December 2011
Volume 11, Issue 14
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Article  |   December 2011
Contrast and stimulus complexity moderate the relationship between spatial frequency and perceived speed: Implications for MT models of speed perception
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Journal of Vision December 2011, Vol.11, 19. doi:10.1167/11.14.19
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      Kevin R. Brooks, Thomas Morris, Peter Thompson; Contrast and stimulus complexity moderate the relationship between spatial frequency and perceived speed: Implications for MT models of speed perception. Journal of Vision 2011;11(14):19. doi: 10.1167/11.14.19.

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Abstract

Area MT in extrastriate visual cortex is widely believed to be responsible for the perception of object speed. Recent physiological data show that many cells in macaque visual area MT change their speed preferences with a change in stimulus spatial frequency (N. J. Priebe, C. R. Cassanello, & S. G. Lisberger, 2003) and that this effect can accurately predict the dependence of perceived speed on spatial frequency demonstrated in a related psychophysical study (N. J. Priebe & S. G. Lisberger, 2004). For more complex compound gratings and high contrast stimuli, MT cell speed preferences show sharper tuning and less dependence on spatial frequency (Priebe et al., 2003), allowing us to predict that such stimuli should produce speed percepts that are less vulnerable to spatial frequency variations. We investigated the perceived speed of simple sine wave gratings and more complex compound gratings (formed from 2 sine wave components) in response to changes in contrast and spatial frequency. In all cases, high contrast stimuli appeared to translate more rapidly. In addition, high spatial frequencies appeared faster—the opposite effect to that predicted by changes in MT cell spatial frequency preferences. Complex grating stimuli were somewhat “protected” from the effect of spatial frequency (compared to simple gratings), as predicted. However, contrary to predictions, the effect of spatial frequency was larger in high (compared to low) contrast gratings. Our data demonstrate that the previously established links between changes in MT cells' speed preferences and human speed perception are more complex than first thought.

Introduction
The ability to accurately and precisely encode the speed of a stimulus is crucial to a number of everyday tasks, yet despite the ability of humans to achieve many such feats with a good degree of success, laboratory studies have repeatedly shown vulnerabilities in our speed perception abilities. Although good precision is often shown by motivated, experienced subjects (e.g., Weber fractions approaching 5%; Buracas, Fine, & Boynton, 2005; McKee, Silverman, & Nakayama, 1986), accuracy can be compromised by the simplest of image manipulations such as changes in contrast or spatial frequency (see Burr & Thompson, 2011; Thompson, 1993 for reviews). Although the physiological details that underlie such speed misperceptions have long remained mysterious to vision scientists, recent studies have helped shed light on the locus and nature of these processes. It has been suggested that the neural substrates responsible for the computation of object speed are located in extrastriate cortical area MT+ (Boyraz & Treue, 2011; Buracas et al., 2005; Churchland & Lisberger, 2001; Huk & Heeger, 2000; Liu & Newsome, 2005; Orban, Lagae, Raiguel, Xiao, & Maes, 1995; Perrone & Thiele, 2001, 2002; Priebe & Lisberger, 2004). Lending weight to these suggestions, several physiological investigations have identified speed tuned cells in this area (Maunsell & Van Essen, 1983; Perrone & Thiele, 2001). 
Recordings of activity from MT motion-sensitive cells to various combinations of spatial and temporal frequencies produce response fields in Fourier space that have various forms. All cells show a peak of sensitivity that might legitimately be referred to as its preferred speed when the entire spatiotemporal Fourier space is considered. For some cells, this response field appears as depicted in Figure 1A, where the patterns of responding to spatial and temporal frequency are entirely independent of each other. This means that as spatial frequency changes, the preferred temporal frequency (denoted by the red cross marks) remains unchanged, and vice versa. Given that speed is the quotient of temporal frequency by spatial frequency, this cell's preferred speed would change as a function of spatial frequency. Other cells' response fields appear quite different, having a distinct tilt in Fourier space. In the example shown in Figure 1B, the preferred temporal frequency is proportional to spatial frequency, such that the cell can be described as having a single preferred speed (in this case, 4 deg/s) across a broad range of combinations of Fourier parameters. Such cells might be described as being “genuinely speed tuned.” Priebe, Cassanello, and Lisberger (2003) established details of the tilt of the response fields for MT neurons finding that although approximately 25% were genuinely speed tuned, showing the same speed preference regardless of spatial frequency, the population of MT cells show a continuum of tilts in Fourier space, and as such, many change speed preference when there is a change in the spatial frequency of simple sinusoids (Priebe et al., 2003). This observation may be able to account for the speed misperception caused by variations in spatial frequency if one considers such MT neurons to be labeled lines, and a vector average computation is applied to the population of responses (Priebe & Lisberger, 2004). For the many neurons that are not genuinely speed tuned, as spatial frequency changes (with speed held constant), the distribution of firing shifts. This causes a change in the identity of the most active neuron to one associated with a different preferred speed. If, instead, all MT cells' speed preferences had been independent of their spatial frequency, this model would have predicted no effect of spatial frequency on perceived speed. 
Figure 1
 
The response fields of two hypothetical MT neurons in Fourier space. (A) A neuron exhibiting spatiotemporal independence, wherein different preferred speeds (red x's) are found for each spatial frequency. (B) A genuinely speed tuned cell, whose preferred speed is independent of spatial frequency.
Figure 1
 
The response fields of two hypothetical MT neurons in Fourier space. (A) A neuron exhibiting spatiotemporal independence, wherein different preferred speeds (red x's) are found for each spatial frequency. (B) A genuinely speed tuned cell, whose preferred speed is independent of spatial frequency.
For V1 cells, responses to compound gratings are well predicted by the responses to isolated gratings (Priebe, Lisberger, & Movshon, 2006), whereas in MT, non-linear processes lead many cells to increase the slope of their response fields in Fourier space, hence increasing the extent to which they are genuinely speed tuned (Priebe et al., 2003). A similar situation exists for high contrast sinusoids, as the slope of the response field is increased at higher contrasts (Priebe et al., 2003, 2006). If human speed perception is consistent with the model of Priebe and Lisberger (2004), we can predict large effects of spatial frequency for low contrast sine wave stimuli, whereas any such spatial frequency dependence should be reduced for stimuli that are high in contrast or contain multiple spatial frequencies. In the present paper, we test the predictions that stimulus complexity and contrast can moderate the effects of spatial frequency on perceived speed, while attempting to account for the final speed percept for compound gratings considering the effects of contrast and spatial frequency on their component sine waves. 
Methods
Subjects
Data concerning stimuli at 2 deg/s were collected from 8 human subjects, while trials at 4 deg/s involved 9. Of these, 3 subjects contributed data at both speeds, including author KB—the only non-naïve participant. All subjects had normal or corrected-to-normal vision and were aged between 18 and 50. 
Design
This experiment was designed to yield measures of perceived speed for various sine wave gratings and compound grating stimuli, presented at two different objective speeds (2 deg/s and 4 deg/s) in separate blocks. Our complex stimuli featured two sine wave gratings moving at the same speed, thus ensuring that they maintained their relative phase with each other over time. Sets of tests at 2 and at 4 deg/s were run independently on separate groups of subjects but were otherwise identical in design and procedure. Measures of perceived speed were established for simple sine wave grating stimuli or more complex compound gratings (the sum of two sine wave gratings). For simple stimuli, four different spatial frequencies were used (0.5, 1, 2, and 4 c/deg), while complex gratings were created by combining the “nearest neighbours” of the four simple stimuli (i.e., 0.5 + 1, 1 + 2, and 2 + 4 c/deg). The use of fixed speeds means that the temporal frequencies of each grating varied in concert with their spatial frequencies. When standard speed was 2 deg/s, they were 1, 2, 4, and 8 Hz, while for 4 deg/s they were 2, 4, 8, and 16 Hz, respectively. For ease of comparison, these stimuli are depicted on the spatiotemporal surface shown in Figure 2. It can be seen that compound gratings will have multiple spatial and temporal frequencies, and hence, these stimuli will be described in terms of the averages of these values (see Results section). 
Figure 2
 
A spatiotemporal surface illustrating the relationship between stimulus speed and the parameters of spatial and temporal frequency. Stimuli used in this study are shown by white (2 deg/s) and black (4 deg/s) circles.
Figure 2
 
A spatiotemporal surface illustrating the relationship between stimulus speed and the parameters of spatial and temporal frequency. Stimuli used in this study are shown by white (2 deg/s) and black (4 deg/s) circles.
Two levels of Michelson contrast were used for both simple and complex stimuli. For simple stimuli, these were 5% (henceforth referred to as “low”) and 45% (“high”), while for complex stimuli these gratings were summed to produce comparable 1 low and high contrast compound gratings. Stimuli drifting leftward and rightward were tested in separate conditions. Overall, for simple stimuli, the experiment could be described as having two parts (one relating to each speed, performed by different groups of subjects), each with a 4 × 2 × 2 design, while all analysed variables (spatial frequency, contrast, and direction) were within subjects. Similarly, for complex stimuli, the experiment had two parts, each with a 3 × 2 × 2 design, this time using three combinations of spatial frequencies. Statistical differences (main effects or interactions) involving the factor of direction were not theoretically relevant and are mentioned no further. 
Apparatus and stimuli
Stimuli were displayed using a Sony Trinitron/Dell P1130 flat screen monitor with a spatial resolution of 1344 × 1008, running at a frame rate of 120 Hz. The monitor was connected to a G5 Power Mac, housing an ATI Radeon HD 4870 graphics card, providing 10-bit grey level precision. Stimuli were programmed and generated through MATLAB, using the psychophysics toolbox (Brainard, 1997; Pelli, 1997). Subjects sat at a viewing distance of 3.44 m, from whence the screen subtended 6.67 × 5 deg. Responses were made via a two-button mouse. The mean luminance of the linearised screen was 47 cd/m2, and all tests took place in a darkened laboratory. 
Greyscale motion stimuli filled the entire screen except for a small, high contrast fixation point at the centre of the display. Standard stimuli—vertical sine wave gratings—had a unique combination of spatial frequency and contrast in each condition, but each had a constant speed. Test stimuli—filtered noise patterns—were identical in spatial form in each trial but could be presented at various speeds. These patterns were isotropic in orientation content but were spatially low-pass filtered with a cutoff frequency of 10 c/deg. Using the entire range of lookup table values, they had a Michelson contrast of 99.98%. 2  
Procedure
We used a yes–no speed discrimination paradigm. In each trial, a standard stimulus and a test stimulus were presented sequentially (arranged in random order), following which the subject was asked to indicate which stimulus (the first or the second) appeared to translate at a higher speed. Subjects were asked to maintain their gaze toward the central fixation point throughout. The first trial was initiated by a button press. After a 1000-ms interval, the two stimuli appeared, separated by an interstimulus interval (ISI) of 500 ms. Following the subject's response, the next trial was initiated automatically, after a minimum intertrial interval (ITI) of 1000 ms. During the ISI and ITI periods, a blank screen at mean luminance was displayed along with the fixation point. While the duration of the standard stimulus (grating) was fixed at 400 ms, the test (filtered noise) had one of five durations selected at random: 300, 350, 400, 450, or 500 ms. This variation was implemented to discourage a strategy of simply comparing extents of displacement between the two intervals. 
Trials were run in sets of randomly interleaved 1-up–1-down staircases, one for each experimental condition. Each staircase featured steps halving in size every three reversals and terminated after 12 reversals. Initial step sizes were 40% of standard speed. During a testing session, subjects were tested in 3 blocks of trials, administered in random order. One featured compound stimuli (12 staircases, lasting approximately 17 min), while the other two featured either the lower spatial frequency (0.5 and 1 c/deg) or higher spatial frequency (2 and 4 c/deg) simple stimuli (8 staircases each, lasting approximately 12 min). 
Analysis
Data from each staircase/condition were fitted with a cumulative Gaussian function by varying the mean and standard deviation to minimise squared error weighted by number of observations. The mean represents the point of subjective equality (PSE)—the speed at which the standard and test stimuli appear equal in speed. PSEs were averaged across subjects and their associated standard errors were calculated. 
Results
PSEs for simple sine wave and complex compound stimuli
Mean PSEs from the 8 subjects tested at 2 deg/s can be seen in Figure 3A. For simple sine wave stimuli (circles, solid lines), there is a separation of the plots for low and high contrast stimuli, with high contrast stimuli showing a higher mean PSE at all levels of spatial frequency. The average size of the difference between PSEs for high and low contrasts, across all subjects and conditions, is 0.4 deg/s (20% of standard speed). In addition, each plot has a clear monotonic positive slope, with progressively higher PSEs for higher spatial frequencies. A repeated measures ANOVA confirmed the statistical significance of these main effects of contrast (F(1, 7) = 18.704, p = 0.003, partial η 2 = 0.728) and spatial frequency (F(3, 21) = 33.989, p < 0.0005, partial η 2 = 0.829). For complex compound gratings, mean PSEs are plotted against the average spatial frequency of the two component gratings (triangles, dashed lines). Here, the situation is similar, with higher mean PSEs for high contrast gratings throughout (mean difference 0.51 deg/s or 25.6%). In addition, each plot has a positive slope, indicating an effect of spatial frequency. A repeated measures ANOVA showed significant main effects of contrast (F(1, 7) = 30.405, p = 0.001, partial η 2 = 0.813) and spatial frequency (F(2, 14) = 38.313, p < 0.0005, partial η 2 = 0.846), as well as an interaction between the two (F(2, 14) = 4.644, p = 0.028, partial η 2 = 0.399). 
Figure 3
 
Mean PSEs for all spatial frequencies and contrasts at (A) 2 deg/s and (B) 4 deg/s. Circles and bold lines represent data from simple sine wave stimuli; triangles and dashed lines refer to complex compounds. Black and white points denote high contrast; light and dark gray points represent low contrast. Error bars represent ±1 SEM throughout.
Figure 3
 
Mean PSEs for all spatial frequencies and contrasts at (A) 2 deg/s and (B) 4 deg/s. Circles and bold lines represent data from simple sine wave stimuli; triangles and dashed lines refer to complex compounds. Black and white points denote high contrast; light and dark gray points represent low contrast. Error bars represent ±1 SEM throughout.
For the 4 deg/s conditions, mean PSEs from 9 subjects are shown in Figure 3B. Again, simple sine wave stimuli (circles, solid lines) show a consistent contrast effect, such that high contrast stimuli appear faster (mean difference 1 deg/s or 25%). The slope of each plot is again positive and monotonic. A repeated measures ANOVA confirmed the main effects of contrast (F(1, 8) = 14.088, p = 0.006, partial η 2 = 0.638) and spatial frequency (F(3, 24) = 54.537, p < 0.0005, partial η 2 = 0.872) for simple sine waves. For complex stimuli (triangles, dashed lines), the contrast effect is again clear, with higher PSEs for high contrast stimuli at all average spatial frequencies (mean difference 1.5 deg/s or 37.5%). Positive slopes are again evident, with higher spatial frequencies being perceived as faster. Main effects of contrast (F(1, 8) = 28.45, p = 0.001, partial η 2 = 0.781) and spatial frequency (F(2, 16) = 37.328, p < 0.0005, partial η 2 = 0.824) were statistically significant. 
Comparisons across complexity
As the spatial frequency content of the simple and complex stimuli were necessarily different, comparisons between these two types of stimuli are somewhat unconventional. Comparison of the size of the contrast effect was performed by averaging the size of the difference between high and low contrast PSEs across all levels of spatial frequency (or average spatial frequency) for each observer and comparing values for simple and complex stimuli using a paired t-test. Comparison of the size of the effect of spatial frequency involves consideration of the slope of plots within Figure 3, which can be seen to be approximately linear over the range of spatial frequencies tested. To achieve this, we established lines of best fit for PSEs across spatial frequency for each subject and condition and extracted the gradient as a measure of the rate of change of perceived speed with spatial frequency for further analysis in the same way for all conditions. 
At 2 deg/s, the size of the contrast effect on complex stimuli was not significantly different to that on simple stimuli. The analysis of the size of the effect of spatial frequency yielded mean gradients that can be seen in Figure 4A. Here, a 2 × 2 ANOVA showed statistically significant main effects of contrast (F(1, 7) = 7.192, p = 0.031, partial η 2 = 0.507) and complexity (F(1, 7) = 19.522, p = 0.003, partial η 2 = 0.736). The effect of spatial frequency was larger for patterns that were higher in contrast but was lower for compounds compared to sine waves. At 4 deg/s, a paired t-test on differences between high and low contrast PSEs for simple vs. complex stimuli reveals a significantly larger contrast effect for complex than for simple stimuli (t(17) = 2.676, p = 0.016). At this speed, an ANOVA on gradients of best fitting lines (see Figure 4B) yielded a statistically significant main effect of complexity (F(1, 8) = 15.890, p = 0.004, partial η 2 = 0.665), again indicating a smaller effect of spatial frequency for compound gratings, compared to sine waves. The effect of contrast was not significant. 
Figure 4
 
Mean gradients describing the relationship between perceived speed and contrast for (A) 2 deg/s and (B) 4 deg/s.
Figure 4
 
Mean gradients describing the relationship between perceived speed and contrast for (A) 2 deg/s and (B) 4 deg/s.
Given the relatively similar patterns of mean PSE data across complexity for some spatial frequencies, we decided to test the observation of Smith and Edgar (1991) that the mean of the sine wave components' perceived speeds predicts the perceived speed of the compound stimuli. Predictions were made for each subject and compound stimulus condition and are shown plotted against actual perceived compound speed in Figure 5. Here, positive values represent rightward motion trials, while negative values represent leftward. At 2 and 4 deg/s, data points appear to be clustered around the line of unity. Notable exceptions are evident for the low contrast 3-cpd condition at 4 deg/s (grey squares) whose predicted speeds are consistently higher than actual recorded PSEs. Values of r 2 involving data from all contrast and spatial frequency conditions were 0.97 and 0.94 for 2 and 4 deg/s, respectively. These values were superior to those produced by an equally elementary model wherein the compound PSE was predicted to be identical to the standard speed (r 2 = 0.94 and 0.84, respectively). However, closer inspection of individual conditions reveals that at 2 deg/s the average component speed model performed no better than the standard speed model for the low contrast 3-cpd (grey squares: r 2 = 0.96) and the high contrast 0.75-cpd (white circles: r 2 = 0.97) conditions. At 4 deg/s, the average component speed model was outperformed by the standard speed model in two cases, both involving low contrast stimuli at 1.5 (grey triangles: r 2 = 0.095 vs. 0.96, respectively) and 3 cpd (grey squares: r 2 = 0.083 vs. 0.93). 
Figure 5
 
Scatter plot of individual subjects' PSEs for compound gratings vs. the predicted perceived speed (based on the average of component speeds) at (A) 2 deg/s and (B) 4 deg/s. The dashed line represents perfect predictions. Note the difference in axis scale for each plot.
Figure 5
 
Scatter plot of individual subjects' PSEs for compound gratings vs. the predicted perceived speed (based on the average of component speeds) at (A) 2 deg/s and (B) 4 deg/s. The dashed line represents perfect predictions. Note the difference in axis scale for each plot.
Discussion
Basic effects of contrast and spatial frequency on perceived speed
This study replicates the well-documented effect of contrast on perceived speed for sine wave and broadband stimuli (Blakemore & Snowden, 1999; Brooks, 2001; Hawken, Gegenfurtner, & Tang, 1994; Johnston, Benton, & Morgan, 1999; Johnston & Clifford, 1995; Snowden, Stimpson, & Ruddle, 1998; Thompson, Brooks, & Hammett, 2006; Thompson, Stone, & Brooks, 1995) and extends it to compound stimuli comprising two components. Although some studies have failed to find clear effects of contrast on perceived speed for complex stimuli (Blakemore & Snowden, 1999; Owens, Wood, & Carberry, 2010; Shrivastava, Hayhoe, Pelz, & Mruczek, 2005), in this case the increase in complexity did not reduce the size of the effect, and at the faster speed in fact increased it. 
Increases in spatial frequency caused an increase in perceived speed (i.e., a positive effect) for all levels of complexity, contrast, and speed. The positive effect of spatial frequency is in agreement with several similar studies (Diener, Wist, Dichgans, & Brandt, 1976; Ferrera & Wilson, 1991; Kooi, Devalois, Grosof, & Devalois, 1992; McKee et al., 1986) and was also evident for complex compound gratings. 
The neural code for perceived speed
The central hypotheses of this study were generated from Priebe and Lisberger's (2004) model of speed computation, which relies on the outputs of motion-selective cells in MT. Specifically, a vector average model was used to show that spatial frequency-induced variations in the activity of cells that are not genuinely speed tuned could effectively predict spatial frequency-induced speed misperceptions. As stimulus contrast or complexity is increased, the majority of MT neurons increase the tilt of their response profile in Fourier space, reducing the dependence of preferred speed on spatial frequency. Indeed, Priebe et al. (2003) comment: “MT neurons seem to derive form-invariant speed tuning in a way that takes advantage of the fact that moving objects in natural scenes comprise multiple spatial frequencies.” If this model of speed perception were implemented, we would predict similarly reduced effects of spatial frequency for complex stimuli (a prediction that is upheld) and for high contrast stimuli (a prediction not upheld). 
While the reduced effect of spatial frequency for complex stimuli would appear to support certain aspects of Priebe and Lisberger's (2004) model, one important factor complicates this interpretation. These authors conducted their physiological investigations using temporally isolated stimuli, yet their psychophysical tests involved the simultaneous presentation of two stimuli. While this small methodological mismatch might often be overlooked, in this case there is explicit evidence that the temporal details of presentation can drastically affect the patterns of perceived speed shown when spatial frequency is varied (Kooi et al., 1992). Two other studies have found a negative relationship between spatial frequency and perceived speed (Kooi et al., 1992; Priebe & Lisberger, 2004; Smith & Edgar, 1990), but such effects are evident only when two comparison stimuli are presented simultaneously rather than being separated in time. This observation was confirmed by Kooi et al. (1992)) who reported negative effects with simultaneous stimuli but positive effects when stimuli were presented sequentially. Our psychophysical data were collected using sequential presentation, which allows a more valid comparison with Priebe and Lisberger's physiological data. The direction of the spatial frequency effect was in fact opposite to the pattern of results that would be predicted given their model and physiological data, even for simple sine wave stimuli. The disagreement of the direction of the effect for simple stimuli renders any predictions of reduced effects for other stimuli quite meaningless. Given that the vector average model is unable to predict the effect of spatial frequency on perceived speed for our simple stimuli, we would be premature in celebrating the same model's success in predicting a reduction in the size of that effect for complex stimuli. Furthermore, our data show that, contrary to predictions, high contrast stimuli are never less susceptible to spatial frequency-induced speed misperceptions, and in some cases (2 deg/s), they are more susceptible. 
The well-established effects of contrast on perceived speed pose a problem for Priebe and Lisberger's (2004) basic vector average model, as changes in contrast caused smaller responses in the majority of cells without altering their spatiotemporal tuning. “Because the identity of the active neurons in area MT is not affected by the contrast of the stimulus, the vector average is not affected either” (Priebe & Lisberger, 2004, p. 1915). To address this shortcoming, Priebe and Lisberger added a Bayesian-style term to their model. However, other authors have reported that changes of contrast do affect the preferred speed of neurons in MT (Krekelberg, van Wezel, & Albright, 2006) and in V1 (Livingstone & Conway, 2007). Although these observations are also inconsistent with labeled-line models of speed perception, they may be consistent with another proposition—that perceived speed is signalled simply by the total firing rate of MT cells or a subpopulation thereof (Komatsu & Wurtz, 1989). The ability of such a model to account for other perceived speed effects, such as those related to changes in spatial frequency, awaits close examination. 
Predicting the perceived speed of compound gratings from component speed
We tested the observation by Smith and Edgar (1991) that compound gratings appear to translate at a rate given by a simple, unweighted average of the perceived speeds of the visible Fourier components. Although this model, which features no free parameters, performs relatively well in some conditions, in several cases the prediction that the compound PSE would be given by the standard speed provides estimates that are as good or even better. That this model fails to accurately predict perceived speed in some cases is perhaps not surprising, given the earlier demonstration that spatial frequency affects perceived speed differently for gratings of different levels of complexity. Indeed, the case where the average component speed model fails most clearly corresponds to the condition wherein the plots of mean PSE are shown to diverge most drastically. However, in some cases, the predictions made by the average of the perceived speeds of the component gratings accounted relatively well for the perceived speed of compounds in quantitative and not just qualitative terms. The same cannot be said for the ability of plaid component speed to account for a plaid's perceived direction (Champion, Hammett, & Thompson, 2007). Although the cases where this model fails make it clear that there must be more to the computation of perceived speed of complex 1D gratings, this may serve as a starting point for future studies wishing to further explore the relationship between the perceived speed of complex stimuli and their Fourier components. 
Acknowledgments
This work was supported by an Australian Research Council grant to author K. Brooks (Discovery Project DP0984948). For helpful comments on previous drafts, we thank Kirsten Challinor. For research assistance, we are indebted to Scott Gwinn and Timothy Priest. 
Commercial relationships: none. 
Corresponding author: Kevin R. Brooks. 
Email: kevin.brooks@mq.edu.au. 
Address: Department of Psychology, Macquarie University, Sydney, NSW, Australia. 
Footnotes
Footnotes
1  Note that when gratings with a spatial frequency ratio of 2:1 are combined, as in this study and previous physiological reports (Priebe et al., 2003; Priebe & Lisberger, 2004), peaks and troughs do not align perfectly. As a result, the Michelson contrast of the complex stimuli in this study was not precisely double that of the simple stimuli. However, as in previous studies, these stimuli were the linear combination of the two component stimuli and, hence, represent a valid comparison condition. Further, experiments reported elsewhere (Brooks, Morris, & Thompson, 2010), which were performed using spatial frequency ratios whose peaks and troughs do align, produce equivalent patterns of results.
Footnotes
2  Michelson contrast is commonly used for periodic stimuli and is given for the filtered noise test stimulus purely for the sake of consistency. The normalized RMS contrast of the test pattern was 0.12.
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Figure 1
 
The response fields of two hypothetical MT neurons in Fourier space. (A) A neuron exhibiting spatiotemporal independence, wherein different preferred speeds (red x's) are found for each spatial frequency. (B) A genuinely speed tuned cell, whose preferred speed is independent of spatial frequency.
Figure 1
 
The response fields of two hypothetical MT neurons in Fourier space. (A) A neuron exhibiting spatiotemporal independence, wherein different preferred speeds (red x's) are found for each spatial frequency. (B) A genuinely speed tuned cell, whose preferred speed is independent of spatial frequency.
Figure 2
 
A spatiotemporal surface illustrating the relationship between stimulus speed and the parameters of spatial and temporal frequency. Stimuli used in this study are shown by white (2 deg/s) and black (4 deg/s) circles.
Figure 2
 
A spatiotemporal surface illustrating the relationship between stimulus speed and the parameters of spatial and temporal frequency. Stimuli used in this study are shown by white (2 deg/s) and black (4 deg/s) circles.
Figure 3
 
Mean PSEs for all spatial frequencies and contrasts at (A) 2 deg/s and (B) 4 deg/s. Circles and bold lines represent data from simple sine wave stimuli; triangles and dashed lines refer to complex compounds. Black and white points denote high contrast; light and dark gray points represent low contrast. Error bars represent ±1 SEM throughout.
Figure 3
 
Mean PSEs for all spatial frequencies and contrasts at (A) 2 deg/s and (B) 4 deg/s. Circles and bold lines represent data from simple sine wave stimuli; triangles and dashed lines refer to complex compounds. Black and white points denote high contrast; light and dark gray points represent low contrast. Error bars represent ±1 SEM throughout.
Figure 4
 
Mean gradients describing the relationship between perceived speed and contrast for (A) 2 deg/s and (B) 4 deg/s.
Figure 4
 
Mean gradients describing the relationship between perceived speed and contrast for (A) 2 deg/s and (B) 4 deg/s.
Figure 5
 
Scatter plot of individual subjects' PSEs for compound gratings vs. the predicted perceived speed (based on the average of component speeds) at (A) 2 deg/s and (B) 4 deg/s. The dashed line represents perfect predictions. Note the difference in axis scale for each plot.
Figure 5
 
Scatter plot of individual subjects' PSEs for compound gratings vs. the predicted perceived speed (based on the average of component speeds) at (A) 2 deg/s and (B) 4 deg/s. The dashed line represents perfect predictions. Note the difference in axis scale for each plot.
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