3D model of the surface of striate visual cortex. Top, The location of an object in visual space is defined by its eccentricity (w) along a meridian angle (θ). This spherical coordinate position maps to a location (r,z,ϕ) on a smoothly curved three-dimensional surface. The equations for the mapping (Rovamo and Virsu, 1984) use the cortical magnification factor and the assumption of local isotropy. For the macaque magnification factor used here, the result is an elongated curved surface extending ∼43 mm from foveal tip to far periphery. Bottom, Viewed from the side the meridian lines meet in the fovea to the left. The meridian lines do not meet at a point in far periphery but end along an arc as shown on the right. In the figure the meridian lines representing increments of 15° are crossed by vertically aligned lines of equal eccentricity incrementing in degrees as indicated by the drop lines above.
Response amplitude contour plot of V4 receptive field. The receptive field is distorted from circular symmetry with respect to the hot spot by compression toward the fovea (center of the horizontal and vertical axis) and expansion toward the periphery. The receptive field contours are based on responses to a short bar (illustrated to scale in the upper left) delivered in rapid succession on a 16 × 16 grid. Responses in raster format to a separate series of flashed stimuli delivered at eight locations (marked with numerals) from fovea to periphery and cutting through the receptive field are shown on the right. Small vertical tics in each row of the raster represent the time of neuronal discharge; each row represents a single presentation of the stimulus at time 0, grouped according to the eight different stimulus locations. Eccentricity of receptive field center is 2.5°.
Back projection of V4 receptive field onto the V1 model surface. A, Distorted receptive field as it appears in normal space mapping. Eccentricity dashed lines at 2° intervals. B, Same receptive field replotted on surface of the V1 model. The apparent circularly symmetric contour plot lines indicate the distortion is the result of the visual field representation at the level of the V1 map. Note the V1 surface is a curved 3D surface seen here as an orthographic projection. C, To measure the symmetry of the receptive field map on V1 surface the receptive field was fitted to a bivariate Gaussian surface. A ratio of the short (S) to long (L) axes of the fit served as an index of the circularity of the receptive field. This index was computed for various orientations (O) of the long axis of the Gaussian with respect to the meridian projecting from fovea to periphery through the RF center.
Circular symmetry of the back-projected receptive fields. A, Median and mean (±1.0 SD) values of the short/long axis ratio for the bivariate fits as a function of the orientation of the long axis of the Gaussian with respect to the meridian that passed through the receptive field center. Additional eccentricity dependent cortical magnification after V1 should produce a minimum near 0, where the long axis parallels the meridian and the short axis is iso-eccentric. There is no evidence for this case. B, The distribution of ratio values at three different analysis orientations for the population of 337 neurons. A large majority of the neurons (238/337) have a ratio index >0.90 for the orientation (OR:0) that parallels the meridians indicating a circular symmetry. OR, Orientation of the long axis of the Gaussian fit with respect to the meridian.
Equal-sized back projections. Left, The two-dimensional visual space illustration of the contour response amplitude receptive fields of three V4 neurons centered, respectively, at eccentricities of 1.0, 5.0, and 15.8°. The dashed circles represent lines of eccentricity at 2, 4, 6, 8, and 10°. Right, Back projections onto the V1 surface for the three V4 neurons. The very different-sized V4 receptive fields map to essentially the same size on the V1 surface, indicating that receptive fields in V4 are constructed from information converging from equivalent circular anatomical patches in V1.
V1 sampling size and receptive field size. The SD of a univariate Gaussian fit (SDfit) of the V4 back projected receptive fields (RF) are used to estimate the size of the sampling area in primary visual cortex (n = 337). A, The size of the sampling areas does not change as a function of eccentricity with a mean SDfit of 3.8 mm. B, V4 RF size as a function of RF eccentricity (gray circles) where RF size is the square root of the area contained by a contour at half the maximum response amplitude. Dashed line is the linear regression of the V4 data. Solid line is the prediction of the RF size based on the sampling of the V1 cortical surface using a radius of 4.5 mm which represents the half amplitude of a two-dimensional Gaussian for the fitted data. Crosses in lower left represent similarly measured RF sizes in area V1 (n = 83).