Fig 1.
”F” marks the fixation point;”P” marks the position of an object. Dgeom, indicates the distance from object, and I indicates interocular distance. The horizontal disparity, δ, is equal to the difference of the vergence angle, v, and the object angle, θ. δ = δr + δl, where δr and δl correspond to the disparity on the left and right retina respectively.
Fig 2.
Proposed brain areas and their connections for distance-dependent size perception.
Red arrows indicate pathways involved in distance perception: fibers carrying signals from V1 (disparity) and FEF (vergence) terminate in MT; MT then projects to LIP, where a map of distance information is constructed. Blue arrows indicate pathways involved in size perception: the distance information from LIP provides feedback signals to MT, which further projects to V1, modulating neural responses of size tuned cells and cortical activity spread in V1. Thus, a distance-dependent size representation is achieved.
Table 1.
Brain areas and their proposed functions in the model.
Fig 3.
Disparity selective cells (see variable a in Eqs (4)–(6)) in V1 are gain-modulated and simulated by Gaussian functions. Vergence selective cells (see variable v in Eq (7)) in FEF are simulated by sigmoidal functions. At the level of MT (see variable B in Eq (3)), vergence and disparity are integrated. At the level of LIP, a distance map (see variable D in Eq (2)) is estimated from a linear combination of MT outputs.
Fig 4.
Simulated tuning curves of disparity-selective cells.
The cell tuning curves in V1 [28, 30] are simulated by subtracting Gaussians. Each curve corresponds to the response of a single cell and exhibits a similar response pattern as Fig 9 in Gonzalez and Perez [30]. For example, the red dashed line resembles the TE cell’s response, which gives maximal responses at zero disparity; the blue open-circle line resembles the TN cell’s response, which has similar disparity tuning function as TE cells but peaks at negative disparity; the green star line resembles the FA cell’s response, which activates over a wide range of positive disparities. TF and NE cells are simulated but not marked in the figure. TI cells are not included in the simulation, since their responses could be simulated by assigning negative output weights to the TE cells.
Fig 5.
Simulated tuning curves of vergence cells.
The modeled tuning curves of multiple vergence cells in FEF are simulated by sigmoids. Each curve corresponds to the response of a single cell to vergence. Similar to Fig 3b in Gamlin [34], our model tuning curves show that cell activity increases as vergence angle increases.
Fig 6.
The distance information (see variable D, Eq (2)) in LIP feeds back to size tuned cells (see variable s, Eq (8)) in V1 through MT. size tuned cells in V1 are gain-modulated and have Gaussian-shaped tuning curves. In area MT, distance scaling functions are constructed. The activity of the size tuned cells is modulated by distance information through distance-dependent shunting equation (Eq (9)).
Fig 7.
Simulated tuning curves of nearness and farness cells.
The cell tuning curves in V1 are simulated by Gaussians. Similar to Fig 1a and 1b in Dobbins et al [10], the magnitudes of the responses of nearness (farness) cells decrease (increase) with viewing distance (Distance 1 < Distance 2 < Distance 3), but the shape and position of the peaks of the tuning curves are similar.
Fig 8.
Simulated tuning curves for MT cells in response to vergence and disparity.
MT cell responses to disparity is gated by vergence, Three examples of cell activity are shown, corresponding to disparity cells (a) tuned to crossed, uncrossed and zero disparity in V1, and vergence cells (v) in FEF with different tuning amplitudes.
Fig 9.
Distance cell response as a function of vergence and disparity in LIP.
The top left panel: geometric distance; middle left: approximate perceived distance, calculated by correcting disparity signal in geometric distance (see text and S1 File); bottom left: distance cell response in LIP, simulated by training a network of gain-modulated units of disparity and vergence cells using perceived distance as teaching signal. The right panels show two examples of distance approximation as a function of vergence/disparity, taken from the cross sections (indicated by the red arrows) of the distance response on the left. Y-axes labels for the right panels are the same as of the left ones.
Fig 10.
Cortical activity in V1 modulated by perceived size.
When a stimulus is presented at a close distance, the activity is strongest in the smaller eccentricity along the calcarine sulcus; when the stimulus with the same angular size (or an afterimage) is presented farther, the activity is stronger in the more eccentric areas. In other words, the bigger the stimuli perceived, the more eccentric the activation in V1. Different colors mark the different eccentric activation corresponding to different viewing distance, e.g., red marks the smallest eccentric activation and purple marks a largest eccentric activation in V1.
Fig 11.
Comparison between experimental data and simulated cortical activity in V1.
Panel (a) shows the BOLD signal change recorded from human visual cortex V1 [14]; Panel (b) shows the simulated cortical activity in V1 by our model, which resembles the experimental data on the left. At the beginning of the time courses, when the stimulus is presented at the nearest distance, the activity was strongest in the smaller eccentricity ROIs (marked in red and orange); when the stimulus with the same angular size is presented at a farther distance (one of the three viewing distances tested), the activity is stronger in the more eccentric ROIs (purple and blue) as viewing distance increased. Distance 1 < Distance 2 < Distance 3. Refer to Fig 10 for color marking. Panel (a) is adapted from Sperandio et al. [14].