Abstract

Single neurons in primate V2 and cat A18 exhibit identical orientation tuning for sinewave grating and illusory contour stimuli. This cue invariance is also manifested in similar orientation maps to these stimuli, but in V1/A17 the illusory contour maps appear reversed. We hypothesized that this map reversal depends upon the spatial frequencies of the inducers in the illusory contours, relative to the spatial selectivities of these brain areas. We employed intrinsic signal optical imaging to measure orientation maps in cat A17/18 to illusory contours with inducers at spatial frequencies from 0.15 to 1.6 cpd. A17 illusory contour maps were indeed reversed compared with grating-driven maps for inducer spatial frequencies <1.3 cpd, whereas A18 maps were invariant. Simulations based on known neurophysiology demonstrated that map reversal can arise from linear filtering, and map invariance can be explained by a nonlinear (filter-rectify-filter) mechanism. The simulation also correctly predicted that A17 could show invariant maps when the inducer spatial frequency is sufficiently high (1.6 cpd), and that A18 maps could reverse at lower inducer frequencies (0.18 cpd). Thus, the map reversal or invariance to illusory contours depends critically on the relationship of the inducer spatial frequencies to the spatial filtering properties of neurons in each brain area.

Introduction

Many neurons in early visual cortex show consistent orientation selectivity for both luminance-defined gratings or bars (Hubel and Wiesel 1965), and also for contours defined by nonluminance cues such as contrast or texture variations. For example, von der Heydt et al. (1984) demonstrated that neurons in primate V2 could respond with similar preferred orientation to luminance gratings (Fig. 1A) and to illusory contours (Fig. 1B) defined by abutting gratings. Zhou and Baker (1993) showed that neurons in cat A17 and A18 can respond with similar orientation selectivity to luminance gratings and to contrast envelopes. Findings like these (Peterhans and von der Heydt 1989; Grosof et al. 1993; Leventhal et al. 1998; Mareschal and Baker 1998a; Song and Baker 2006) showed that such neurons respond to both luminance- and nonluminance-defined stimuli with very similar orientation preferences. Because boundaries between occluding surfaces in natural images often contain spatially coincident changes in both luminance and nonluminance cues (Johnson and Baker 2004), the “form-cue invariance” (Albright 1992; Geesaman and Andersen 1996) of neuronal orientation selectivity might be a critical feature of early visual neurons in supporting figure-ground segregation and object perception.

Figure 1.

Schematic illustration of cortical orientation map invariance and map reversal. (A) Luminance-defined sinewave grating stimulus, with spatial frequency of SF_lum, and vertical or horizontal orientation. (B) Abutting grating illusory contour stimulus, composed of low spatial frequency squarewave grating envelope (SF_envelope) which modulates the phase of a high spatial frequency carrier grating (SF_carrier). (C) Cartoon example of optically imaged orientation difference response in cat A18 (or primate V2) to a pair of orthogonally oriented sinusoidal gratings (A). (D) Vertical/horizontal abutting grating contours produce a similar response pattern as in (C)—that is, the orientation map is invariant to the type of stimulus. (E) Example of orientation difference response in cat A17 (or primate V1) to sinusoidal gratings. (F) Orientation difference map to a comparable set of abutting grating contours (B) shows a reversed pattern—dark areas in F correspond to the bright areas in E and vice versa.

Figure 1.

Schematic illustration of cortical orientation map invariance and map reversal. (A) Luminance-defined sinewave grating stimulus, with spatial frequency of SF_lum, and vertical or horizontal orientation. (B) Abutting grating illusory contour stimulus, composed of low spatial frequency squarewave grating envelope (SF_envelope) which modulates the phase of a high spatial frequency carrier grating (SF_carrier). (C) Cartoon example of optically imaged orientation difference response in cat A18 (or primate V2) to a pair of orthogonally oriented sinusoidal gratings (A). (D) Vertical/horizontal abutting grating contours produce a similar response pattern as in (C)—that is, the orientation map is invariant to the type of stimulus. (E) Example of orientation difference response in cat A17 (or primate V1) to sinusoidal gratings. (F) Orientation difference map to a comparable set of abutting grating contours (B) shows a reversed pattern—dark areas in F correspond to the bright areas in E and vice versa.

Figure 2.

Examples of invariant and reversed orientation maps. Data are from 2 animals to the same sinewave grating and abutting grating contour stimuli (insets in the middle). (A) Difference response to orthogonal sinusoidal gratings (0.18 cpd) in A18. (B) Difference response to orthogonal abutting grating contours from the same cortex as in (A); carrier spatial frequency = 0.75 cpd, envelope spatial frequency = 0.08 cpd. Superimposed rectangles and circles are shown to facilitate spatial comparison of corresponding image regions. Note that the response pattern is similar to that in (A). (C, D) Difference response to same stimuli as in (A) and (B), imaged simultaneously in A17/18 (dashed line indicates A17/A18 border). Again A18 (lower-left part of image) shows an invariant orientation map compared with the grating response in (C). However, the pattern in A17 (upper-right part of image) appears reversed compared with the response in the same area to sinewave gratings in (C).

Figure 2.

Examples of invariant and reversed orientation maps. Data are from 2 animals to the same sinewave grating and abutting grating contour stimuli (insets in the middle). (A) Difference response to orthogonal sinusoidal gratings (0.18 cpd) in A18. (B) Difference response to orthogonal abutting grating contours from the same cortex as in (A); carrier spatial frequency = 0.75 cpd, envelope spatial frequency = 0.08 cpd. Superimposed rectangles and circles are shown to facilitate spatial comparison of corresponding image regions. Note that the response pattern is similar to that in (A). (C, D) Difference response to same stimuli as in (A) and (B), imaged simultaneously in A17/18 (dashed line indicates A17/A18 border). Again A18 (lower-left part of image) shows an invariant orientation map compared with the grating response in (C). However, the pattern in A17 (upper-right part of image) appears reversed compared with the response in the same area to sinewave gratings in (C).

Consistent with the above single unit electrophysiology, optically measured neuron population responses to luminance and illusory contours displayed similar patterns in cat A18 (Sheth et al. 1996; Zhan and Baker 2006) and in primate V2 (Ramsden et al. 2001). If the response in V2/A18 shows a pattern as cartooned in Figure 1C to sinewave gratings, a similar response pattern (Fig. 1D) would be activated by abutting grating contours. However, orientation maps in primate V1 for the 2 kinds of stimulus appeared spatially reversed (Ramsden et al. 2001); such a reversal in cat A17 is also suggested in the data of Sheth et al. (1996), and will be explicitly demonstrated below in this study. This map reversal in V1/A17 (Fig. 1E,F) suggests a 90° difference in neuronal orientation tuning to the 2 types of visual stimulus. Note that the vertical and horizontal abutting grating contours used in the experiments of Ramsden et al. (2001) were formed by identical oblique inducing gratings, so the map reversal cannot be accounted for simply in terms of selectivity for carrier orientation.

The observed map reversal challenges the role of V1/A17 for “form-cue-invariance,” which has been supported by single unit neurophysiology studies of responses to stimuli defined by a variety of other nonluminance cues (Zhou and Baker 1993, 1996; Chaudhuri and Albright 1997; Leventhal et al. 1998; Zhou et al. 2001). To reconcile this issue, it is crucial to reveal the underlying mechanisms leading to the map reversal. Sheth et al. (1996) suggested that the reversal arises from anatomical differences in the map organizations in the 2 areas—that is, that a greater proportion of the cortical surface in A17 was devoted to luminance responses rather than to cue-invariant mechanisms. Ramsden et al. (2001) accounted for the V1 map reversal in terms of a model involving feedback from V2.

We surmised that the map reversal might arise as a consequence of 2 elementary properties of neurons within each brain area. Firstly, early visual neurons exhibit spatial selectivity, which can be understood in terms of linear spatial filtering (e.g., De Valois et al. 1979). Secondly, neurons in V2/A18 are selective for lower spatial frequencies than those in V1/A17 (Movshon et al. 1978; De Valois et al. 1982; Foster et al. 1985).

Early visual neurons can respond selectively to narrow bands of Fourier energy (De Valois et al. 1979) in a way that can be modeled as linear spatiotemporal filtering (Movshon et al. 1978). However, the linear filtering model can only explain neural responses to visual contours defined by differences in net luminance at an appropriate spatial scale (i.e., stimuli whose Fourier energy falls in the neuron's orientation/spatial frequency passband). A nonlinear filter-rectifier-filter (F-R-F) model, on the other hand, is required to account for orientation-selective responses to nonluminance-defined contours (Zhou and Baker 1993, 1996; Wilson et al. 1992). A combination of these 2 models provides a dual mechanism for early visual processing (for review, see Baker 1999).

Analyzing the Fourier power spectra of abutting grating contours and their relation to the neurons' spatial frequency selectivity (Movshon et al. 1978; Issa et al. 2000), we hypothesized that the map reversal may critically depend on the spatial frequency of abutting gratings, which form the contours. To examine this possibility we employed optical imaging of cortical responses from cat areas 17 and 18 to sinewave gratings and to abutting grating contours with carriers at different spatial frequencies. For appropriate stimulus parameters, we found similar phenomena as in previous studies—invariant cortical maps to these 2 types of stimuli in A18, and reversed maps in A17. Our simulation of the spatial and orientation selectivity for neurons in both areas indicate that the linear and F-R-F filtering mechanisms can account for the results. The model further predicted a systematic relation between map reversal, spatial frequency of carriers in abutting grating contours, and neurons' spatial frequency passbands. Thus, the map reversal is not a characteristic property of specific brain areas, but instead critically depends on the relationship between the power spectra of the visual stimuli in relation to the passbands of neuron populations in those areas.

Materials and Methods

Animal Preparation and Maintenance

Young adult cats (n = 9, 1.5–3.5 kg) were used in these experiments, in accordance with the guidelines and policies of the Canadian Council on Animal Care. Procedures for anesthesia, surgery, and paralysis (approved by the Animal Care Committee of McGill University) were conventional and have been described previously (Mareschal and Baker 1999). A 7 × 10 mm craniotomy (H-C P0/L3) exposed the crown of the lateral gyrus containing the midline representation of the A17/18 border (Tusa et al. 1979; Ohki et al. 2000). In some cases, the craniotomy was shifted either anteriorly (A3/L4) or posteriorly (P3/L1) to focus on either A18 or A17, respectively. The dura was reflected, and a plastic chamber was attached to the skull with dental acrylic, filled with 2% agarose, and sealed with a cover slip. The eyes were focused at a distance of 28 or 57 cm, using appropriate spectacle lenses and artificial pupils. The animal's physiological state and anesthesia level were constantly monitored (electroencephalography, electrocardiography, expired CO2, temperature, heart rate) and maintained at appropriate levels.

Visual Stimuli

Visual stimuli were computer generated (Macintosh G4) using custom software based on the Psychophysics Toolbox (Brainard 1997). The stimulus display CRT monitor (NEC FP1350, 20″, 1024 × 768 pixels, 85 Hz) was gamma-corrected at a mean luminance of 28 cd/m2. Luminance contours consisted of vertical or horizontal drifting sinewave gratings (Fig. 1A), with spatial frequency equal to SF_lum indicated in the figure. Abutting grating contours (“illusory contours,” Fig. 1B) were constructed from drifting low spatial frequency squarewave grating envelopes (vertical or horizontal, spatial frequency of SF_envelope), which modulated the phase of carriers (here, oblique gratings) at various spatial frequencies (0.18–1.6 cpd—SF_carrier in Fig. 1B). Orientations of carrier and envelope were either perpendicular or differing by ±45°. Two to 8 equally spaced orientations in a 0–180° range were used to measure orientation-selective responses. The spatial and temporal frequencies of the luminance and abutting grating contours were 0.18 cpd and 2 Hz (1 or 4 Hz) to chart the full-orientation map in both A17 and A18. Although these parameters are optimal for A18 (Movshon et al. 1978), the same stimuli also activated A17 sufficiently to provide orientation maps. High spatial frequency sinewave gratings of 0.50 (or 0.75) cpd, which are ineffective in A18, were used to map the A17/18 border (Bonhoeffer et al. 1995; Sheth et al. 1996; Ohki et al. 2000). Although this kind of measurement correlates well with the anatomy (Orban et al. 1980; Sheth et al. 1996), in some cases it was also confirmed by imaging the representation of the ipsilateral visual field (Payne 1990; Ohki et al. 2000). Unless specified, the envelope spatial frequency (SF_envelope) of abutting grating contours was fixed at 0.18 cpd. The Michelson contrast of all these stimuli was set at 70%.

Optical Imaging Data Acquisition and Processing

Intrinsic signal optical imaging (Bonhoeffer and Grinvald 1996) was used to measure the cortical response to visual stimuli. Our imaging system (Zhan et al. 2005) consisted of a 720-nm illuminator, a CCD camera (2/3″ format, 30 fps, 56 dB; Cohu 4812, CA), a macro zoom lens (f = 18–108 mm, F/2.5), or tandem-lens (Ratzlaff and Grinvald 1991) formed by 2 Nikor lenses (f = 50 mm, F/1.2), a digital video processor (12-bit precision, 640 × 480 pixels; DVP-32, InstruTech, NY), and a host computer (PIII, 800 MHz). Raw image data were online spatiotemporally binned to 320 × 240 pixels at about 2 fps, and streamed to a fast RAID disk. Each recording trial lasted about 35 s: 6.4-s prestimulus baseline, 8.5-s stimulus duration, 3.7-s poststimulus period, and the remaining intertrial interval of about 16 s (Zhan et al. 2005). Different stimuli in an experiment were presented in random order, typically for 20–40 repetitions.

Our image data processing procedures were largely conventional (Bonhoeffer and Grinvald 1996). Raw image data were first averaged across 20–40 repetitions, then normalized by a pure blank (average of prestimulus images) to correct for uneven illumination. Visually driven optical responses were time averaged over a window of about 3–11 s following the stimulus onset (Zhan et al. 2005) and results for orthogonal conditions were subtracted to yield raw difference images. For some quantitative analysis, a conservative filtering (Gaussian kernel, σL = 54 μm, σH = 810 μm) was necessary to suppress the impact of noise at low spatiotemporal frequencies (e.g., vasomotion) and at high frequencies (e.g., from the CCD camera) while avoiding signal distortion. In these cases blood vessels were removed and interpolated prior to the filtering (Zhan et al. 2005; Zhan and Baker 2006). However, pixels within these interpolated blood vessel regions were always excluded from later quantitative analysis. A vectorial summation algorithm (Bonhoeffer and Grinvald 1996) was used to calculate full-orientation maps.

Intrinsic optical signals are known to be vulnerable to noise originating from diverse sources (Bonhoeffer and Grinvald 1996; Mayhew et al. 1996; Sirovich and Kaplan 2002). We therefore applied a statistical significance test to evaluate the optical signal reliability based on the trial by trial difference maps (Zhan and Baker 2006). Theoretically, each pixel has zero-mean in the difference maps across repetitions (i.e., μ = 0) unless it is reliably activated by the visual stimuli. Thus, a pixelwise t-test [forumla] was conducted to examine this hypothesis, where forumlai is the mean intensity and Si the standard deviation of the i-th pixel across the n repetitions. Only pixels with t-scores indicating significant activation (P < 0.1) were used for quantitative analysis. We chose to use this relatively high P-value to avoid unduly excluding excessive numbers of pixels in the raw difference images, which were not subjected to any spatial smoothing or blood vessel removal.

A polygonal region of interest (ROI) was manually defined, based on the responsiveness of difference images and their t-score maps. “Pixels of interest” (POIs) consisted of those within the ROI, but excluding those with low t-scores or within blood vessel regions. The standard deviation of these pixel values was used to quantify the amplitude of the visually driven optical response (Schuett et al. 2001; Zhan et al. 2005). Similarity between differential orientation maps was indicated by the correlation coefficient between their POIs.

We used “response profile analysis” (Basole et al. 2003) to extract the orientation best represented by orientation difference maps. Our procedures for this analysis have been described in detail (Zhan and Baker 2006); briefly, there were 4 steps: 1) based on a full-orientation map measured using luminance gratings (e.g., Fig. 3C), the cortical surface was segregated into iso-orientation subdomains (e.g., colored contours in Fig. 4A,B); 2) the pixel values within these subdomains for each orientation were averaged; 3) the resulting average responses were plotted as a function of their corresponding orientations to form a “response profile” (e.g., Fig. 4C); 4) the response profile was fit with one full cycle of a cosine function, O(θ)=B×cos[2π(θ+θp)/180], where O is the optical response strength as a function of θ, the iso-orientation value (0–165° in 15° steps). Thus, each response profile could be parameterized with 2 fitted parameters: B, the response amplitude and θp, the orientation best represented by the optical response pattern.

Figure 3.

Mapping the A17/18 border. (A) Orientation map to sinusoidal gratings at high spatial frequency (0.75 cpd) optimal for A17. Stimuli consisted of 4 orientations spanning 0–180°, in which the grating was drifted back and forth in opposite directions. Same cortex as in Figure 2C,D. (B) Response amplitude map corresponding to (A). (C) Orientation map to sinusoidal gratings at low spatial frequency (0.18 cpd) optimal for A18. (D) ROIs for A17 and A18, based on orientation maps (A, C) and response amplitude map (B). Dashed contours in (B) and (D) represent the A17/A18 border.

Figure 3.

Mapping the A17/18 border. (A) Orientation map to sinusoidal gratings at high spatial frequency (0.75 cpd) optimal for A17. Stimuli consisted of 4 orientations spanning 0–180°, in which the grating was drifted back and forth in opposite directions. Same cortex as in Figure 2C,D. (B) Response amplitude map corresponding to (A). (C) Orientation map to sinusoidal gratings at low spatial frequency (0.18 cpd) optimal for A18. (D) ROIs for A17 and A18, based on orientation maps (A, C) and response amplitude map (B). Dashed contours in (B) and (D) represent the A17/A18 border.

Figure 4.

Invariant difference response to abutting grating contours in A18. (A) Difference map in A18 to vertical–horizontal sinusoidal gratings (right insets, S1 and S2). (B) Difference map to left versus right oblique gratings (right insets, S3 and S4). (C) Response profiles indicate that 0/90 (cyan) and 45/135 (purple) orientations are encoded in the difference maps in A and B, respectively. (D, E) Difference map to vertical–horizontal abutting grating contours. Stimuli in D (S5 and S6) and E (S7 and S8) differ only in carrier orientation—left or right oblique, respectively. (F) Corresponding profiles for D (blue) and E (red) indicate that both optical maps encode the vertical–horizontal contours independently of the carrier orientations. Superimposed color iso-orientation contours were derived from A18 ROI of Figure 3B, which was recorded from the same cortex, for response profile analysis.

Figure 4.

Invariant difference response to abutting grating contours in A18. (A) Difference map in A18 to vertical–horizontal sinusoidal gratings (right insets, S1 and S2). (B) Difference map to left versus right oblique gratings (right insets, S3 and S4). (C) Response profiles indicate that 0/90 (cyan) and 45/135 (purple) orientations are encoded in the difference maps in A and B, respectively. (D, E) Difference map to vertical–horizontal abutting grating contours. Stimuli in D (S5 and S6) and E (S7 and S8) differ only in carrier orientation—left or right oblique, respectively. (F) Corresponding profiles for D (blue) and E (red) indicate that both optical maps encode the vertical–horizontal contours independently of the carrier orientations. Superimposed color iso-orientation contours were derived from A18 ROI of Figure 3B, which was recorded from the same cortex, for response profile analysis.

Model and Simulation

We simulated 2 visual processing mechanisms to explore the possible roles of different carrier spatial frequencies in population responses to the abutting grating contours: a conventional linear filter model (Movshon et al. 1978) of responses to luminance-defined stimuli, and an F-R-F model (Wilson et al. 1992; Kingdom et al. 2003) which can extract the envelope orientation of second-order stimuli such as abutting gratings (Wilson 1999; Song and Baker 2006).

We modeled the spatial frequency selectivity for each cortical area (Fig. 6A) with a Gaussian function of log-scaled spatial frequencies: RS (f) = exp{-[log2(f)-log2(fp)]2/(2σf)}, where f is the stimulus spatial frequency, fp the average preferred frequency for neurons in a specific cortical area, and σf the half-bandwidth in octaves. Following Movshon et al. (1978) and Issa et al. (2000), fp = 0.18 cpd for A18, and fp = 0.80 for A17; σf = 0.56 octaves for A18 and σf = 0.69 octaves for A17.

Figure 5.

“Reversed” difference response to abutting grating contours in A17. (A, B) Orientation maps in A17 to the same stimuli as for Figure 4A,B. (C) Response profiles correctly indicate the stimulus orientations, as in Figure 4C. (D, E) Orientation maps to the same abutting grating contours (vertical vs. horizontal) as for Figure 4D and E. Although the carrier orientations are orthogonal, the 2 maps look similar. Compared with the response to the vertical–horizontal sinewave grating in (A), these orientation maps appear reversed—bright regions in (D) and (E) correspond roughly to the dark regions in A. (F) Response profiles for (D) and (E) do not show invariance as in Figure 4F, but instead are shifted away from 0/90, with direction of shift dependent on carrier orientation.

Figure 5.

“Reversed” difference response to abutting grating contours in A17. (A, B) Orientation maps in A17 to the same stimuli as for Figure 4A,B. (C) Response profiles correctly indicate the stimulus orientations, as in Figure 4C. (D, E) Orientation maps to the same abutting grating contours (vertical vs. horizontal) as for Figure 4D and E. Although the carrier orientations are orthogonal, the 2 maps look similar. Compared with the response to the vertical–horizontal sinewave grating in (A), these orientation maps appear reversed—bright regions in (D) and (E) correspond roughly to the dark regions in A. (F) Response profiles for (D) and (E) do not show invariance as in Figure 4F, but instead are shifted away from 0/90, with direction of shift dependent on carrier orientation.

Figure 6.

Simulation of cue-invariant orientation difference response in A18. (A) Model probability distribution function of spatial frequency preferences of cat A17 and A18 neurons, on log-frequency axis. (B, C) Model orientation and spatial frequency selectivity of A17/A18 neurons, illustrated in Fourier space (linear frequency axes). (D) Model orientation preference function for A17/18 neurons. (E, F) Abutting grating contours (left column, S5 and S6) used in Figures 4D and 5D, and their corresponding Fourier power spectra (right column) which are distributed outside of A18 neurons' spatial frequency passband (circle). Accordingly, the energy versus orientation profiles are uniformly zero (I); and their difference is also zero (J). (G, H) Filtered and rectified version (left column, S5′ and S6′) of the stimuli in (E) and (F), and their corresponding Fourier power spectra (right column). Note these demodulated images recover the orientations and spatial scales of the abutting grating contours, and the power spectra of the contours now falls within the passband of A18 neurons. (K) Fourier energy profiles for demodulated responses (S5′ and S6′), showing narrow bands of energy at 0° (E5′, dark vertical lines) and at 90° (E6′, light vertical lines). Convolution with neural orientation filter (D) gives smoothed energy profiles (dark- and light-dashed curves). (L) Orientation difference response profiles. Energy differences appear only in narrow bands; after convolution with orientation filter, simulated neural response profile (dark-dashed curve) shows peak at 0 and trough at 90. The differential optical response profile (solid curve), simulated by inverting the neural response profile, is similar to those in Figure 4F.

Figure 6.

Simulation of cue-invariant orientation difference response in A18. (A) Model probability distribution function of spatial frequency preferences of cat A17 and A18 neurons, on log-frequency axis. (B, C) Model orientation and spatial frequency selectivity of A17/A18 neurons, illustrated in Fourier space (linear frequency axes). (D) Model orientation preference function for A17/18 neurons. (E, F) Abutting grating contours (left column, S5 and S6) used in Figures 4D and 5D, and their corresponding Fourier power spectra (right column) which are distributed outside of A18 neurons' spatial frequency passband (circle). Accordingly, the energy versus orientation profiles are uniformly zero (I); and their difference is also zero (J). (G, H) Filtered and rectified version (left column, S5′ and S6′) of the stimuli in (E) and (F), and their corresponding Fourier power spectra (right column). Note these demodulated images recover the orientations and spatial scales of the abutting grating contours, and the power spectra of the contours now falls within the passband of A18 neurons. (K) Fourier energy profiles for demodulated responses (S5′ and S6′), showing narrow bands of energy at 0° (E5′, dark vertical lines) and at 90° (E6′, light vertical lines). Convolution with neural orientation filter (D) gives smoothed energy profiles (dark- and light-dashed curves). (L) Orientation difference response profiles. Energy differences appear only in narrow bands; after convolution with orientation filter, simulated neural response profile (dark-dashed curve) shows peak at 0 and trough at 90. The differential optical response profile (solid curve), simulated by inverting the neural response profile, is similar to those in Figure 4F.

Orientation tuning was modeled as a wrapped Gaussian: RO(θ) = exp(−(θ−θp)2/(2σo2)), where θ is the stimulus orientation, θp the preferred orientation, and σo = 35°, the average orientation tuning width (Maldonado et al. 1997; Rao et al. 1997). To a given stimulus of specific spatial frequency and orientation, the neuronal response is determined by the compound effects of spatial frequency selectivity RS(f) and orientation preference RO(θ).

To simulate the neuron population response based on conventional linear (Fourier energy) filtering, we Fourier-transformed the visual input and multiplied it with the Fourier-domain spatial frequency filter of each area. For example, Figure 6B,C represents the Fourier-domain spatial frequency filters for A17 and A18, respectively, where the orientations are color mapped; the second columns in Figures 6E–H and 7A–D describe the Fourier spectra of the corresponding visual stimuli shown at their left.

Because the orientation tuning of early visual neurons is independent of the spatial frequency at which it is measured (Webster and De Valois 1985; Issa et al. 2000; Mazer et al. 2002; and our own data, e.g., Fig. 3), the filtered Fourier energy at each orientation was pooled irrespective of the spatial frequency, and plotted as an “energy profile” function of orientation, evaluated at each of 180 orientations. For comparability with our optical imaging analysis: 1) the difference Fourier spectra for the 2 orthogonal contour conditions was calculated, and a difference “energy profile” was obtained; 2) because each neuron can be activated only by Fourier energy falling within its orientation passband, the energy at each orientation in the difference Fourier spectra for the 2 orthogonal contour conditions was circularly convolved with the orientation preference model (RO(θ), shown in Fig. 6D); 3) the summation of responses in step 2 gives the simulated neuronal response profile; 4) because the optically imaged signal is inverted (i.e., reduced at locations of stronger neuronal activity), the optically measured response profile is inverted with respect to the neuronal response profile.

To simulate the F-R-F mechanism, the abutting grating contours were first spatially filtered with quadrature filters at the carrier spatial frequency and orientation, and then the output was squared and summed. After this filtering and rectification (first 2 stages of the F-R-F model), we obtained the filtered and rectified version of the abutting grating contours (e.g. Fig. 6G,H). The second filter in the F-R-F model was simulated as described above to obtain the orientation “energy profile” and “response profile.” Although an extended bank of filters at a range of spatial frequencies and orientations would provide a more biologically realistic simulation for the first stage of filtering, this simplified version is sufficient for our purposes because each pair of orthogonal abutting grating contours were formed by carriers of only one spatial frequency and orientation.

Results

Invariance and Reversal of the Cortical Orientation Maps

Luminance contours (sinewave gratings) and abutting grating contours were employed to map orientation-selective neuron population responses. Sinewave gratings (top insets in Fig. 2) had a spatial frequency of 0.18 cpd, which is in the optimal range for cat A18 neurons but also able to activate A17 (Movshon et al. 1978; Issa et al. 2000). Abutting grating contours (Fig. 2, bottom insets) were formed by modulating the phase of high-frequency stationary carrier gratings (0.75 cpd) with a drifting periodic squarewave envelope (0.08 cpd). Figure 2A,B shows optical difference responses measured from A18 (centered around H-C A3/L4; Tusa et al. 1979) to the 2 types of stimuli. These difference images (unfiltered, blood vessels removed) reveal typical dark/bright regions representing vertical/horizontal orientations of the visual stimulus pairs. The similarity between the optical response patterns in Figure 2A,B, visualized with the aid of superimposed symbols to facilitate comparison, is consistent with previous findings that A18 neurons have similar orientation preference to gratings and illusory contours (von der Heydt et al. 1984; Song and Baker 2006) and the uniform distribution of illusory contour responsive neurons in cat A18 (Zhan and Baker 2006).

Figure 2C,D shows optical difference responses along the A17/18 border (H-C P0/L3—Tusa et al. 1979; Ohki et al. 2000) to the same stimulus configuration as for Figure 2A,B. These 2 images show similar patterns in the lower-left part of the imaged region, but a reversed pattern in the upper right. Based on the anatomy of the cat visual system (Tusa et al. 1979), retinotopic mapping (Bonhoeffer et al. 1995; Ohki et al. 2000), and neurophysiology (Movshon et al. 1978; Zhou and Baker 1996; Mareschal and Baker 1999), the upper right and lower-left patches correspond to A17 and A18, respectively (see below for mapping procedure). Qualitatively, these findings are consistent with optically recorded maps in cat A17/18 (Sheth et al. 1996) and macaque V1/V2 (Ramsden et al. 2001), in that A18/V2 shows invariant orientation maps (Zhan and Baker 2006), whereas A17/V1 exhibits reversed maps to these 2 types of visual stimuli.

Quantification of Map Invariance and Reversal

To examine whether the map invariance/reversal is cortical area specific, we mapped the A17/18 border to enable separate quantification of response from each area. We employed response profile analysis (Basole et al. 2003; Zhan and Baker 2006) to quantify the similarity between optical response patterns, and their relation to the stimulus orientations.

A stereotaxically guided rectangular craniotomy parallel to the midline exposed the crown of the lateral gyrus containing the lower hemifield representations of Areas 17 and 18, through which the A17/18 border (midline representation) typically traces a diagonal locus (Tusa et al. 1979; Issa et al. 2000). To map the border between these areas we exploited their difference in spatial frequency selectivity—the A17 neuron population is optimally responsive to a spatial frequency of about 0.80 cpd, whereas A18 neurons are poorly responsive to stimuli at spatial frequencies higher than about 0.50 cpd (Movshon et al. 1978; Ferster and Jagadeesh 1991). This difference has been validated by studies combining electrophysiology, anatomy, and visuotopic representation (Orban et al. 1980; Payne 1990; Bonhoeffer et al. 1995; Ohki et al. 2000).

Figure 3A shows an orientation preference map measured with sinewave gratings at a high optimal frequency for A17 (0.75 cpd). The upper-right (medial-posterior) part of the image exhibits clear pinwheel patterns characteristic of well-formed orientation maps (e.g., Bonhoeffer and Grinvald 1996), whereas the lower-left (lateral-anterior) part does not. The corresponding response strength map (Fig. 3B) confirms that only the upper-right part gives a strong response. At a lower spatial frequency of 0.18 cpd, which should optimally activate A18 neurons (but also drive A17—Movshon et al. 1978; Ferster and Jagadeesh 1991), a clear pinwheel response appears throughout the entirety of the exposed cortex (Fig. 3C), again corroborated by the quite uniform response strength map (Fig. 3D). Comparing the 2 orientation maps (Fig. 3A,C), we see that A17 can be readily activated by low spatial frequency stimuli, with almost identical upper-right parts of the maps. Guided by the response strength map to the high spatial frequency stimuli (Fig. 3B), we define the A17/18 border with a dashed line (Fig. 3B,D) and ROIs for A17 and A18 (overlaid polygons in Fig. 3D) to be used in subsequent quantitative analysis.

The independence of the orientation preference from the spatial frequency at which it is measured (Fig. 3; Webster and De Valois 1985; Issa et al. 2000; Mazer et al. 2002) and the response of both areas to the same low spatial frequency sinewave gratings allow us to use the orientation map measured with a single low spatial frequency stimulus (e.g., Fig. 3C) as a template to quantify the orientation encoded by the neuron population using response profile analysis (see Materials and Methods; Basole et al. 2003; Zhan and Baker 2006). Figure 4A,B shows the difference maps for A18 (ROI defined as in Fig. 3D) to orthogonal pairs of sinewave gratings (insets at right). The superimposed color contours delineate iso-orientation preferences (derived from the full-orientation map, Fig. 3C)—pixels within each subdomain (bounded by adjacent contours) prefer similar orientations. The response profile for the vertical–horizontal response (Fig. 4C, cyan curve) clearly shows a peak at 90° and a trough at 0°, whereas the response to the oblique stimuli (Fig. 4B) yields a profile (Fig. 4C, purple curve) showing a trough–peak at [45, 135] degrees. Thus, the profile analysis extracts the stimulus orientations represented by the neuron population response.

The difference map to the vertical–horizontal pair of abutting grating contours (Fig. 4D) shows a dark–bright pattern which resembles that produced by the correspondingly oriented sinewave gratings (Fig. 4A). This impression is confirmed by its response profile (Fig. 4F, blue), which also has a trough–peak at [0, 90] degrees. Another pair of abutting grating contours, whose carrier orientation is orthogonal to those in Figure 4D, activated a similar difference map (Fig. 4E). The corresponding response profile also shows a trough–peak at [0, 90] degrees (Fig. 4F, red), demonstrating that the response depends on the envelope and not the carrier orientation. This “form-cue invariance” of the orientation maps was observed in each of the n = 7 animals tested in this way. These results are consistent with previous neurophysiology and optical imaging studies (von der Heydt et al. 1984; Sheth et al. 1996; Ramsden et al. 2001; Song and Baker 2006; Zhan and Baker 2006), which reported that A18 or V2 neuron populations prefer similar orientations of luminance and abutting grating contours.

Area 17 optical responses to the same stimuli were also recorded, often in the same data sets as A18 responses (e.g., ROI defined in Fig. 3D). The difference maps for sinewave grating responses (Fig. 5A,B) again yield response profiles that correctly recover the stimulus orientations (Fig. 5C)—that is, a trough–peak of [0, 90] for vertical–horizontal (cyan) and [45, 135] for the oblique pair (purple). However, unlike the A18 results, the difference-map responses to vertical–horizontal abutting grating contours (Fig. 5D) show a quite different pattern from that produced by correspondingly oriented sinewave gratings (Fig. 5A). Indeed, the 2 patterns appear somewhat like the reverse of one another, consistent with previous observations in cat A17 (Sheth et al. 1996) and macaque V1 (Ramsden et al. 2001). This impression is borne out by the response profile (Fig. 5F, blue) which shows a trough–peak shifted to about [60, 0] degrees, instead of [0, 90] degrees for the vertical–horizontal contours. The difference map to the second pair of vertical–horizontal abutting grating contours (Fig. 5E) is also seemingly almost reversed from that to luminance gratings. The corresponding response profile (Fig. 5F, red) is also significantly shifted, but in the opposite direction, with a trough–peak at about [120, 0] degrees. Similar near-reversals of orientation maps for the 2 kinds of stimuli were found in each of the n = 6 cases examined.

Thus, the results in Figures 4 and 5 quantitatively confirm that A17 and A18 respond quite differently to the same abutting grating contours, with an almost reversed pattern of response. The area 18 difference maps reflect the abutting grating contour orientations, and the representation is invariant to the carrier (component) orientations (Sheth et al. 1996; Ramsden et al. 2000; Zhan and Baker 2006). However, the area 17 results show abutting grating contour responses, which qualitatively appear almost reversed (Sheth et al. 1996; Ramsden et al. 2001) from those to correspondingly oriented luminance stimuli. The response profile analysis on the difference maps (Fig. 5D–F) reveals that: 1) the maps are approximately but not exactly reversed; 2) the response pattern is carrier orientation dependent; and 3) the maps do not represent the carrier orientations.

Models and Simulation

A prominent difference between early visual cortex areas of the cat is that A17 neurons have smaller receptive fields and are selective for higher spatial frequencies than neurons in A18 (Movshon et al. 1978; Ferster and Jagadeesh 1991; Issa et al. 2000); an analogous distinction holds for primate V1 versus V2, at finer spatial scales (De Valois et al. 1982; Foster et al. 1985). Because the abutting grating contour stimuli are constructed from a high spatial frequency carrier whose phase changes at a low spatial frequency, it seemed possible that the orientation map reversal in A17 might be understood in terms of linear spatial filtering at the scale of the carrier. Although these studies employed oblique carriers that were identical in the stimulus pairs used for difference imaging (Sheth et al. 1996; Ramsden et al. 2000), the stimuli may nevertheless have contained differential Fourier components that could drive orientational responses. Orientation invariance, on the other hand, requires a fundamentally nonlinear demodulation to extract the envelope pattern. To assess these ideas we implemented neurophysiologically based models of 2 types of cortical processing: a linear filtering model to extract Fourier energy (Movshon et al. 1978; De Valois and De Valois 1988), and a F-R-F model to simulate response to second-order stimuli (Zhou and Baker 1996; Wilson et al. 1992) to examine the orientation energy captured by neuron populations in these brain areas.

We modeled the cat A18 spatial frequency passband as a log-Gaussian spanning ∼0.07–0.5 cpd (Movshon et al. 1978; Issa et al. 2000) with an optimum of 0.18 cpd (Fig. 6A, dotted curve). Because we found that optical response in cat A17 could be readily activated by luminance gratings at 0.18 cpd (Fig. 3D), we extended the A17 neuronal passband (∼0.25–2.0 cpd, Movshon et al. 1978) to ∼0.15–2.0 cpd, with a peak at 0.80 cpd (Fig. 6A, dot-dashed curve)—the need for this adjustment is probably due to our A17 optical recordings being near the A17/18 “transition zone” within which neurons exhibit intermediate spatial selectivities between those of the 2 brain areas (Issa et al. 2000; Ohki et al. 2000). When these spatial frequency selectivites are expanded (isotropically) in the orientation dimension, they define Fourier-domain passbands as shown in Figure 6B,C, where brightness represents the probability density of neurons' preferred spatial frequencies (now on a linear axis) and colors indicate the orientation preference.

Linear filtering was implemented by an inner product of the filter selectivity (Fig. 6B,C) and the Fourier amplitude spectra of the visual stimulus. The visual stimuli (Fig. 6E,F, left) used in our experiments (carrier 0.75 cpd, envelope 0.15 cpd, and carrier orientation 45°) are transformed into the Fourier domain (Fig. 6E,F, right). Because the Fourier energy falls beyond the A18 passband (black circles), no Fourier energy component can activate the linear filtering model of the A18 response. Therefore, the “energy profile” for linear filter response to each of these stimuli is uniformly zero (Fig. 6I), and their difference is also zero (Fig. 6J).

Because cortical neurons show narrow tuning to carrier spatial frequency (e.g., Zhou and Baker 1996; Song and Baker 2006), we model the F-R-F response by first convolving the stimuli with a Gabor filter whose peak response is at the stimulus carrier frequency, and then rectifying (see Materials and Methods). This operation recovers the contour orientations (Fig. 6G,H, left), whose Fourier energy (Fig. 6G,H, right) now falls within the A18 passband (black circle). In the corresponding orientation response profiles, this Fourier energy produces narrow bands at 0° and 90° (dark and light lines, for stimuli in Fig. 6G,H, respectively). The neural population response is simulated by convolving the stimulus spectra with a Gaussian whose width corresponds to the neuronal orientation bandwidth (Fig. 6D), yielding neural response profiles (Fig. 6K) whose magnitudes peak at 0° (dark-dashed curve) and 90° (light-dashed curve), respectively. The neural difference profile (Fig. 6L, dashed curve) has a peak at 0° and trough at 90°. To simulate the optical response profile, the neural profile was inverted because increased activation gives a darker image in our analysis (Zhan et al. 2005)—the result (Fig. 6L, solid curve) is comparable with that observed in our A18 experiments (Fig. 4F). Orthogonal carrier orientations produced identical results (not shown—see Zhan and Baker 2006), because the nonlinear processing (rectification) recovers the envelope orientations in the abutting grating contours irrespective of the carrier orientation. Thus, the F-R-F model can account for the cue-invariant orientation responses observed in Figure 4D–F, and as reported elsewhere (Sheth et al. 1996; Ramsden et al. 2000; Zhan and Baker 2006).

Figure 7 illustrates how these same stimuli, which activate invariant orientation maps in A18 (Fig. 4D,E), result in reversed orientation maps in A17 (Fig. 5D,E). These stimuli (Fig. 7A–D, left) contain Fourier energy within the grating passband of cat A17 neurons (Fig. 7A–D, right, annular region between 2 black circles superimposed on the Fourier spectra). Because this stimulus energy is well below the A17 carrier frequency passbands for second-order stimuli (∼1.5–3.0 cpd, Zhou and Baker 1996), the model F-R-F responses are negligible and are not illustrated. The energy profiles of the first pair of stimuli (Fig. 7E, thin vertical dark and light lines) show complex structure due to the rich harmonic content of the stimuli. These stimulus energy profiles are convolved with the neuronal orientation passband (Fig. 6D) to yield neural response profiles (dotted curves) which both peak near the carrier orientation of 45°. These curves are not identical, however, and have a significant difference profile (Fig. 7F, dotted curve) showing a peak near 90°. The simulated optical response profile (Fig. 7F, solid curve) shows a trough near 90°, which is similar to our experimental result for A17 (Fig. 5F, blue). The simulated response to the stimulus pair with orthogonal carrier orientation (Fig. 7C,D) is shown similarly in Figure 7G,H. Here the simulated optical response profile (Fig. 7H, solid curve) again has a trough near 90°, comparable with the experimental result (Fig. 5F, red). Thus, the model illustrates how linear filtering properties of A17 can extract Fourier energy from these stimuli, to produce reversed orientation maps for abutting grating stimuli.

Figure 7.

Simulation of reversed orientation difference responses in A17. (AD) Stimuli (left column) used in the experiments in Figures 4 and 5, and their corresponding Fourier power spectra (right column) with superimposed circles demarcating spatial frequency passband of A17 neurons. (E) Response profiles of stimulus energy captured by A17 neurons, for left-oblique carriers (A, B). Fine dark and light vertical lines indicate Fourier energy as function of orientation, evaluated at 180 orientations—note fine structure due to harmonic content of stimulus spectra. Convolution with neural orientation filter (Fig. 6D) gives simulated neural response profiles (dotted curves), showing response mainly distributed around the carrier orientation of 45°. (F) Fine vertical lines indicate energy differences at each orientation, which yield neural response profile (dotted curve), and simulated optical response (solid curve) with trough near 90°. As compared with those in (E), neural response profile has been scaled up (×6) for illustration on the same ordinate scale. (G) Same as (E), but for stimuli with left oblique carriers (C, D). Most energy is distributed near the carrier orientation of 135°. (H) Same as (F), but for stimuli in (C) and (D). Simulated optical response (solid curve) again shows trough near 90°.

Figure 7.

Simulation of reversed orientation difference responses in A17. (AD) Stimuli (left column) used in the experiments in Figures 4 and 5, and their corresponding Fourier power spectra (right column) with superimposed circles demarcating spatial frequency passband of A17 neurons. (E) Response profiles of stimulus energy captured by A17 neurons, for left-oblique carriers (A, B). Fine dark and light vertical lines indicate Fourier energy as function of orientation, evaluated at 180 orientations—note fine structure due to harmonic content of stimulus spectra. Convolution with neural orientation filter (Fig. 6D) gives simulated neural response profiles (dotted curves), showing response mainly distributed around the carrier orientation of 45°. (F) Fine vertical lines indicate energy differences at each orientation, which yield neural response profile (dotted curve), and simulated optical response (solid curve) with trough near 90°. As compared with those in (E), neural response profile has been scaled up (×6) for illustration on the same ordinate scale. (G) Same as (E), but for stimuli with left oblique carriers (C, D). Most energy is distributed near the carrier orientation of 135°. (H) Same as (F), but for stimuli in (C) and (D). Simulated optical response (solid curve) again shows trough near 90°.

Figure 8.

Map invariance in A17 and reversal in A18 to abutting grating contours. (A) Orientation difference map in A18 to vertical–horizontal sinusoidal gratings (0.18 cpd) shows typical dark–bright interlaced pattern (same cortex as Fig. 2A). Superimposed color iso-orientation contours derived from separate data set for grating response. (B) Orientation difference map to vertical–horizontal abutting grating contours in same cortex as (A), with a low carrier spatial frequency (0.18 cpd), showing optical response pattern almost reversed compared with that in (A). (C) Response profiles for A18 orientation response, from results in (A) and (B). Note abutting grating response profile (blue, scaled up ×8 for illustration) is reversed from grating profile (cyan), indicating map reversal. (D) Difference map in A17 (same cortex as Fig. 2C,D, near A17/18 border) to vertical–horizontal sinusoidal gratings (0.18 cpd), showing typical dark–bright interlaced pattern. Superimposed color iso-orientation contours derived from separate data set for grating response. (E) Difference map to vertical–horizontal abutting grating contours (right insets) with high carrier spatial frequency at 1.66 cpd. Note similar dark–bright pattern as in (D). (F) Same as (E), but with lower carrier spatial frequency at 0.75 cpd. Note almost reversed dark–light pattern compared with that in (D). (G) Response profiles for orientation response of A17 pixels in results of (D)–(F); abutting grating responses are scaled up (×10) for illustration. Note abutting grating profile is similar to that for gratings (cyan) at higher carrier spatial frequency (black), but is nearly reversed at lower frequency (blue).

Figure 8.

Map invariance in A17 and reversal in A18 to abutting grating contours. (A) Orientation difference map in A18 to vertical–horizontal sinusoidal gratings (0.18 cpd) shows typical dark–bright interlaced pattern (same cortex as Fig. 2A). Superimposed color iso-orientation contours derived from separate data set for grating response. (B) Orientation difference map to vertical–horizontal abutting grating contours in same cortex as (A), with a low carrier spatial frequency (0.18 cpd), showing optical response pattern almost reversed compared with that in (A). (C) Response profiles for A18 orientation response, from results in (A) and (B). Note abutting grating response profile (blue, scaled up ×8 for illustration) is reversed from grating profile (cyan), indicating map reversal. (D) Difference map in A17 (same cortex as Fig. 2C,D, near A17/18 border) to vertical–horizontal sinusoidal gratings (0.18 cpd), showing typical dark–bright interlaced pattern. Superimposed color iso-orientation contours derived from separate data set for grating response. (E) Difference map to vertical–horizontal abutting grating contours (right insets) with high carrier spatial frequency at 1.66 cpd. Note similar dark–bright pattern as in (D). (F) Same as (E), but with lower carrier spatial frequency at 0.75 cpd. Note almost reversed dark–light pattern compared with that in (D). (G) Response profiles for orientation response of A17 pixels in results of (D)–(F); abutting grating responses are scaled up (×10) for illustration. Note abutting grating profile is similar to that for gratings (cyan) at higher carrier spatial frequency (black), but is nearly reversed at lower frequency (blue).

Model Predictions

To account for the orientation map invariance in A18 and map reversal in A17 to the same stimuli, we employed a model using parallel processing by a linear filter and by a nonlinear F-R-F cascade, in which the filters represent passbands of neural populations of the respective brain areas rather than those of single neurons. When the Fourier energy of the stimulus is within the linear filtering (grating) passband for a specific neuron population, the linear mechanism takes effect; if the stimulus energy falls within the early-stage F-R-F passband, then that mechanism is engaged; note that for any given neuron the 2 passbands are nonoverlapping (Mareschal and Baker 1999; Song and Baker 2006), so a given stimulus will drive one or the other but not both.

Because the formation of abutting grating contours involves modulation of the carrier phase, the Fourier energy of the low frequency envelopes is shifted to high frequencies near that of the carrier (Fig. 6; Zhan and Baker 2006). Thus, the Fourier energy of these stimuli depends critically on the carrier spatial frequency, and this parameter plays a pivotal role in determining the model's response in either brain area. The model therefore predicts that 1) if we decrease the carrier spatial frequency sufficiently to bring the Fourier energy into A18's linear filter passband, then this area could show reversed orientation maps to abutting gratings vs. luminance stimuli; 2) conversely, if we increase the carrier spatial frequency sufficiently to shift the Fourier energy outside the linear filter passband of A17, and into its early-stage F-R-F passband, this area should now show cue-invariant maps. To test these predictions we measured response patterns in cat A17 and A18 to abutting grating contours with different carrier spatial frequencies, here illustrated in the same recording experiments as those in Figure 2.

The first model prediction is that very low carrier spatial frequencies can lead to orientation map reversals in A18. For reference the A18 optical response to luminance gratings at 0.18 cpd is shown in Figure 8A (same as Fig. 2A), but with superimposed iso-orientation contours (measured from a separate data set); Figure 8B shows the response of the same cortex to abutting gratings whose carrier was 0.18 cpd, sufficiently low to bring the Fourier energy within the luminance passband of A18 neurons. A comparison between the 2 maps shows that the dark regions in Figure 8A correspond to bright regions in Figure 8B, and vice versa—that is, a map reversal, in contrast to the cue-invariant result for A18 in Figure 2A. These results are quantified as response profiles in Figure 8C, demonstrating that the abutting grating response (blue) is reversed from that to gratings (cyan). Similar results were found in each of the n = 3 animals tested.

The converse prediction of the model is that a sufficiently high carrier spatial frequency can produce a cue-invariant response in A17. We tested this prediction in the same cortex as in Figure 2C,D, using an ROI for A17 pixels—for reference Figure 8D shows the orientation map to conventional sinusoidal gratings, with superimposed iso-orientation contours constructed from a separate data set. Figure 8E shows responses of the same cortex to abutting grating contours with a high carrier spatial frequency (1.6 cpd), well above that used in Figure 2C. This spatial frequency falls in the carrier passbands of A17 neurons (Zhou and Baker 1996; Song and Baker 2006), and has an appropriate ratio of carrier to envelope frequency (Mareschal and Baker 1998b). Note that the A17 dark/light pattern reveals very similar orientation domains as those driven by luminance gratings (Fig. 8D), as confirmed in the response profiles (cyan and black) in Figure 8G—that is, an invariant map, the converse of the result in Figure 2D. However, at a lower carrier spatial frequency (0.75 cpd), the same cortex now shows a reversed map (Fig. 8F; blue in Fig. 8G). Similar results were observed in each of the 3 animals tested in this way. Thus, the same region of A17 can exhibit a cue-invariant orientation map at a sufficiently high carrier spatial frequency, or a reversed map at a lower carrier spatial frequency.

Discussion

Our results have shown that either A17 or A18 can exhibit cue invariance or reversal of orientation maps, depending on the spatial scale of the stimulus. These results can be understood in terms of a model based on previous neurophysiology, in which either linear or nonlinear (F-R-F) mechanisms are engaged, dependent upon the carrier spatial frequency.

Using a single set of abutting grating contours we observed orientation map invariance in A18 and reversal in A17, similar to that described previously for primate V2 and V1. By manipulating the carrier spatial frequency, we were able to control the invariance or reversal of orientation maps in each of the 2 areas. Modeling and simulation demonstrated that the map reversal can be understood in terms of linear filtering mechanisms (Fourier energy), whereas invariance can be accounted for by nonlinear filtering, with their relative prevalence determined critically by the carrier spatial frequency. The dependence of map reversal and invariance on spatial scale provides compelling evidence for the coexistence of dual mechanisms in the early visual cortex—linear (Movshon et al. 1978; De Valois et al. 1979; Foster et al. 1985; Basole et al. 2003) and nonlinear (Baker 1999; Wilson 1999) energy filtering.

The Neural Basis for Map Invariance and Reversal

We observed cortical map invariance in A18 (Fig. 4) and reversal in A17 (Fig. 5) to the same set of abutting grating contours, consistent with earlier optical imaging results in cat A17/18 (Sheth et al. 1996) and macaque monkey V1/V2 (Ramsden et al. 2001). The different response patterns of these 2 areas might be related to the intrinsic properties of neurons within them, such as their hierarchical level in the visual system and spatiotemporal selectivity. Although there are differences in the pattern of geniculocortical projection in cats and primates (Payne and Peters 2002; Sincich and Horton 2005), in both species the 2 areas differ from one another in their spatial frequency selectivity. Movshon et al. (1978) and Issa et al. (2000) found that on average cat A17 prefers ca 5-fold higher spatial frequency than A18; De Valois et al. (1982) and Foster et al. (1985) demonstrated a similar ratio between spatial frequency preference in macaque monkey V1 and V2 neurons. From a computational point of view, early visual neurons can be considered as spatiotemporal filters and characterized in the Fourier domain (e.g., Movshon et al. 1978; De Valois et al. 1979). We thus inferred that spatial frequency could play a critical role in determining the cortical map reversal and invariance, in a similar manner in both cats and primates.

Earlier results (Sheth et al. 1996) had indeed shown that greater spacing of the inducer lines (i.e., lower carrier spatial frequency) could induce a partial reversal of the A17 orientation map, but their result was ambiguous due to the use of inducing lines (carriers), which were kept orthogonal to the contours (envelopes). In this study, as in Ramsden et al. (2001), identical oblique carriers were used, so that differential optical signals could not be driven by the carrier orientation per se. Nevertheless, this maneuver does not necessarily preclude differential signals from Fourier components arising along the inducing line terminations.

Our simulation of neuronal orientation and spatial frequency selectivity demonstrated that the same set of abutting grating contours could act differently in the 2 cortical areas (Figs. 6 and 7). If the Fourier energy of a visual stimulus is outside the neurons' passband (Fig. 6E,F), a linear filter model gives no response (Fig. 6I,J), which contradicts the experimental results (Fig. 4). Based on previous neurophysiology (Zhou and Baker 1996), we augment the model with a parallel path consisting of an F-R-F cascade. Our simulation results (Fig. 6G,H,K,L) correspond well with the experimentally observed cue-invariant orientation responses. However, as shown in Figure 7, the same visual stimuli provide differential Fourier energy within the A17 passband, which can activate neurons via a linear filtering mechanism. Closer inspection of the Fourier spectra (Fig. 7A–D, second column) reveals that the contour orientation is represented with multiple harmonics, which are introduced by the sharp alternation of carrier phases. Clearly, the Fourier energy of an abutting grating contour stimulus is not a simple summation of those of its carrier and envelope. Thus, a simple subtraction (Sheth et al. 1996; Ramsden et al. 2001) of the optical responses to a pair of such stimuli does not necessarily provide the net response to the contours. Instead, the difference energy peaks at an orientation close to 90°, as indicated by the energy profile in Figure 7F and H, and leads to a map reversal like that observed in A17. By manipulating the carrier spatial frequency to be higher than the passband of A17 (Fig. 8E) or lower than the passband of A18 (Fig. 8B), the orientation map can be cue-invariant in A17 and reversed in A18. Based on envelope and carrier spatial frequencies used in Ramsden et al. (2001) and neuronal spatial frequency selectivity in macaques (De Valois et al. 1982; Foster et al. 1985), our simulation would also similarly predict the map invariance in V2 and reversal in V1 observed in their data; we have confirmed that this result holds also for the line-carriers used in their stimuli. We conclude that carrier spatial frequency plays a critical role in determining the visual processing mechanism for abutting grating contours.

Implications

The use of simple visual stimuli such as luminance gratings has proven useful in characterizing early visual processing, but does not necessarily lead straightforwardly to prediction of responses to more complex, broadband stimuli. One example from neuroimaging of visual cortex was the response to moving patterns of short line segments (Basole et al. 2003), which produced differential maps for line orientation or direction of motion which were not simply related to those from drifting gratings. In that case the results could, however, be understood in terms of stimulus Fourier energy and the spatiotemporal bandwidths of cortical neurons (Basole et al. 2003), which in principle could be modeled based on grating responses. A quite different example is the response to second-order stimuli, formed by modulation of nonluminance (texture) properties such as contrast or phase, which are not predictable at all from simple grating responses (Zhan and Baker 2006). Our results here indicate that abutting grating contours can activate either first- or second-order mechanisms, depending on stimulus energy distribution and the neurons' spatial frequency passband. Our preliminary data also show that other complex visual stimuli, for example, contrast envelopes (Zhou and Baker 1993), can also activate invariant (Zhan and Baker 2006) or reversed maps (data not shown) depending on carrier spatial frequency.

Both of the above examples highlight the importance of understanding visual processing through models of neural mechanisms, rather than in terms of categorical descriptions of stimuli. Models based on signal filtering, either linear filters or filter-rectify-filter cascades, have proven especially powerful metaphors for understanding neuronal stimulus selectivity—such models respond to a broad range of patterns which have energy falling with specified frequency ranges, regardless of the stimulus “features” from which those Fourier components originate. The F-R-F model applies the principle twice, at 2 very different spatial scales, providing it with a cue-invariant selectivity for a wide variety of stimuli defined by nonluminance cues (Kingdom et al. 2003; Zhan and Baker 2006). Models based on stimulus “features” will tend to be too narrowly specific to particular stimulus categories—for example, a model requiring the alignment of terminators might detect illusory contours (e.g., Grossberg and Mingolla 1985; Heitger et al. 1992), but it would lack robustness (cue invariance) for other kinds of stimuli such as contrast modulation (Song and Baker 2007). Although our results support the filter/energy type of models, they do not fully clarify how such an F-R-F operation might be implemented in neural circuitry. The selectivity for relatively high carrier spatial frequencies (Zhou and Baker 1996) suggests that the early filters probably arise, either directly or indirectly, from a subset of A17 neurons (i.e., those tuned to the highest spatial frequencies). The neural basis of the late filter is quite unclear—we have never recorded from neurons which are responsive exclusively to second-order stimuli.

Modeling neural responses of the early visual cortex to complex images is crucial to understanding its function in more ecologically relevant settings, and this research is a step in that direction. However, it seems unlikely that our model would successfully predict responses to arbitrary complex stimuli, or more importantly, to images of natural scenes (e.g., David et al. 2004). For example, we have not modeled gain control mechanisms or surround suppression, which are likely to be engaged by natural images that are sparse and therefore rich in higher-order statistics (Carandini et al. 2005).

The abundance of low-level visual components in natural scenes raises the question: when a given stimulus activates different sets of neural mechanisms, which may be signaling seemingly contradictory stimulus attributes, how does the brain resolve which will drive perception? For example, when the carrier and envelope are activating different mechanisms/brain areas, the competition as to which drives perception might be substantially tilted or resolved by the system's spatial filtering characteristics.

It seems very likely that our model would work well for visual stimuli with boundaries defined by other texture/contrast cues (Song and Baker 2006; Zhan and Baker 2006), and we would conjecture that the approach could be generalized for motion-defined boundaries. However, it is not apparent that Kanisza-type “long-range” illusory contours could be explained within the F-R-F framework.

The idea that a response's mediation by first- or second-order mechanisms depends on the system's spatial frequency bandwidth has potentially much broader applicability. Such a finding has already been described at the single unit level (Song and Baker 2006), where a given cat A18 neuron showed a bimodal dependence on carrier spatial frequency of abutting grating stimuli, with responses at low frequencies mediated by its conventional luminance (linear) passband, and responses within a limited range of high frequencies reflecting a nonlinear (second-order) mechanism. Other examples could readily arise, for example in human psychophysics. Because the range of effective spatial frequencies is shifted to coarser scales with increasing retinal eccentricity, a given subject's percept of some second-order stimuli might shift from first- to second-order attributes with more eccentric viewing. The relative balance between conflicting first- and second-order responses might similarly be affected by the changes in overall spatial bandwidth in early development (Movshon and Kiorpes 1988), or with advancing age (Owsley et al. 1983). Thus, the assessment of responses to complex stimuli, such as second-order patterns, should always be interpreted with respect to the relationship between the spatial scale of the stimuli and the spatial filtering of the system under study.

Funding

Canadian Institutes of Health Research grant (MA-9685); and a McGill University Stairs equipment grant to C.B.

We thank Lynda Domazet, Aaron Johnson, and Yuning Song for assistance with the experiments. Conflict of Interest: None declared.

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