The Berkeley Wavelet Transform (BWT) STRF model used to describe each neuron, and the procedure used to fit the model. The BWT models a neuron as a sum of half-wave rectified Gabor-like wavelet channels. For each neuron, the BWT of each image in the stimulus set was first calculated, and each wavelet channel was half-wave rectified. Boosting was then used to calculate a weighting function, h, that quantifies the importance of each wavelet in describing the responses of the neuron. The STRF of each neuron is represented as a weighted, rectified BWT pyramid. When each estimated STRF is used to filter an image, it provides a prediction of the corresponding neuron's response to that image.

Dendrogram summarizing cluster analysis of the STRFs from the combined sample of 46 V1 and 96 V2 neurons. Lengths of horizontal lines quantify the difference between pairs of STRFs. Bars on right identify neurons from V1 (white) and V2 (black). There are two significantly separated major clusters (Clusters A and B, indicated by the pale red and blue regions; p < 0.001, randomization test; the p = 0.01 criterion is indicated by t). Cluster A contains 43% (41/96) of the V2 neurons in the sample and 78% (36/46) of the V1 neurons. Cluster A has two significant sub-clusters, A1 and A2 (p = 0.043; randomization test). Neurons in sub-cluster A1 have conventional excitatory tuning and minimal suppressive tuning, whereas neurons in sub-cluster A2 are weakly tuned for orientation. Taken together, neurons in cluster A have functional properties consistent with those reported previously in V1. Cluster B contains 57% (55/96) of the V2 neurons and only 22% (10/46) of the V1 neurons. Cluster B also has two significant (p < 0.001; randomization test) sub-clusters. Neurons in both sub-clusters have conventional excitatory tuning, but also show strong suppressive tuning which is not observed in V1. This suppressive tuning is strongest in sub-cluster B2.

Excitation index, E, quantifying the relative strength of excitatory versus suppressive tuning in each neuron. (Inset) E is calculated as a contrast ratio between the summed excitatory (h⁺) and suppressive (h^-) weights assigned to the wavelets in each STRF. a. Histogram of E across the sample of 46 V1 neurons. The median (0.73) and the cell shown in Fig. 5a are marked. b. Histogram of E for the sample of 96 V2 neurons. The median (0.28) and the cell shown in Fig. 5b are marked. The median value of E is significantly lower in V2 than in V1 (p = 0.0042; Kruskal-Wallis one-way ANOVA; df = 141), indicating that suppression is substantially stronger in V2 than in V1. The V2 distribution is significantly non-unimodal at p = 0.002 (Hartigan's dip test using 1000 bootstraps). The V1 distribution is not significantly non-unimodal (p = 0.70). c. Distribution of E for all neurons, broken down into the clusters identified in Fig. 4. Cluster B (pink, orange) contains neurons with significantly stronger tuned suppression than cluster A (cyan, purple; p ≪ 0.001, Welch's t-test, df = 121). The complete V1-V2 distribution is significantly non-unimodal at p = 0.005 (Hartigan's dip test using 1000 bootstraps). d. Breakdown of Excitation index by animal, for V1 neurons. e. Breakdown of Excitation index by animal for V2 neurons. No significant differences in the Excitation index were found for different animals in this study. e. Suppressive tuning in V2 is not caused merely by surround suppression. The Rectified BWT STRF for each V2 neuron was analyzed to determine the relative contributions of the CRF and nCRF to suppressive tuning. The suppressive coefficients in each STRF were classified according to whether they were in the CRF (central square of the STRF at scale level 2; see Fig. 1b) or nCRF (surrounding squares). The coefficients in the CRF and nCRF were summed separately, and a contrast index was calculated: C = (Σh^CRF-Σh^nCRF)/(Σh^CRF+Σh^nCRF). The distribution of C across the sample of 96 V2 neurons is shown here. A value of 1 would indicate that tuned suppression came purely from the CRF; a value of -1 would indicate that tuned suppression came purely from the nCRF. For most V2 neurons, the suppressive coefficients are mainly found in the CRF (values greater than 0). This indicates that the tuned suppression we observe in V2 cannot accurately be described as surround suppression.

Measures of possible bias in the Excitation index. a. Scattergram showing log of the summed negative coefficients in each Rectified BWT STRF against log of the summed positive coefficients. V2 neurons (filled circles) tend to have stronger negative coefficients than V1 neurons (open circles), regardless of the overall strength of the coefficients. This indicates that the difference between V1 and V2 is not merely an artifact of overall coefficient strength (as might be expected if the model simply provided a worse fit to V2 neurons than to V1 neurons). b. Scattergram showing Excitation index against prediction correlation coefficient (Pearson's r). If Excitation index were an artifact of fit quality, we would expect to see a strong relationship between these two variables. In fact, we find that there is no strong relationship, indicating that the difference between Excitation index in V1 and V2 is not merely an artifact of fit quality.

STRF of one V2 neuron that pools across spatial frequency. The excitatory STRF of this neuron (top four rows) is tuned for horizontal orientation at several spatial scales (and so several spatial frequencies), both within and beyond the CRF. A mechanism that pools information at a single orientation, but across spatial position and spatial scale, may confer selectivity for both real and illusory contours in natural images.

Wavelet decomposition of stimuli. a. Random sequences of natural scenes were presented, centered on the classical receptive field (CRF) of each neuron and covering approximately 3 times the CRF diameter, r. b. Each stimulus frame was decomposed using a wavelet pyramid (the Berkeley Wavelet Transform or BWT), containing odd- and even-symmetric wavelets, over a region covering 3r × 3r. To demonstrate the range of spatial scales of the BWT analysis, this panel presents examples of these wavelets at 3 spatial scales (f, 3f, 9f). c. Two complete scales of the wavelet pyramid. The wavelets cover 4 orientations (0°, 90°, 180°, 270°) at 3 scales (f, 3f, 9f; although only the lower two scales are shown here), and tile the x-y plane.

Wavelet classification for cluster analysis. Each STRF was estimated at multiple lags, from 0 to 167ms, resulting in a 1458-dimensional time-varying vector. For cluster analysis, dimensionality of the STRF was reduced to a single length-25 vector. a. First, the peak neural response latency, t′, was found based on the standard deviation of the STRF. All STRF latencies from 0 to t′+16.7ms were considered transient; those from t′+33.3ms onward were considered sustained. b. The STRF weights were used to construct a STRF with separate transient and sustained components. c. Each wavelet in these two STRFs was classified according to its relationship with the strongest excitatory wavelet in the STRF. This classification described the wavelets along several dimensions: transient/sustained, excitatory/suppressive, on/off/cross orientation, and location within the classical receptive field (CRF) or outside (nCRF). Also, the strongest excitatory wavelet was taken separately, producing a length-25 vector providing an efficient representation of each neuron's STRF. The use of relative orientation tuning (on/off/cross) means that the vectors are independent of the orientation preference of each neuron. Spatial frequency information is collapsed, so that the vectors are also independent of the spatial frequency preference of each neuron.

Representative STRFs for neurons in areas V1 and V2. These images are constructed by taking each BWT wavelet, multiplying it by its weighting in the Rectified BWT STRF, and summing the result. Excitatory (positive; shown here in red-green) and suppressive (negative; blue-yellow) coefficients are shown separately. a. STRF for a typical V1 neuron from cluster A (sub-cluster A1). The STRF is a spatial map of the tuning of the neuron (only the peak temporal response latency is shown). It is separated into excitatory (red-green; top 4×4 panels) and suppressive components (blue-yellow; bottom 4×4 panels). These are further subdivided by phase (rows) and orientation (columns). Each panel represents a region encompassing three times the size of the neuron's classical receptive field (CRF). (Top) The strongest excitatory wavelet is tuned for vertical orientation and intermediate spatial frequency, at all phases. (Bottom) Several weak suppressive wavelets tuned for horizontal orientation are located both within and outside the CRF. This is a classical V1 neuron with weak cross-orientation suppression. b. STRF for a typical V2 neuron from cluster B (sub-cluster B2). Structure of panel same as in Fig. 5a. (Top) The excitatory tuning of this neuron is similar to that shown in Fig. 5a. (Bottom) Suppression in this STRF is strong in multiple wavelet channels. Although the excitatory STRF of this neuron is compatible with the classical Gabor model of V1, the suppressive STRF will confer complex feature selectivity quite different from that found in V1.

Mean excitatory and suppressive tuning for orientation energy of the sub-clusters of the combined V1/V2 sample. For each neuron, orientation tuning was estimated by summing separately the positive and negative wavelet coefficients at each orientation (0°, 45° or 90°) in the corresponding STRF. Orientation tuning was then averaged across the neurons in each sub-cluster (A1, A2, B1, B2, as in Fig. 4). Neurons in sub-clusters A1 and A2 are dominated by tuning at 0° (i.e. parallel to the strongest excitatory wavelet in their STRFs), and show very little suppressive tuning. Neurons in sub-clusters B1 and B2 have excitatory tuning similar to those in sub-clusters A1 and A2, but they also have strong suppressive tuning. Suppression is strongest in sub-cluster B2. Error bars give the standard error of the mean.

Functional consequences of suppressive tuning in V1 and V2. a. The STRF of a typical V1 neuron from cluster A1, decomposed into separate excitatory and suppressive hyper-channels. The x-axis quantifies the response of the excitatory hyper-channel and the y-axis the suppressive hyper-channel. Red, yellow and blue regions identify the images that elicit strong, medium and no responses from the neuron, respectively. Each hyper-channel was used to filter 40,000 natural images. A subset of the images is plotted according to the responses of the hyper-channels. The excitatory hyper-channel of this neuron (x-axis) is vertically tuned, and so responds to any image containing vertical structure (observe the variety of images in rightmost columns). The suppressive hyper-channel (y-axis) is weakly tuned for horizontal structure. This channel suppresses responses to images that contain horizontal structure, so the neuron responds more strongly to isolated vertical edges (red region) than to complex images containing vertical and horizontal structure (yellow region). However, these suppressive effects are weak in V1 and in the weakly suppressed neurons in V2. b. Similar decomposition of the STRF of a typical strongly-suppressed V2 neuron. The excitatory hyper-channel (x-axis) of this neuron is also tuned for vertical structure, and the suppressive hyper-channel (y-axis) is tuned for horizontal structure. In this neuron, the suppressive hyper-channel is much stronger than the one shown in Fig. 9a. Therefore, many more images produce only weak or zero responses (compare the number of images in the blue and white regions in Figs. 9a and 9b). A smaller proportion of images are in the yellow and red regions in Fig. 9b than in Fig. 9a, indicating that tuned suppression has increased the selectivity of the V2 neuron relatively to the weakly-suppressed neuron in Fig. 9a.