Ординатура / Офтальмология / Английские материалы / Seeing_De Valois_2000

294 Andrew Derrington

(a) The intersection of constraints diagram for a type II plaid. Both components are moving to the right of vertical but the intersection of constraints is vertical. (b) A block diagram of Wilson et al.’s (1992) model of 2-D direction-of-motion analysis. Direction of motion is computed by summing the outputs of orientation-selective motion-energy filters operating directly on the spatiotemporal image and those of motion-energy filters that operate on the squared outputs of linear spatial-frequency-selective filters.

These perceptual properties of type II plaids can be explained by a model, outlined in Figure 18b, which proposes that the visual system computes the axis of motion of a 2-D pattern by summing its 1-D motion vectors rather than by computing the intersection of constraints. In addition to the 1-D vectors provided by the sinusoidal grating components of the plaid pattern, the model also uses 1-D vectors provided from extra frequency components, generated in the so-called nonFourier pathway through the model by first filtering the image then squaring it and filtering it again at a lower spatial frequency (Wilson et al., 1992).

The model accounts for the fact that the perceived axis of motion of a plaid pattern lies further from its true axis if the pattern is presented in the periphery rather than in the center of the visual field by assuming that the relative weight assigned to the non-Fourier motion signals is lower in the peripheral visual field (Wilson et al., 1992). The aspect of the model that accounts for the way the perceived axis of motion of a type II plaid changes with its presentation duration is that the nonFourier pathway operates more slowly than the direct pathway (there is independent evidence in support of this that will be reviewed in section V.B). Consequently,

in short presentations the only 1-D vectors that contribute to the vector-sum computation are those derived from the grating components of the plaid; hence the plaid appears to move in the vector-sum direction. At longer presentation durations the non-Fourier 1-D motion vectors become available and the perceived axis of motion moves closer to the true axis of motion. In simulations the model can replicate the e ects of varying duration and eccentricity (Wilson et al., 1992).

Although the vector-sum model accounts satisfactorily for changes in the perceived direction of motion of Type II plaid stimuli, it is not without its problems. Perhaps the most serious is that although the delay in the non-Fourier pathway accounts nicely for the improvement, with increasing presentation duration, in the accuracy with which observers perceive the axis of motion of a type II plaid, it is unlikely to be a complete explanation of this phenomenon. As Figure 19 shows, a similar improvement in performance occurs although over a somewhat longer time course, with type II plaid stimuli whose components are non-Fourier gratings (Cropper, Badcock, & Hayes, 1994). It may be that the increase over time in the accuracy with which we perceive the axis of motion occurs because the precision with which motion vectors can be estimated, and the sensitivity with which motion

FIGURE 19 Perceived axes of motion of type I and type II plaids presented for di erent durations. (a) Results obtained with plaids made by summing sinusoidal luminance gratings. (Data replotted from Vision Research, 32, Yo, C., & Wilson, H. R. Perceived direction of moving two-dimensional patterns depends on duration, contrast and eccentricity, 135–147. Copyright 1992, with permission of Elsevier Science.) (b) Results obtained with plaids made by summing second-order gratings. (Data replotted from Vision Research, 34, Cropper, S. J., Badcock, D. R., & Hayes, A. On the role of second-order signals in the perceived motion of type II plaid patterns, 2609–2612. Copyright 1994, with permission of Elsevier Science.) In both cases the perceived direction of motion of type II plaids is initially incorrect and gradually improves with time. The time course of the improvement is much slower when the plaids are made from second-order grating patterns.

296 Andrew Derrington

components can be detected, improve with time, both for first-order and for sec- ond-order motion stimuli. Consistent with this we have found that the accuracy with which subjects estimate the motion of type I plaids—even when the plaid components are at orientations 90 apart so that vector sum, non-Fourier vector sum, and intersection of constraints computations all give exactly the same result— improves with stimulus duration.

Thus although the vector-sum model makes a number of successful predictions, it seems clear that the errors in the perceived direction of motion of type II plaids are not solely due to a di erence in the time it takes to process second-order motion signals.

V. SECOND-ORDER MOTION MECHANISMS

One unusual aspect of the vector-sum model is that it seeks to integrate first-order and second-order motion analysis mechanisms. It exploits the fact that in most normal situations the two mechanisms act in harmony, providing alternative ways of deriving the same information from the same image. However, in order to investigate second-order mechanisms in isolation, it is necessary to devise stimuli in which first-order and second-order cues are either isolated or set into conflict with one another, since this is the only way in which one can isolate second-order mechanisms to assess their properties. It is worth pointing out that the same caveat applies to investigations designed to reveal the properties of first-order mechanisms, although it is usually ignored.

A. Importance of Second-Order Motion Signals

When the signals provided by first-order mechanisms are inadequate, second-order mechanisms may occasionally come to the rescue. For example, if a large textured object consists mainly of very high spatial frequency components, its motion may induce such large phase changes in its visible spatial frequency components that their direction of motion is ambiguous. In the limit, the spatial frequency of the components may be too high to allow any reliable motion analysis, in which case sec- ond-order analysis of the motion of the contrast envelope is the only possible way of sensing motion. In the natural world, striped animals like zebras and tigers may have this property; in the laboratory, a pattern composed by adding together two sinusoidal gratings of the same orientation and contrast and slightly di erent spatial frequencies makes an excellent substitute.

Figure 20 shows that second-order motion may be perceived when the first order motion that gives rise to it is invisible. The first order stimulus was a sinusoidal grat-

FIGURE 20 Discriminating the direction of a sudden jump of a high spatial frequency grating when it is presented alone or added to a stationary grating of similar spatial frequency so that it forms a low spatial frequency beat that jumps much farther than the high spatial frequency grating; if the stationary grating has higher spatial frequency, the beat moves in the opposite direction. (a) Space–time plots of the

298 Andrew Derrington

ing of spatial frequency 30 cycles/degree that underwent a phase shift half-way through its presentation. A space-time plot is shown in Figure 20a. The data in Figure 20b show that a subject was unable reliably to discriminate the direction of motion of this very high spatial frequency pattern. However, adding a second stationary grating of 28 or 32 cycles per degree to the stimulus introduces a secondorder pattern, a spatial variation in contrast known as a beat, that can be seen clearly in the space-time plots in Fig 20a.

The beat moves much further than the grating, and its direction of motion depends on the spatial frequency of the added grating. Observers are able to discriminate its motion without di culty.The fact that the direction of their responses reverses when the stationary grating has higher spatial frequency than the moving grating indicates that they are responding to the motion of the beat.Thus the human visual system is clearly able to analyze the motion of contrast modulations, the question is, how does it do it?

B. What Sort of Mechanism Analyzes the Motion of Contrast Variations?

Before considering how the visual system analyses the motion of contrast patterns it is important to establish what are the minimum requirements for such an analysis, since these set a limit on the ways in which it might be carried out. The model outlined in Figure 18 makes the point that a combination of filtering and squaring will turn a non-Fourier motion signal into a signal that can be analyzed by a standard motion filter. This is true of a wide range of non-Fourier motion stimuli (Chubb & Sperling, 1988, 1989). A general model of non-Fourier motion analysis would combine sets of filters to extract spatial variations in the motion carrier, followed by standard motion analysis based on one of the possible spatio-temporal comparators described earlier (Cavanagh & Mather, 1989).

When the second-order motion signal is carried by contrast variations the situation is much simpler. There is no need for filtering. Squaring, or any of a wide range of nonlinearities in transduction or transmission will turn a contrast signal into a luminance signal (Burton, 1973).4 Thus one possibility is that a nonlinearity very early in the visual pathway could cause the contrast signal to act in exactly the same way as a luminance signal (Burton, 1973; Derrington, 1987; Henning et al., 1975; Sekiguchi, Williams, & Packer, 1991) and to stimulate exactly the same motion-selective filters, there would be no need for a separate pathway to extract the motion of contrast envelopes. It is important to exclude this possibility before

4The simplicity with which the contrast signal can be transformed into the same form as a luminance signal brings complications. The range of nonlinearities that will produce the required transform is immense and includes the typical nonlinear relationship between luminance and driving voltage of a cathode-ray-rube monitor (Henning, Hertz, & Broadbent, 1975). This means that great care must be taken in generating and displaying contrast patterns in order to avoid inadvertently supplementing the contrast signal with a luminance signal before it enters the visual pathway.

proposing the existence of a special mechanism for analyzing the motion of contrast patterns, whether it be based on filtering, like that shown in Figure 23, or on tracking features in the contrast waveform.

Thus the limits imposed by the processing required to extract the motion of contrast patterns are extremely broad, and suggest three main possibilities. First, nonlinear distortion early in the visual pathway could cause the contrast pattern to generate exactly the same signal in exactly the same neural elements as would be generated by a luminance pattern, so the motion would be analyzed by the standard motion pathway. There is some evidence that this is what happens when contrast is very high. Second, the motion could be analyzed by a separate set of motion filters dedicated to the analysis of contrast patterns. Finally, the motion might be analyzed by tracking features in the contrast waveform, either with a dedicated mechanism or simply by paying attention (Cavanagh, 1992). Since features can be tracked in any type of pattern, we must be able to analyze the motion of contrast patterns by tracking features too. The big question is whether there is any kind of dedicated mechanism for analyzing contrast motion or whether we always accomplish this task by tracking features.

1. Psychophysics

A number of psychophysical experiments show di erences between our ability to discriminate the motion of contrast patterns and our ability to discriminate the motion of luminance patterns. These di erences are of the sort that we would expect if there were no special-purpose mechanism for analyzing the motion of second-order contrast patterns: temporal resolution is worse with contrast patterns than with luminance patterns, and motion discriminations with contrast patterns are more vulnerable to pedestals than are motion discriminations with luminance patterns. However, temporal resolution improves with contrast, as one would expect if a nonlinearity early in the visual pathway were to cause contrast patterns to generate signals in the visual mechanisms that normally respond only to luminance patterns (Burton, 1973). Unfortunately, there are some di erences between results obtained in di erent laboratories and between results obtained using di erent carriers which cloud the issue slightly.

Figure 21 shows the highest and lowest temporal frequencies at which observers could discriminate the direction of motion of a luminance pattern (a 1 c/deg grating) and a contrast pattern (a 1 c/deg beat between gratings of 9 c/deg and 10 c/ deg) plotted as functions of contrast. Lower thresholds of motion are not very di erent; thresholds are slightly lower for the grating than for the beat at all except the lowest contrast. This is possibly a reflection of the fact that at low spatial and temporal frequencies the high spatial frequency components of the beat are more visible than the 1 c/deg grating. However, the resolution limits, the maximum temporal frequencies at which direction of motion can be discriminated, show clear di erences between the grating and the beat. The limit for the grating changes only

300 Andrew Derrington

Upper and lower thresholds for discriminating the direction of motion of smoothly moving luminance patterns (1 c/deg sinusoidal gratings) and contrast patterns (1 c/deg beats between gratings of 9 and 10 c/deg) plotted as functions of the contrast of the pattern. At all contrasts the range of temporal frequencies over which the motion of the beat pattern can be discriminated (fine hatching) is smaller than the range of temporal frequencies over which the motion of the luminance pattern (coarse hatching). (Data replotted from Vision Research, 25, Derrington, A. M., & Badcock, D. R. Separate detectors for simple and complex grating patterns?, 1869–1878. Copyright 1985, with permission of Elsevier Science.)

slightly with contrast, increasing by about a factor of two, from about 8 Hz to about 20 Hz, over about two log units of contrast. The limit for the beat is generally much lower and increases much more sharply with contrast, rising from about 0.5 Hz at the lowest contrast to about 5 Hz 2 log units higher.

There is other evidence that mechanisms detecting the motion of contrast patterns are more sluggish. It is impossible to discriminate the direction of motion of beat patterns that are presented for less than about 200 ms, whereas the motion of

luminance or color patterns can be distinguished at durations down to 20 ms or less (Cropper & Derrington, 1994; Derrington, Badcock, & Henning, 1993). The reversed motion of plaid patterns shown in Figure 21, which is attributed to the intrusion of second-order mechanisms, only occurs at low temporal frequencies (Derrington et al., 1992).

There is a suggestion in Figure 21 that the increase in temporal resolution for the beat pattern is not a gradual change, but that it occurs suddenly. When the contrast reaches about 0.2 resolution jumps from around 1 Hz to around 5 Hz, as if there were two di erent mechanisms involved, a high temporal resolution mechanism active at high contrast and a low temporal resolution one active at low contrast.

In the beat patterns used to collect the data in Figure 21, the contrast was always modulated between zero and the maximum possible, which makes it impossible to distinguish between changes in sensitivity and changes in resolution. Figure 22 shows sensitivity measurements made with contrast-modulated gratings. Direction discrimination performance was measured as a function of the depth of modulation of a contrast envelope of fixed mean contrast, and the reciprocal of the threshold was plotted as a function of the temporal frequency.

The resulting temporal modulation sensitivity functions show clearly that raising the contrast improves the relative sensitivity as well as the resolution of the mechanisms that detect the motion of contrast waveforms. When the mean contrast is 0.1, sensitivity falls rapidly for frequencies above 2 Hz. Raising the mean contrast to 0.5 produces a slight improvement in overall sensitivity and a huge improvement in temporal resolution: sensitivity remains high up to 16 Hz. At high mean contrast the temporal resolution in discriminating the direction of motion of contrast modulations is comparable to that shown when the task is simply to detect the motion of the envelope. Temporal resolution of sinusoidally amplitude-modu- lated 2-D noise patterns with high mean contrast is also extremely good (Lu & Sperling, 1995).

The most likely explanation for the excellent temporal resolution that occurs at high contrasts is that under these circumstances the moving contrast patterns are processed by mechanisms similar or identical to those that normally process moving luminance patterns. There are several ways that this could happen.

One possibility is that the visual system contains an array of second-order motion sensors that process the motion of contrast-modulated patterns and that have identical temporal resolution to first-order motion sensors (Lu & Sperling, 1995). Although this represents an attractive possibility, it is surprising that this array of sensors should be completely insensitive to contrast patterns with sinusoidal carriers of low or moderate mean contrast. It is also slightly suspicious that sensitivity varies in exactly the same way with changes in temporal frequency as in the mechanisms that process luminance patterns. Consequently, it is worth considering the possibility that the motion sensors that support this high temporal resolution are in fact the same ones that process moving luminance patterns. There are three ways in which this could come about.

302 Andrew Derrington

Modulation-sensitivity functions for detecting (circles) and discriminating the direction of motion (squares) of moving contrast-modulation envelopes of sinusoidal gratings of di erent contrast. Modulation sensitivity (the reciprocal of the modulation depth at which performance in the task reaches 75% correct) is plotted as a function of temporal frequency. When the carrier contrast is 0.1 (open symbols) sensitivity in the direction-discrimination task falls o rapidly at temporal frequencies above 2 Hz and was too low to measure at 8 Hz; sensitivity in the detection task, which could be performed simply by detecting the slight first-order flicker associated with the second-order motion, falls o very slowly and is still measurable at 16 Hz. When the carrier contrast is raised to 0.5 (solid symbols), the two tasks show very similar, shallow declines in sensitivity with temporal frequency, as though the direction of motion of the contrast envelope were being signaled by a standard motion filter, although performance is still better in the detection task than in the discrimination task.

First, in the case of modulated random-noise patterns, the display itself is likely to contain local patches of moving luminance patterns. These should arise because the noise carrier contains a very wide range of spatial frequencies, so we should expect that within relatively large local patches of the pattern there will be slight deviations from the mean luminance, although these will average out over large areas. When the noise is multiplied by the moving sinusoidal envelope, the areas of higher or lower mean luminance will generate local patches of moving luminance

grating. Motion sensors that integrate over large areas would not sense these signals, but ones that integrate over small areas would. It is di cult to be certain whether such local luminance signals could account for the high temporal resolution that occurs with moving contrast-modulated noise patterns (Lu & Sperling, 1995). On the one hand, resampling the noise on every frame, which should remove any systematic local luminance signals, reduces temporal resolution (Smith & Ledgeway, 1998) on the other, a computer simulation of a motion-energy sensor failed to detect any systematic motion signal in contrast-modulated noise (Benton & Johnston, 1997).

A second possibility is that the same motion sensor might be sensitive both to luminance patterns and to contrast patterns.The multichannel gradient motion sensor can be implemented in a way that makes it sensitive both to first-order and to second-order motion (Johnston et al., 1992). This is an attractive possibility, but it does not explain why temporal resolution for contrast patterns should be so much worse when carrier contrast is low, unless the multichannel gradient sensor is sensitive only when carrier contrast is high.

A third possibility is that distortion within the visual pathway causes the contrast pattern to generate a signal (a “distortion product”) in the luminance pathway.There is independent evidence for nonlinearities early in the visual pathway that would have exactly this e ect (MacLeod,Williams, & Makous, 1992). Scott-Samuel (1999) found that observers were able to discriminate consistent motion when a contrastmodulated grating flickers in alternation with a sinusoidal grating of the same spatial frequency as the envelope. The direction of motion of the compound stimulus suggests that an internal luminance-like signal (a distortion product) is generated from the contrast-modulated grating by a compressive nonlinearity (Scott-Samuel, 1999). The magnitude of the distortion product should grow in proportion to the product of the carrier contrast and the modulation depth. This accelerated growth would explain why it is only when contrast is high that second-order contrast patterns support good temporal resolution in motion discriminations: high contrast is needed to ensure that the distortion product is large enough to be processed by the “standard” motion processing filters. How then is the motion of these patterns processed when contrast is low?

The simplest assumption is that the visual system does not have a motion filter that analyzes the motion of contrast patterns and that their motion is simply inferred from the displacement of features over time. Indirect evidence for this is that these patterns do not support a normal motion aftere ect (Derrington & Badcock, 1985) and they do not give rise to optokinetic nystagmus (Harris & Smith, 1992).

More direct evidence comes from the fact, illustrated in Figure 23, that the contrast needed to discriminate the direction of motion of a beat pattern increases when a stationary pedestal is added to the moving pattern. The impairment of motion discrimination performance by the addition of a pedestal is an indication that the motion discrimination depends on feature-tracking rather than on filtering (Lu & Sperling, 1995). Figure 23 also confirms that motion discrimination of