disparity field and its derivatives at the fovea.

Stereo vision and strabismus

“…This, together with the other laws governing eye movements, 2,3 means that matches generally lie at essentially the same vertical position in both eyes. 4 The visual system simplifies further by considering only potential matches that are at very similar horizontal locations in the two eyes, within a degree or so (Figure 2). The effect of this is to limit the search to objects at or near the fixation distance.…”

What is stereoscopic vision good for?

“…In animals like humans with mobile eyes, stereo correspondence is in principle two-dimensional -an object projecting to a given point in the left retina could in principle project anywhere in a 2D patch of the right retina, depending on where the person is looking 9 . In practice, the human visual system tries to "fudge" stereo correspondence into a 1D problem by imposing tight constraints on binocular eye movements 10 .…”

Disparity energy model using a trained neuronal population

“…This problem is solved by introducing, for each cell orientation, a vertical position shift which compensates the phase component: ∆x pos = ∆x enc − ∆φ · (cos(θ)/2πf ) and ∆y pos = ∆y enc − ∆φ · (sin(θ)/2πf ), with ∆x enc and ∆y enc being the preferred horizontal and vertical disparities and subscript "enc" meaning encoding. We note that ∆y enc = 0 for all cells, as the vertical disparity of the cells in the fovea is expected to be zero, although it can be non-zero at other retinotopic positions [14]. The left (ρ L ) and right (ρ R ) RFs of the binocular simple cell are defined by…”