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Quantitative Characterization of Disparity Tuning in Ventral Pathway Area V4

Department of Neuroscience, The Johns Hopkins University School of Medicine and Zanvyl Krieger Mind/Brain Institute, The Johns Hopkins University, Baltimore, Maryland

Submitted 1 April 2005; accepted in final form 20 June 2005

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
We performed a quantitative characterization of binocular disparity-tuning functions in the ventral (object-processing) pathway of the macaque visual cortex. We measured responses of 452 area V4 neurons to stimuli with disparities ranging from –1.0 to +1.0°. Asymmetric Gaussian functions fit the raw data best (median R = 0.90), capturing both the modal components (local peaks in the –1.0 to +1.0° range) and the monotonic components (linear or sigmoidal dependency on disparity) of the tuning patterns. Values derived from the asymmetric Gaussian fits were used to characterize neurons on a modal x monotonic tuning domain. Points along the modal tuning axis correspond to classic tuned excitatory and inhibitory patterns; points along the monotonic axis correspond to classic near and far patterns. The distribution on this domain was continuous, with the majority of neurons exhibiting a mixed modal/monotonic tuning pattern. The distribution in the modal dimension was shifted toward excitatory patterns, consistent with previous results in other areas. The distribution in the monotonic dimension was shifted toward tuning for crossed disparities (corresponding to stimuli nearer than the fixation plane). This could reflect a perceptual emphasis on objects or object parts closer to the observer. We also found that disparity-tuning strength was positively correlated with orientation-tuning strength and color-tuning strength, and negatively correlated with receptive field eccentricity.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
One of the major cues used to infer three-dimensional (3D) visual information is horizontal position disparity between the two eye images. The neural representation of binocular disparity has been studied extensively in primary (V1) and secondary (V2) visual cortex (Barlow et al. 1967; Gonzalez and Perez 1998; Pettigrew et al. 1968; Poggio and Fischer 1977). Some neurons in V1 and V2 show acute modal (peaked) tuning for specific disparity values, whereas others show monotonic (linear or sigmoidal) tuning patterns favoring either crossed (near) or uncrossed (far) disparities (Poggio and Fischer 1977). It was long assumed that this binocular disparity information was routed primarily to the dorsal visual pathway, based on a combination of anatomical and neurophysiological findings (DeYoe and Van Essen 1985; Hubel and Livingstone 1987; Maunsell and Van Essen 1983; Shipp and Zeki 1985). Recent studies, however, have demonstrated a rich representation of binocular disparity information in macaque ventral pathway areas V4 (Hinkle and Connor 2001, 2002; Watanabe et al. 2002) and IT (Janssen et al. 2000a,b; Uka et al. 2000).

Neural tuning patterns for binocular disparity were historically described in qualitative terms and categorized subjectively. Recently, however, there have been two large-scale quantitative analyses of disparity-tuning patterns in V1 (Prince et al. 2002a,b) and dorsal pathway area MT (DeAngelis and Uka 2003). The approach in both studies was to model response patterns of individual neurons with mathematical functions, iteratively adjusting function parameters to provide an optimal fit to the neural data. The distributions of these fitted parameters were then used to characterize disparity tuning at the population level. These analyses revealed a continuum of disparity-tuning patterns in V1 and MT, with no evidence of categorical grouping according to modal or monotonic patterns.

In the present study we took a similar quantitative approach in a ventral pathway area. In contrast to the V1 and MT studies we used solid-figure stimuli rather than random dot stereograms (RDS). Because the primary functional role of the ventral pathway is to represent objects, and ventral pathway neurons typically respond more strongly and selectively to shapes than to textures, we consider disparity tuning for solid-figure stimuli more relevant to understanding depth representation in area V4. We found that V4 disparity-tuning patterns could be most effectively characterized with asymmetric Gaussian functions. We used the fitted asymmetric Gaussian parameters to analyze the distribution of disparity-tuning characteristics across a sample of 452 neurons. We found that the distribution was continuous and showed strong biases reflecting the type of stereoscopic depth information emphasized in the ventral pathway. We also compared the distribution of disparity-tuning properties against receptive field position, orientation tuning, and color tuning. Finally, we used the results of our analyses to compare the representation of stereoscopic depth in ventral pathway area V4 with the representation in V1 and in dorsal pathway area MT.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Stimuli and recording procedures

Stereoscopic visual stimuli were generated on an Octane workstation (Silicon Graphics, Mountain View, CA) using OpenGL 1.1 graphics libraries. Images for the left and right eyes were presented in alternate frames. Separate presentation of images for the two eyes was accomplished using a NuVision stereoscopic liquid crystal shutter (MacNaughton, Beaverton, OR) attached to the monitor, and passive circular-polarized lenses placed immediately in front of the monkey's eyes. We compensated for cross talk between the two eye channels by adding to each eye's image a low-contrast, negative version of the opposite eye image. Contrast levels of the negative image for each stimulus color were adjusted manually and verified with a luminance meter. This procedure produced stimuli that were free of any appreciable interference between eye channels.

Eye position was monitored with a scleral coil system (Riverbend Instruments, Birmingham, AL) and a video-based system (ISCAN, Burlington, MA). In one monkey the positions of both eyes were monitored during experiments using two scleral coils. In the other monkey the position of only one eye was monitored during experiments, but the positions of both eyes were monitored during experiment-like trials using the video system. Analysis of eye position data for both monkeys showed that there was no significant correlation between eye vergence angle and stimulus disparity. Thus the disparity-based response differences reported here did not arise from vergence eye movements (Hinkle 2004; Hinkle and Connor 2001, 2002).

The scleral coil of fine insulated wire was surgically implanted beneath the conjunctiva of the eye (Judge et al. 1980). The coil was attached to the sclera with instant adhesive (Loctite, Rocky Hill, CT) in three locations to prevent slippage. A head-restraint post and recording chamber were implanted in separate surgical procedures. All procedures conformed to the National Institutes of Health and USDA guidelines and were approved by The Johns Hopkins University Animal Care and Use Committee.

Tungsten microelectrodes with epoxy insulation (A-M Systems, Carlsborg, WA) were used to isolate single units in the V4 lower field parafoveal representation on the prelunate gyrus and adjoining banks of the lunate and superior temporal sulci. As in previous studies (Hinkle and Connor 2001, 2002; Pasupathy and Connor 1999), recording locations were based on skull landmarks, stereotaxic coordinates, retinotopy, and inferred positions of the sulci. Across repeated electrode penetrations we constructed a retinotopic map in each animal. These maps showed, in agreement with previously published V4 maps (Gattass et al. 1988), that the vertical meridian is represented posteriorly, in and near the lunate sulcus, and the horizontal meridian is represented anteriorly, in and near the superior temporal sulcus. The fovea is represented ventrally, near the tip of the inferior occipital sulcus, and receptive field (RF) locations become more eccentric as one proceeds dorsally along the prelunate gyrus. The identity of area V4 was further confirmed by response properties, especially the prevalence of strong color tuning, and by RF sizes and their relationship to eccentricity (Gattass et al. 1988). Spikes were isolated on-line using a custom-made dual-window time–amplitude spike discriminator. Spikes were isolated using several waveform features in conjunction: the initial slope of the spike waveform plus two time–amplitude windows relative to the slope trigger point and the DC voltage level. Our recording setup typically produced large single units that were easily discriminated using these criteria.

At the start of recording sessions the monkey's stereoscopic depth perception was verified with an RDS behavioral test. The stimulus display was a 25 x 35° RDS containing nine 2.8° squares in a 3 x 3 grid with 6.5° center-to-center spacing. One of the squares, the target, was offset in depth either in front of (crossed disparity) or behind (uncrossed disparity) the zero disparity plane. The other eight squares, the distractors, were offset in depth in the opposite direction. The monkey was required to fixate within 3.1° of the center of the target square for 2.5 s to receive a reward. The position of the target square varied randomly from trial to trial. Each of the nine positions was tested multiple times. Performance was typically >90%.

The behavioral task during data collection was to maintain fixation within a 0.5° radius window centered on a 0.1° white spot positioned directly in front of the monkey's eyes. The required fixation duration ranged from 2.7 to 6.0 s. Continuous fixation throughout the entire trial was rewarded with water or juice. When a neuron was first isolated, its response properties and RF location were determined with drifting and flashed bars and with other shapes. Our sampling strategy was biased toward neurons that could be studied with rectangular bars (n = 403). As we observed in previous V4 experiments, some neurons would not respond to bar stimuli but were responsive to other shapes (Hinkle and Connor 2001; Pasupathy and Connor 1999). These neurons (n = 49) were studied with angles, ellipses, or circles.

Automated tests were conducted to determine the neuron's optimal stimulus orientation, width, and color, and to verify the position of the RF center. The RF extent was carefully measured to ensure that flashed stimuli with large disparities did not fall outside the RF. This was especially important for neurons near the fovea, which have small RFs. We tested eight or 16 orientations at 22.5 or 11.25° intervals, using flashed or drifting bars or both. We tested four bar widths (1/16, 2/16, 3/16, and 4/16 of the RF diameter). Bar length was usually set to either 0.5 or 2.0 x the estimated RF diameter. RF diameter was estimated from eccentricity based on the previously reported V4 diameter–eccentricity relationship (Gattass et al. 1988). This relationship closely matched the results of our RF measurements using both hand-plotting and automated tests. We tested eight colors: yellow (7.5 cd/m²), cyan (6.6 cd/m²), green (6.0 cd/m²), red (2.8 cd/m²), magenta (2.2 cd/m²), blue (2.1 cd/m²), black (0.1 cd/m²), and white (8.0 cd/m²). For all colors except black, this was the maximum luminance achievable through the two polarized filters and the conducting glass interposed between the screen and the eyes. All stimuli were presented against a gray background (1.1 cd/m²). In most tests a texture of small randomly oriented line segments was applied to the stimulus surface to enhance the stereoscopic depth effect. Like stimulus width and length, texture element size and spacing were scaled with the neuron's estimated RF size. As an example, for a neuron with an eccentricity of 9° and an RF diameter of 6.6°, the texture elements were small gray lines of width 0.04° and length 0.24°, positioned at random orientations and random locations with an average density of seven elements per square degree (Hinkle and Connor 2002). Texture element size and spacing were consistent across the stimulus surface and thus provided no monocular depth cues. Some neurons were tested without texture (n = 121). Disparity-tuning pattern results were similar with and without surface texture, so all the data are presented here together.

Optimal stimuli were presented at horizontal disparities ranging from –1.0° (near, crossed) to +1.0° (far, uncrossed) in 0.2, 0.1, or 0.05° increments. Most neurons were tested with bars drifted back and forth across the RF. Drift speed was 4°/s, and drift path length was 2 x RF diameter. The number of sweeps depended on the RF size, and varied from one to seven sweeps per trial. Some neurons (n = 139) were tested with flashed stimuli. Four or five randomly selected stimuli were flashed during each trial (presentation time, 0.75 s; interstimulus interval, 0.25 s). For both drifting and flashed stimuli, the entire stimulus set was presented as a block within which stimulus order was randomized. The number of block repetitions ranged from three to 20, depending partly on response consistency.

Data analysis

Response rates for drifting and flashed stimuli were calculated by summing action potentials across the entire presentation period and dividing by presentation time. Response rates were averaged across presentations. Response rates that differed from the mean by >3.0 SD were excluded from these calculations as a means of filtering out occasional noise interference during some recording sessions. Except where noted, all analyses were performed without subtracting the spontaneous rate. The spontaneous rate was derived from null stimulus periods interspersed randomly among stimulus presentations. Spontaneous rates were typically low, with a median of <8% of the maximum firing rate.

Tuning patterns were quantified by fitting neural responses with asymmetric Gaussian and Gabor functions. Optimal fits were achieved by minimizing the sum of the squared residuals (least-squares method) using a constrained minimization function (lsqcurvefit, Matlab; The MathWorks, Natick, MA). For all neurons the mean of the residuals was not significantly different from zero for either function (t-test, P < 0.05). This analysis and visual inspection indicated that the tuning patterns have no significant additional structure beyond what the fitted curves capture. Our motivation for using curve fitting is to allow a quantitative characterization of the neural-tuning patterns. We are not claiming that the asymmetric Gaussian function represents the underlying mechanism by which the tuning patterns are constructed.

Across the entire population the asymmetric Gaussian fits were good, accounting for 80% of the response variance (median). Gabor fits accounted for 74% of the response variance. The asymmetric Gaussian functions had the following form

(1)

The two equations describe the two half-Gaussians, which join at the point where stimulus disparity (d) is equal to the Gaussian mean (µ, constrained to be within the ±1° range of tested disparities). The two half-Gaussians have separate background rates (B_L and B_R). The two amplitude parameters (A_L and A_R) are constrained to be equal at µ. Therefore, together, they constitute one free parameter (not two). The amplitudes were also constrained to have the same sign. The SDs of the two half-Gaussians (_L and _R) were constrained to be 0.1°. The Pos function represents half-wave rectification to prohibit negative response rates. In total, the asymmetric Gaussian function has six free parameters.

We derived several descriptive parameters from the fitted asymmetric Gaussian functions. The total response range (difference between the highest and lowest function values within the ±1° domain) was divided into two components: 1) modal-tuning strength (S_Mod) and 2) monotonic-tuning strength (S_Mon). The first component, S_Mod, was defined as the portion of the response range between the Gaussian peak (µ) and the nearer of the two tails. This reflects the magnitude of the local tuning peak (or trough) component of the curve. For a classic tuned excitatory or tuned inhibitory pattern, S_Mod would represent the entire response amplitude range. The second component, S_Mon, was defined as the remaining portion of the response range, between the two tails. It corresponds to the linear or sigmoidal component of the curve. For a classic near- or far-tuning pattern, S_Mon would represent the entire response amplitude range. The position on the fitted curve at the center of the S_Mon range was used to define the inflection point (IP). The disparity value at that position represents where the monotonic-tuning component is centered on the disparity domain. It would correspond to the inflection point of a pure sigmoid tuning pattern. The steepness of the inflection or step portion of the monotonic tuning was characterized by ₁, the SD of the higher-amplitude half-Gaussian. The breadth of modal tuning was characterized by the sum of the two SDs (₁ and ₂).

One measure of the appropriateness of a fitted curve is the percentage of variance accounted for (see above). This measure indicates that the fitted curves accurately reflect the firing rate means. It is also important that the variance in the firing rate be small relative to the features of the fitted curve we are analyzing. Across the population (n = 324), the median SE is 11% of the total tuning strength (S_Mod + S_Mon), which indicates that the variability of the firing rate is indeed small relative to the tuning pattern.

In addition to the asymmetric Gaussian function, we fit the data for each neuron with a Gabor function of the following form

(2)

The Gabor function has six free parameters: R_Mean is the mean height of the curve (also known as vertical offset), A is the amplitude of the Gaussian envelope, µ is the center of the Gaussian envelope, is the SD of the Gaussian envelope, f is the frequency of the sinusoidal component, and is the phase relative to the center of the Gaussian envelope (µ). The Pos function again represents half-wave rectification. The mean parameter (µ) was constrained to be within the tested range of disparities (±1°). The SD parameter () was constrained to be 0.01°. To ensure that the frequency parameter (f) appropriately reflected the spatial scale of the disparity modulation, we adopted the fitting procedure used by Prince et al. (2002a,b). This procedure allows for direct estimation of the frequency. First, we fit the data with a Gabor function, allowing f to vary freely. Second, the Fourier transform of the curve was calculated (by subtracting the mean firing rate and multiplying each data point by a pair of orthogonal sinusoidal functions). Third, the frequency parameter was set to the frequency with the largest amplitude in the Fourier transform. With that parameter fixed, we then refit the data with a Gabor function.

We measured two-dimensional (2D) orientation tuning using drifting or flashed bars sampled at either eight or 16 orientations in 22.5 or 11.25° increments. We fit the orientation data with a standard symmetric Gaussian function (Eq. 3), taking into account the circular nature of the data

(3)

From this fitted curve we calculated the orientation-tuning peak (µ) and tuning width at half-maximum amplitude.

To characterize the disparity-tuning strength of V4 neurons, we used a disparity-tuning index (DTI)

(4)

where R_Max and R_Min represent the maximum and minimum values of the fitted curve.

To facilitate comparison of our V4 results with previous studies of other cortical areas, we also characterized disparity-tuning strength with three additional indices. The binocular interaction index (BII)

(5)

is similar to the DTI except for the +R_min term in the denominator. The disparity modulation index (DMI)

(6)

is similar to the DTI except that spontaneous rate (S) is subtracted from the denominator. The disparity discrimination index (DDI) has the following form

(7)

where SSE is the "sum of squared errors" about the mean responses, N is the total number of stimulus presentations, and M is the number of different disparities tested. The other indices characterize tuning amplitude in relation to maximum and minimum rates, whereas DDI characterizes tuning amplitude in relation to response variability, thus providing a measure of discriminability (for an ideal observer).

We used indices analogous to DTI to measure strength of orientation tuning (orientation-tuning index [OTI])

(8)

and strength of color tuning (color-tuning index [CTI])

(9)

Because luminance was not balanced between colors (see above), we calculated this index separately for three colors in the 6.0–7.5 cd/m² range (green, yellow, cyan) and three colors in the 2.1–2.8 cd/m² range (red, magenta, blue), taking the higher of the two values. This procedure provides only an approximate measure of color tuning because it could overestimate (as a result of the remaining luminance differences within groups) or underestimate (by ignoring response differences between the two color groups).

It has been shown that variance in neuronal firing rates can be correlated with mean firing rate (Tolhurst et al. 1983). For data sets where this is true, the homogeneity of variance assumption underlying regression analysis is violated. Prince et al. (2002a,b) and others have suggested compensating with a square-root transformation of response rates. Therefore we repeated all our regression analyses using the square-root transform. Significance results were the same in all cases. P values reported here are based on the untransformed data.

The data shown in Figs. 7 and 9–11 may not satisfy the normality assumption underlying regression analysis. Therefore we repeated our regression analyses using a randomized correlation test (Manly 1991) and using Spearman's rank correlation. Values of R and P were very similar and significance results were the same in all cases; reported values of R and P are from the nonrandomized Pearson's correlation tests.

View larger version (18K): [in this window] [in a new window]   FIG. 7. A: absolute value of the fitted curve's modal center (|µ|) as a function of receptive field eccentricity. Dotted line indicates the significant positive linear relationship (n = 324, R = 0.19, P = 0.0006). B: monotonic tuning width (1) as a function of receptive field eccentricity. Dotted line indicates the significant positive linear relationship (n = 324, R = 0.18, P = 0.001). C: disparity-tuning index as a function of receptive field eccentricity. Dotted line indicates the significant negative linear relationship (n = 324, R = –0.14, P = 0.01). Four neurons (mean eccentricity = 17.86°) fall outside the plotted ranges.

View larger version (24K): [in this window] [in a new window]   FIG. 9. Comparison of orientation-tuning index (abscissa) with disparity-tuning index (ordinate). Dotted line indicates the significant positive relationship (n = 408, R = 0.23, P << 0.0001). Two histograms show the distribution of neurons along the 2 tuning index dimensions. Arrows indicate means (orientation, 0.71; disparity, 0.50).

View larger version (22K): [in this window] [in a new window]   FIG. 11. Comparison of color-tuning index (abscissa) with disparity-tuning index (ordinate). Dotted line indicates the significant positive relationship (n = 344, R = 0.29, P << 0.0001). Two histograms show the distribution of neurons along the 2 tuning index dimensions. Arrows indicate means (color, 0.63; disparity, 0.51).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

Disparity-tuning function shape

Disparity-sensitive neurons have historically been categorized into four groups based on subjective assessment of disparity-tuning curve shape: 1) tuned excitatory, with a symmetric local peak at a particular disparity; 2) tuned inhibitory, with a symmetric local trough (inverted peak) at a particular disparity; 3) near, responding best to a broad range of crossed disparities in front of the fixation plane, and 4) far, responding best to a broad range of uncrossed disparities behind the fixation plane (Poggio and Fischer 1977). These canonical tuning patterns as well as intermediate patterns have recently been characterized mathematically for neurons in V1 (Prince et al. 2002a,b) and dorsal pathway area MT (DeAngelis and Uka 2003). We applied similar analyses to our sample of ventral pathway area V4 neurons.

Figure 1 shows the normalized mean responses (data points connected by a dotted line) of an individual V4 neuron to an optimal bar stimulus presented at disparities ranging from –1.0 to +1.0° in 0.1° steps. This neuron had an intermediate tuning pattern, consisting of an excitatory peak at +0.12° combined with a preference for far (positive) disparities. This pattern was closely approximated with an asymmetric Gaussian function (composed of two half-Gaussians sharing the same mean and peak amplitude; solid curve), which captures both the local peak and the amplitude difference between the near and far tails, producing a strong correlation between observed and fitted response values (R = 0.99). Similar close fits were obtained for the other neurons with significant disparity sensitivity (mean R = 0.91; n = 324). The close fits obtained with these single-peaked functions demonstrate what was also clear by inspection—that V4 tuning patterns are largely unimodal, with only one derivative zero-crossing (i.e., a single peak or single trough). In contrast, V1 and MT tuning patterns are often multimodal and thus are better characterized by Gabor functions (DeAngelis and Uka 2003; Prince et al. 2002a,b). For our V4 sample, Gabor functions provided a close but slightly less accurate fit in most cases (299/324; mean R = 0.88).

View larger version (18K): [in this window] [in a new window]   FIG. 1. Disparity-tuning pattern for an example neuron. Response rates are normalized to the maximum firing rate (33.0 spikes/s). Disparity was tested over a range from –1.0° (near) to +1.0° (far). Mean response rates (filled circles), linear interpolation (dotted line), and fitted asymmetric Gaussian curve (solid line) are shown. Fitted asymmetric Gaussian parameters include 2 SD parameters (1 and 2) on either side of the peak (µ). Gaussian amplitude is divided into 2 components: modal tuning strength (SMod) and monotonic tuning strength (SMon). Inflection point (IP) is the disparity corresponding to the point on the curve bisecting SMon. Vertical lines on each data point represent the SE.

View larger version (35K): [in this window] [in a new window]   FIG. 2. Distribution of monotonic (SMon, abscissa) vs. modal (SMod, ordinate) tuning strengths for the neural population with significant disparity tuning (n = 324). Example neurons with classic tuning patterns fall at the extremes of the Cartesian axes: excitatory (B), inhibitory (E), near (D), and far (C). Example intermediate patterns include (A), with excitatory and near characteristics, and the Fig. 1 example neuron (red square), with excitatory and far characteristics. Bottom histogram: distribution of monotonic tuning strengths (SMon, abscissa). Right histogram: distribution of modal tuning strengths (SMod, ordinate). Arrows in each histogram indicate the distribution means. Arrows in A, B, and D indicate the response to a monocular stimulus (left eye, filled arrow; right eye, open arrow). Maximum firing rates for these example neurons (A–E) are: 17.4, 30.4, 25.5, 7.2, and 10.3 spikes/s, respectively. Overall population mean firing rate is 19.7 spikes/s. Vertical lines on each data point represent the SE.

There are two clear biases in the Fig. 2 distribution. On the modal tuning dimension (see histogram at right) there is a bias toward excitatory tuning (yellow) and against inhibitory tuning (blue); the mean along this axis (0.16) is significantly >0 (P < 0.0001, two-tailed t-test). This excitatory bias is consistent with the previously reported rarity of inhibitory tuning in V1 and V2 (Poggio and Fischer 1977). On the monotonic tuning dimension (see marginal histogram at bottom), there is a bias toward near tuning (magenta) and against far tuning (green); the mean along this axis (–0.09) is significantly <0 (P < 0.0001, two-tailed t-test). This bias toward stimuli closer than the plane of fixation may have implications for the types of object information emphasized in area V4 (see DISCUSSION).

The transition zone (rising or falling portion) of the monotonic component can be limited in width (for a sigmoidal function) or can extend across the –1.0 to +1.0° range (in the case of a linear function). In Fig. 3 this transition zone width is represented by the SD of the larger-amplitude half-Gaussian (₁, vertical axis), which is plotted against transition zone center (IP, horizontal axis). To separate the near and far tuning distributions, ₁ values are arbitrarily plotted on the upper vertical axis for near tuned neurons and on the lower vertical axis for far tuned neurons. Monotonic tuning strength is indicated by color saturation (magenta for near tuning, green for far tuning). The marginal histograms are summations weighted by tuning strength. For many neurons, especially those with near tuning (e.g., Fig. 2D), the transition is quite steep, which is represented in Fig. 3 by clustering at or near the smallest ₁ value allowed by the fitting procedure (0.1°). Most ₁ values are <1° (weighted mean = 0.47°), indicating a sigmoidal pattern rather than a steady linear progression across the –1.0 to +1.0° range. Transition zone center points (IP) are broadly distributed, mainly in the –0.5 to +0.5° range. The bottom histogram shows that the mode of the IP distribution is slightly shifted toward negative disparities, although the mean is not significantly different from 0. Summed tuning strength is much greater for near neurons (magenta) than for far neurons (green; see histograms).

View larger version (29K): [in this window] [in a new window]   FIG. 3. Distribution of IPs (abscissa) and monotonic tuning widths (1, ordinate). Color axis (right) indicates the strength of monotonic tuning (SMon). Bottom histogram: weighted sum of the monotonic tuning strengths collapsed across the monotonic tuning width dimension. Arrow indicates weighted mean. Left histogram: weighted sum of the monotonic tuning strengths collapsed across inflection point positions. Arrows indicate near and far weighted means. Four neurons with slightly broader monotonic tuning widths (mean 1 = 2.28) and average monotonic tuning strength (mean |SMon| = 0.29) fall outside the plotted range.

View larger version (28K): [in this window] [in a new window]   FIG. 4. Distribution of modal tuning centers (µ, abscissa) vs. modal tuning width (1 + 2, ordinate). Color axis (right) indicates the strength of modal tuning (SMod). Bottom histogram: weighted sum of the modal tuning strengths collapsed across the modal tuning width dimension. Arrow indicates weighted mean. Left histogram: weighted sum of the modal tuning strengths collapsed across modal center positions. Arrows indicate excitatory and inhibitory weighted means. Forty neurons with broad modal tuning width (mean 1 + 2 = 8.74) and very weak modal tuning strength (mean |SMod| = 0.002) fall outside the plotted range.

View larger version (27K): [in this window] [in a new window]   FIG. 5. Tuning patterns averaged and summed across the population. Before summation the mean and spontaneous firing rates were subtracted and each curve was normalized. A: average of the normalized fitted curves for all neurons with significant disparity tuning. B–E: average curve for each of 4 groups. Neurons were assigned to the 4 groups based on the relative strengths of modal and monotonic tuning. Excitatory and inhibitory groups had stronger modal tuning; the near and far groups had stronger monotonic tuning. F: sum (not the average) of the normalized firing rates for each neuron by individual group and, in black, the sum for all the groups combined.

View larger version (15K): [in this window] [in a new window]   FIG. 6. Monotonic tuning strength as a function of the fitted curve's modal center (µ). For neurons with excitatory modal tuning, SMon values are plotted in the negative range for near-tuned neurons and the positive range for far-tuned neurons. This assignment of polarity is reversed for inhibitory neurons so that a positive correlation is predicted for all neurons. To eliminate the effects of shoulder cutoff, we included only neurons for which the modal peak was at least 2 SDs away from either end of the tested disparity range (n = 161). There was a strong and highly significant positive correlation (R = 0.49, P < 0.00001).

Figures 7 and 8 illustrate the relationship between disparity tuning and RF eccentricity. There was a modest but highly significant tendency for neurons with more eccentric RF centers to have modal tuning centers (µ) more offset from the fixation plane (Fig. 7A; R = 0.19, P = 0.0006). The slight tendency of modal tuning width (₁ + ₂) to increase with eccentricity (R = 0.06) was not significant (P = 0.31). This tendency was more pronounced and significant (R = 0.20, P = 0.002) for modal tuning widths 1.0° (n = 241). There was a significant tendency for monotonic tuning width (₁) to increase with eccentricity (Fig. 7B; R = 0.18, P = 0.001). There was no significant relationship between IP (monotonic inflection point) and eccentricity. Overall disparity-tuning strength (modal + monotonic) decreased slightly with increasing eccentricity (Fig. 7C, R = –0.14, P = 0.01). The overall correlation is not a result of the relationship between eccentricity and monotonic tuning strength (|S_Mon|, n = 324, R = 0.003, P = 0.96); rather, it results from the relationship between eccentricity and modal tuning strength (|S_Mod|, n = 324, R = –0.13, P = 0.02). In other words the strength of an excitatory peak (or inhibitory trough) declines as eccentricity increases, but the near/far component remains undiminished. No significant relationship of this kind was observed for orientation-tuning strength (R = –0.07, P = 0.15) or color-tuning strength (R = 0.04, P = 0.50).

View larger version (21K): [in this window] [in a new window]   FIG. 8. Disparity discriminability (ordinate) as a function of disparity (abscissa) and eccentricity (4 panels). Disparity discriminability is defined as the absolute value of the change in a neuron's firing rate per unit change in disparity—that is, the absolute value of the tuning pattern's slope at each point along the disparity axis. Disparity discriminability is averaged across all disparity-significant neurons grouped by eccentricity (n = 324).

Relationship to orientation tuning

One of the major shape dimensions represented in area V4 is edge orientation (Desimone and Schein 1987). The relationship between overall disparity-tuning strength and orientation-tuning strength for all 408 neurons in our sample is depicted in Fig. 9. There is a significant positive correlation (R = 0.23, P << 0.0001). In addition, disparity-tuning strength was negatively correlated with orientation bandwidth (width at half-height; R = –0.19, P < 0.0001). Thus stronger, sharper orientation tuning is associated with stronger disparity tuning. Mean disparity-tuning strength (0.51) was about 70% of mean orientation-tuning strength (0.71). (Because our sample was preselected for orientation sensitivity, the true ratio may be higher.) This argues that disparity-based depth is one of the major stimulus dimensions represented in area V4.

Oriented bar stimuli convey disparity information through the contrast border at their edges. For a vertically oriented bar, this disparity information is conveyed by the long edges of the bar. For a horizontally oriented bar, the disparity information is conveyed by the terminal ends of the bar. As the orientation shifts from vertical to horizontal, the disparity information conveyed by the stimulus contour shifts from the long edges of the bar to the terminal ends of the bar. So for a bar with near horizontal orientation and a length that places the ends of the bar outside the receptive field, the amount of disparity information contained within the RF is low. To enhance the stereoscopic perception of depth, small texture elements were added to the stimulus surface for all orientations (see METHODS). Therefore stimuli at all orientations conveyed disparity information and, across the population, neurons at all orientations showed strong disparity tuning. Nevertheless, stimuli with nonhorizontal orientations conveyed more disparity information and that extra information may be reflected in the overall tuning strength. Figure 10 shows that disparity-tuning strength has a significant positive relationship with the deviation of bar orientation from horizontal (n = 408, R = 0.14, P = 0.004).

View larger version (29K): [in this window] [in a new window]   FIG. 10. Disparity-tuning index as a function of stimulus orientation deviation from horizontal. An abscissa value of 0° indicates horizontal, 90° indicates vertical. Intermediate values correspond to both clockwise and counterclockwise rotations (i.e., 45° corresponds to stimulus orientations of both 45° and 135°). Dotted line indicates the significant positive relationship (n = 408, R = 0.14, P = 0.004). High disparity-tuning index values occur at all orientations, including horizontal.

Color is another major tuning dimension in area V4. Some evidence has suggested that color is processed separately from stereoscopic depth (Hubel and Livingstone 1987). Figure 11 shows, however, that in area V4 color-tuning strength is positively correlated with disparity-tuning strength (n = 344, R = 0.29, P << 0.0001). Mean disparity-tuning strength (0.51) was about 80% of mean color-tuning strength (0.63; this may be an underestimate because of the limited number of colors tested). This argues for the importance of disparity as a tuning dimension in V4.

Sinusoidal periodicity

In our analysis so far we have used an asymmetric Gaussian function to characterize quantitatively the disparity-tuning patterns. Asymmetric Gaussians provide a good fit to the data and allow us to describe key aspects of the tuning patterns. However, it is useful to consider the results of fitting with a Gabor function. Note that the asymmetric Gaussian function and the Gabor function have the same number of free parameters (six). We fit our population of disparity-selective neurons (n = 324) using a Gabor function (see METHODS). Overall, the Gabor functions fit the tuning data well (mean R = 0.88), although not quite as well as the asymmetric Gaussian functions (mean R = 0.91). Asymmetric Gaussian functions fit better than Gabor for 92% (299/324) of the neurons. For a small number of neurons the asymmetric Gaussian fit was significantly better (F-test, 24/324); for none of the neurons was the Gabor fit significantly better (F-test, 0/324).

For the parameters of the fitted Gabor curve to reflect accurately the disparity-tuning properties of the neuron, it is critical that the frequency parameter be adequately constrained. That is why the frequency parameter was set to the principal frequency of the tuning pattern determined by a Fourier transform (see METHODS). Examination of the frequency parameter indicates that most neurons are of a low frequency relative to the tested disparity range. A majority of neurons (69%; 223/324) have a frequency <0.50 cpd (median = 0.40 cpd), indicating that for such neurons there is less than a full cycle within the –1.0 to +1.0° tested range. Furthermore, of the 101 neurons with a frequency >0.50 cpd, 43 have a Gaussian envelope SD () of <0.50. These neurons, despite having the potential for more than one cycle, are limited by the Gaussian envelope to a single cycle (or less) within the tested range. In comparison, the tuning patterns for area V1 (median 0.89 cpd; DeAngelis and Uka 2003; Prince et al. 2002b) are approximately double the frequency of V4 (median 0.47 cpd). The V4 sample used in this comparison (n = 233) is restricted to an eccentricity range ([2–8°]) that overlaps with the previous studies by Prince et al. (2002b) and DeAngelis and Uka (2003). In summary, for a large majority of the V4 neurons (82%; 266/324) there appears to be little sinusoidal periodicity in their disparity-tuning pattern.

Although this analysis suggests that sinusoidal periodicity is not an important factor in V4 disparity tuning, it does not mean that there is no sinusoidal component. It remains possible that if tested beyond the –1.0 to +1.0° range the tuning patterns may contain a sinusoidal component. Indeed, through visual inspection of the tuning patterns one can find examples where the tail does potentially indicate the beginning of a sinusoidal pattern (for example, the left tails of Fig. 2, C and E). Nevertheless, any small sinusoidal component at the tails of the tested range or beyond is unlikely to be of great physiological significance. As the analysis shown in Fig. 8 makes clear, the important range of disparity information conveyed by most neurons is centered around 0° and not the –1.0 or +1.0° tail regions.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Our analysis of disparity tuning function shape in area V4 suggests several trends in the ventral pathway representation of depth. Most V4 tuning functions were best characterized mathematically as a single peak or trough superimposed on a sigmoidal near/far bias (Figs. 1 and 2)—i.e., a combination of modal and monotonic tuning. In contrast, disparity tuning in V1 (Prince et al. 2002a,b) and dorsal pathway area MT (DeAngelis and Uka 2003) is frequently multimodal and therefore requires a sinusoidal component in the fitting function. The smoother tuning functions in V4 suggest that the ventral pathway integrates lower-order disparity signals so as to eliminate side peaks. This would serve to decrease the depth coding ambiguity produced by multiple regions of the disparity domain mapping to the same response rates.

One difference between our findings in V4 and the findings of Uka et al. (2000) in IT is the shift in the percentage of neurons with symmetric tuning patterns (excitatory and inhibitory) relative to the percentage of neurons with asymmetric tuning patterns (near and far). Across our total V4 population we found that 33% of the neurons (151/452) had an excitatory- or inhibitory-tuning pattern. This contrasts sharply with the Uka et al. (2000) finding of about 5% across their IT population. There are potentially significant methodological differences between the studies; for example, the range of disparities tested varied slightly, and Uka et al. (2000) used a "purely subjective" classification procedure. Nevertheless, if this sixfold difference between V4 and IT is supported by future studies, it would represent a dramatic shift in ventral pathway disparity-tuning patterns from the modal-dominated tuning of V1/V2, through the equally weighted modal/monotonic tuning of V4, to the monotonic-dominated tuning of IT.

The varying combinations of modal and monotonic components form a 2D continuum spanning between the extremes of pure modal (excitatory/inhibitory) and pure monotonic (near/far) tuning (Fig. 2). This continuum reveals three clear inhomogeneities. First, in the modal tuning dimension, excitatory patterns far outnumber inhibitory patterns (Figs. 2, 4, and 5), consistent with previous results throughout visual cortex. Second, a subset of neurons shows purely monotonic tuning without a strong modal component; these are the points clustered along the horizontal axis in Fig. 2. There is no comparable clustering along the vertical axis that would correspond to pure modal tuning. This may reflect a trend in the ventral pathway toward monotonic tuning, which would represent a further reduction in coding ambiguity because monotonic functions map only one disparity range to any given response rate.

Third, the distribution is biased along the monotonic dimension toward crossed disparities, i.e., depths nearer than the fixation plane (Fig. 2). We first reported this bias in Hinkle and Connor (2001); the much larger sample in the present study confirms that observation. The weighted distribution of monotonic tuning strengths shows this bias even more clearly (Fig. 3, IP histogram). There are twice as many neurons exhibiting a near tuning pattern (115) as those exhibiting a far tuning pattern (58) resulting in much stronger population response in the near range (Fig. 5; n = 324, binomial probability, P << 0.0001). This 2:1 difference was common across all four hemispheres tested. The distribution of modal tuning peak positions is also significantly shifted toward near disparities (Fig. 4). Watanabe et al. (2002) also reported that the response to near disparities was significantly greater than the response to far disparities across their population (n = 121) and in both monkeys tested. Taken together, these results seem to firmly establish the existence of a near disparity bias in dorsal V4 (lower visual hemifield).

It is interesting to consider whether the near bias is uniform throughout the visual field or has a nonuniform vertical distribution. For example, there might be a bias for near objects at the bottom of the visual field and for far objects at the top of the visual field, consistent with the psychophysical tilt of the horopter (Nakayama et al. 1977). Our data were recorded in dorsal V4 and therefore our RFs were located within the lower visual hemifield, although we could still examine the correlation between near/far tuning strength and RF elevation (y-axis position) within that hemifield. Our data indicate that the near bias is uniform along the vertical axis. There is no significant correlation between near/far tuning strength and elevation (y-axis position; n = 324, R = 0.06, P = 0.32). For comparison, there is also no significant correlation between near/far tuning strength and azimuth (x-axis position; n = 324, R = 0.01, P = 0.80). Therefore our results suggest that the near bias is uniform throughout the visual field.

The presence of a similar bias in ventral V4 (upper visual hemifield) remains to be established through electrophysiology experiments. However, recent fMRI experiments indicate that the strong near bias we found in dorsal V4 is also present in ventral V4. Further analysis of the experiments described in Tsao et al. (2003) strongly indicates that the near bias is present throughout both dorsal and ventral V4 (DY Tsao, personal communication). In IT, Uka et al. (2000) reported an overall bias toward neurons classified as near versus those classified as far, but this bias was not observed in both monkeys tested.

A parallel bias toward near disparities has been reported in the dorsal pathway. In V3d, Adams and Zeki (2001) classified more neurons as near (22) than far (11) (n = 100, binomial probability, P = 0. 018). DeAngelis and Uka (2003) reported more MT disparity-tuning function peaks in the near range, with mean preferred disparity significantly <0 (n = 471, P < 0.0001), consistent with earlier MT studies (Bradley and Andersen 1998; Maunsell and Van Essen 1983). In MST, Gonzalez et al. (2001) classified more neurons as near (86) than far (61) (n = 175, binomial probability, P = 0.016). Roy et al. (1992) also reported more near neurons (98) than far neurons (75) in MST (n = 252, binomial probability, P = 0.034). No bias appears to exist in V1 (Prince et al. 2002a,b). In V2 Poggio observed a preponderance of near tuning patterns over far tuning patterns (personal communication) and von der Heydt et al. (2000) also found more near neurons (25%) than far neurons (12%; n = 162, binomial probability, P 0.003).

The perceptual significance of the near bias is unclear. One possibility is that the near bias reflects a perceptual emphasis on objects closer to or object parts projecting toward the viewer. This could relate to the greater behavioral relevance of nearby stimuli and/or to the greater perceptual importance of convex object parts (Hoffman and Richards 1984), which may also have a neural correlate in the 2D domain (Pasupathy and Connor 1999). Another possibility is that the near bias reflects the perceptual distinction between figures, which tend to be closer, and backgrounds, which tend to be farther away. Consistent with this interpretation, Bradley and Andersen (1998) reported that the bias toward near disparities in MT classical RFs was reversed in suppressive surround regions, suggesting a figure–ground segregation mechanism.

Our analyses allowed us to examine relationships between disparity tuning and other properties. The clearest result is that disparity sensitivity (slope of local response rate changes) is focused near zero disparity for neurons with RFs in the high acuity foveal–parafoveal region. This is consistent with the greater likelihood of stimuli close to the center of gaze being near the plane of fixation (Fig. 8). At increasing RF eccentricities, sensitivity is weaker and more broadly distributed across the –1.0 to +1.0° disparity range. This trend is consistent with several other modest but significant relationships between eccentricity and tuning function parameters: displacement of the modal-tuning peak from zero disparity increases with RF eccentricity (Fig. 7A), monotonic tuning width increases (Fig. 7B), and overall disparity-tuning strength decreases (Fig. 7C). All these trends reflect the emphasis on foveal processing in the ventral pathway and underscore the role of disparity tuning in fine form discrimination.

Disparity-tuning strength was correlated with orientation-tuning strength (Fig. 9), again supporting the connection between disparity and form processing. There was also a weak trend toward stronger disparity tuning in neurons with more vertical orientation-tuning peaks (Fig. 10), but in general disparity sensitivity was strong at all orientation preferences. Disparity tuning was also correlated with color sensitivity, showing that depth and color information are not segregated in area V4 (Fig. 11). Across the total population of neurons the distribution of disparity-tuning strength was centered near 0.5 (i.e., a 2:1 response difference). The means for orientation and color tuning were higher and the distribution modes were near 1.0. However, the distributions overlapped to a large extent, showing that disparity is one of the major stimulus parameters represented in V4.

In our experiments we tested disparity in the –1.0 to +1.0° range. What happens to tuning patterns at larger disparities? As disparity levels increase binocular fusion becomes impossible. At disparity levels exceeding the RF diameter only one monocular image can occupy the RF at a given time. Thus at large disparities, response rates are bound to return to baseline, and the overall tuning pattern across a large disparity range is bound to be modal. However, our discriminability analyses (Fig. 8) suggest that the –0.5 to +0.5° is the most functionally relevant disparity range for V4 depth coding. Within the tested range, our results show that monotonic tuning is prominent.

Hegdé and Van Essen (2005) recently reported that V4 disparity-tuning patterns sometimes differ for bar and RDS stimuli, in contrast to the consistent tuning reported in other visual areas: V1, V2, V3–V3A, and CIP (Gonzalez and Perez 1998; Poggio 1990, 1995; Poggio et al. 1985; Prince et al. 2002a; Taira et al. 2000). Hegdé and Van Essen's finding could be considered to limit the generality of our conclusions. However, we would argue that solid-figure stimuli (e.g., bars) are more relevant for understanding depth coding in V4 because they contain the kind of contour-related disparity information that characterizes most real objects. Moreover, RDS stimuli necessarily include a relative disparity component because they contain adjacent figure and ground regions at contrasting depths. Because earlier visual areas are sensitive to relative disparity (V2; Cumming and Parker 1999; Thomas et al. 2002) and V4 is known to be sensitive to disparity gradients (Hinkle and Connor 2002), it seems plausible that contrasting results with RDS stimuli are explained by the multiple-depth planes they contain. If so, then bars and other solid figure stimuli are more relevant for understanding absolute disparity-tuning profiles without reference to relative disparity effects.

Technical differences between studies make cross-area comparisons difficult. Factors such as the type of stimulus used (RDS vs. solid figure) and the stimulus display time can influence results. Keeping these important methodological differences in mind, we compared disparity tuning across several published studies to get an approximate idea of how disparity-tuning strength varies across areas.

The V4 representation of disparity appears roughly comparable in strength to that in early visual cortex (V1), more anterior ventral pathway cortex (IT), and slightly weaker than in dorsal pathway cortex (MT). Average disparity-tuning strength is compared for these areas in Fig. 12, using the various indices for which average values have been published (BII, DMI, DDI; see METHODS). DTI is the index used elsewhere in this study. The mean BII value across all neurons we studied in area V4 (n = 452) was 0.45 (i.e., greater than a doubling of response rate between peak and trough, which equates to 0.33). This was slightly higher than the mean BII of 0.38 in V1 estimated from Fig. 2A of Prince et al. (2002b; n = 789). The median BII in our sample (0.41) was slightly higher than the median BII of 0.36 in IT reported by Uka et al. (2000; n = 225). The median DDI in our V4 sample was 0.56, close to the median V4 DDI of 0.50 reported by Watanabe et al. (2002; n = 121). Thus disparity-tuning ratios average near 2:1 throughout the ventral pathway.

View larger version (24K): [in this window] [in a new window]   FIG. 12. Mean and median for multiple tuning indices—BII (Eq. 5), DMI (Eq. 6), and DDI (Eq. 7)—are calculated for area V4 to allow for comparison of tuning indices with other cortical areas: V1 (Prince et al. 2002a,b), MT (DeAngelis and Uka 2003), and IT (Uka et al. 2000).