The stimulus devised by Rainville and Wilson (
2004,
2005) is a path of Gabor patches. In the null stimulus the centers of the Gaussian windows of the Gabor patches lie on a circular path and their gratings are stationary and tangential to the path. This null stimulus can be manipulated in two ways. In the spatial manipulation of the stimulus the positions of the Gabor patches are modulated sinusoidally from the circular path with the gratings remaining tangential to the path. Earlier experiments have shown observers to be extremely sensitive to such spatial RF deformations in continuous contours (Bell et al.,
2007; Loffler et al.,
2003; Wilkinson et al.,
1998). The motion manipulation of the stimulus involves introducing a sinusoidal radial speed distribution to the gratings of the Gabor patches. Sensitivity to this manipulation implies either that the visual system is sensitive to a sinusoidal modulation of radial speed in the absence of a spatial deformation cue, or that local motion introduces an apparent displacement to each of the Gabor patches in the direction of the motion, which is interpreted by the form system as a distortion of the path. Rainville and Wilson (
2004,
2005) favored the first of these interpretations citing evidence that motion RF modulation pedestals had a detrimental effect on discrimination thresholds for spatial RF deformation both in phase and out of phase with the test pattern modulation. However, the perceived form of a motion RF pattern has amplitude maxima at the points where the motion is maximally centrifugal and spatial RF patterns have been shown to elicit spatial RF after effects of opposite phase (Anderson et al.,
2007) which raises the question of whether motion RF patterns exhibit spatial RF after effects of opposite phase. The spatial RF after effect is independent of the contrast of the adapting stimulus (Anderson et al.,
2007) suggesting the neural mechanisms responsible for encoding the shape are downstream of those effecting contrast gain control.
Experiment 1 of this study demonstrates that the after effect develops over a very short adaptation period (40 ms) and in the absence of an intervening stimulus the adaptation is persistent in comparison to the rise time.
Experiment 2 shows that a spatial RF pattern of the same phase as an adapting motion RF pattern nulls the after effect.
Experiment 3 confirms the reciprocal effect, that a motion RF pattern of the same phase as an adapting spatial RF pattern nulls the after effect. The phase specificity and linear relationship between the after effect of adaptation to spatial RF patterns and the percept of the form of the motion RF patterns suggests that the reconciliation of the spatial and motion RF information might occur earlier in the visual system than proposed by Rainville and Wilson.
Experiment 4 shows that the perceived displacement of a Gabor patch due to the motion position illusion is related linearly to the speed of the grating in the patch, and is a large proportion of the extrapolated displacement of a single cycle of the grating over the course of the stimulus presentation. This is true for an isolated patch and also for a patch incorporated into a closed path. If the form processing stream of the visual system were to use the perceived positions rather than the actual positions in the analysis of form then the motion in the motion RF patterns would result in the encoding of this deformation in the form system.
Experiment 5 tests whether this deformation would be sufficient to account for sensitivity to motion RF patterns. The parameters of the motion RF pattern stimuli used in
Experiment 5 approximated those used by Rainville and Wilson but with an additional d.c. component of centrifugal motion to ensure that in all conditions the motion of all patches was in the same direction (centrifugal) to preclude the use of local speed discontinuities to perform the task. Sensitivities to 1, 2 and 3 cycles of deformation of motion RF patterns and spatial RF patterns were compared through the application of a transfer function relating the size of the motion position illusion to grating speed in a patch. The spatial deformation of motion RF patterns at their detection threshold that can be attributed to the motion position illusion is comparable to the thresholds for detection of spatial RF patterns. Moreover, the indices of the power functions describing the decrease in threshold with increasing numbers of cycles of deformation were comparable across motion and form conditions and were indicative of summation of signal across cycles. Also, we showed that no deformation could be perceived in a motion RF stimulus composed of hard edged patches on a dark background, a stimulus which does not support the motion position illusion. The motion position illusion is therefore necessary for the perception of deformation in motion RF patterns. We conclude that the most parsimonious explanation for the perceived deformation of motion RF patterns is the integration of perceived positions of independent patches displaced in the direction of motion of the gratings within them by an amount proportional to the speed of the gratings. Rainville and Wilson (
2004,
2005) rejected this conclusion primarily on the basis that; a) integration over progressively larger numbers of Gabor patches and hence cycles of speed modulation improves sensitivity (the reciprocal of threshold) at a rate which is steeper than linear and b) their measures of the displacement of the perceived positions of Gabor patches with gratings moving at speeds corresponding to the maxima of speed modulation in motion RF patterns at detection threshold was inadequate to produce a spatial RF of detectable amplitude. However data from panels D, E and F of Figure 3 of Rainville and Wilson (
2005) suggest that detection of the motion RF patterns in their task (discriminating a pattern with a sector of coherent speeds from a pattern where the speeds have been permuted across patches) is local. The data points represented by unfilled symbols, which represent thresholds for patterns where the position of the coherent sector was known to the observers, show constant rather than reducing thresholds with increasing numbers of coherently moving patches. This suggests that the improvement reported by Rainville & Wilson may have been a consequence of reducing spatial uncertainty when larger sectors of coherently moving patches were presented, rather than global spatial summation. This might also explain the fact that Rainville and Wilson (
2004) saw no systematic change in threshold for detection of motion RF patterns across radial frequency (Figure 3 of their paper). Rainville and Wilson (
2005) show that motion RF2s can be discriminated from RF3s, and RF3s from RF4s at particular thresholds (panels B and C of
Figure 3) when modulation occupies the complete stimulus (threshold increasing sharply when it is not complete). However, as it appears that these data have been normalized within the data set (thresholds for discriminating between the wholly coherent patterns = 1), we cannot compare the thresholds for discrimination between RF patterns with differing frequencies with those for discriminating motion RF patterns from patterns with speeds permuted across patches. It seems possible that in the studies undertaken by Rainville and Wilson observers were most sensitive to local coherence in speed rather than the global speed modulation. This argument does not explain the small displacements in perceived position for control stimuli illustrated in Figure 5 of Rainville and Wilson (
2005) at motion RF threshold velocities. However, in the alignment task used to derive their transfer function the target patch and reference patches were part of the same path defined by the Gaussian contrast envelopes of the patches. The gratings of the target and reference patches were in relative motion but the path could be considered to be a kinetic edge (Ramachandran & Anstis,
1990; Ramachandran & Inada,
1985) as average luminance contrast to background is close to zero. Under such circumstances the gratings might be treated as texture and perceived as moving in synchrony. However, perhaps the most compelling evidence that distortion of motion RF patterns is simply the result of a systematic change in the motion position illusion around the pattern is the fact that motion RF patterns composed of patches which do not support the motion position illusion do not appear distorted. Even for speed modulation amplitudes an order of magnitude larger than the threshold for detection of deformation in the typical motion RF patterns the patterns with a dark background and hard edged patches did not show any deformation.