Abstract

Contour curvature (CC) is a vital cue for the analysis of both form and motion. Using functional magnetic resonance imaging, we localized the neural correlates of CC for the processing and perception of rotational motion. We found that the blood oxygen level–dependent signal in retinotopic area V3A and possibly also lateral occipital cortex (LOC) varied parametrically with the degree of CC. Control experiments ruled out the possibility that these modulations resulted from either changes in the area of the stimuli, the velocity with which contour elements were actually translating, or perceived angular velocity. We conclude that neurons within V3A and perhaps also LOC process continuously moving CC as a trackable feature. These data are consistent with the hypothesis that V3A contains neural populations that process trackable form features such as CC, not to solve the “ventral problem” of determining object shape but in order to solve the “dorsal problem” of what is going where.

Introduction

The goal of this research was to employ functional magnetic resonance imaging (fMRI) and psychophysics to characterize brain circuitry that uses contour curvature (CC) as a primary cue for the computation of 2-dimensional (2D) rotational object motion. It has been widely recognized that CC is an important cue for shape processing (Attneave 1954; Kristjansson and Tse 2001). In this paper, we investigate the possibility that CC may also be an important cue in motion processing.

How the visual system constructs the perception of motion from the temporal dynamics of the retinal image is a fundamental question that continues to challenge vision scientists. This is true even for the perception of relatively simple stimuli such as those completely defined by a closed contour. At the heart of the problem is the fact that an infinite number of 3D velocity fields can generate the same 2D retinal sequence. The local motion information at any point along a contour is consistent with an infinite number of possible motions that all lie on a “constraint line” in velocity space (Adelson and Movshon 1982) for the 2D case. The problem of interpreting this many-to-one mapping is commonly termed the “aperture problem” (Fennema and Thompson 1979; Adelson and Movshon 1982; Marr 1982; Nakayama and Silverman 1988).

Explaining how the aperture problem is solved is perhaps the most basic challenge that must be met by any model of motion perception. Although there are several theoretical solutions to the aperture problem that account for many aspects of motion perception, no single general theory has yet emerged that can explain how the visual system actually processes motion in every instance. Several models that provide reasonable solutions to the aperture problem for the case of translational motion, such as “intersection of constraints” and “vector summation” models, fail to provide unique solutions in the case of rotational motion.

An account that provides a solution to the aperture problem in the case of both translational and rotational motion is that based upon the tracking of “trackable features” (TFs, Ullman 1979). Image features, such as contour corners, terminators, and junctions, can provide unambiguous motion signals when they correspond to attributes that are intrinsically part of the moving object.

This paper seeks to isolate the neural circuitry underlying the processing of CC as a TF for the perception of motion in general and rotational motion in particular.

Materials and Methods

Subjects

Results Psychophysics Experiment 3

The results of the psychophysics are illustrated in Figure 3B and demonstrate that as the degree of CC increased so did the subjectively perceived speed of rotation. This was demonstrated by the fact that stimulus groups 4 and 5 (greater CC than the control, shown as the yellow and pink bumps in Fig. 1d) had to be rotated slower than 126°/s to be perceived to be rotating at the same angular velocity as the control group. In contrast, stimulus groups 1 and 2 (less CC than control, shown as the red and green bumps in Fig. 1d) had to be rotated faster than 126°/s to be perceived to rotate at the same angular velocity as the control group. Overall, as the degree of CC increased, so did the perceived speed of rotation.

Figure 3.

Experiment 3: Psychophysics. (A) Psychophysics paradigm: a group of 13 control stimuli (Fig. 2d blue) rotating at 126°/s was presented to subjects for 500 ms. Subjects were then presented with a test group, adjusted for size according to experiment 2, for 500 ms rotating either faster or slower than the control stimulus. Subjects indicated via a button press whether the test group was rotating faster or slower than the control. (B) Results of experiment 4 psychophysics: the color of the plotted bars corresponds to the stimuli bounded by similar color in Figure 2d corrected for size as in experiment 2. The magnitude of the bars indicates how much faster or slower in percentage relative to the control group, each test stimulus group needed to be rotated in order to be perceived as rotating at the same angular velocity (point of subjective equality) as the control group (blue). As the degree of CC increased, the point of subjective equality decreased. This indicates that the higher curvature bumps were perceived to rotate faster than lower curvature ones. Error bars indicate the standard error of the mean across subjects.

Figure 3.

Experiment 3: Psychophysics. (A) Psychophysics paradigm: a group of 13 control stimuli (Fig. 2d blue) rotating at 126°/s was presented to subjects for 500 ms. Subjects were then presented with a test group, adjusted for size according to experiment 2, for 500 ms rotating either faster or slower than the control stimulus. Subjects indicated via a button press whether the test group was rotating faster or slower than the control. (B) Results of experiment 4 psychophysics: the color of the plotted bars corresponds to the stimuli bounded by similar color in Figure 2d corrected for size as in experiment 2. The magnitude of the bars indicates how much faster or slower in percentage relative to the control group, each test stimulus group needed to be rotated in order to be perceived as rotating at the same angular velocity (point of subjective equality) as the control group (blue). As the degree of CC increased, the point of subjective equality decreased. This indicates that the higher curvature bumps were perceived to rotate faster than lower curvature ones. Error bars indicate the standard error of the mean across subjects.

Results fMRI Experiment 3

Psychophysical data allowed the presentation of stimuli in the fMRI portion of the experiment to be individually calibrated for each subject so that the perceived speed of rotation was the same across stimulus groups. Retinotopic ROIs were available for all 12 of the subjects who participated in this experiment. In addition, hMT+ and LOC were localized for 9 of the subjects. Figure 2C indicates the degree to which percent BOLD signal varies parametrically with CC in each of the ROIs. Table 3 provides the statistical results of the repeated-measures ANOVA. Parametric variation of percent BOLD signal change with increasing CC was only observed in area V3A.

Table 3

Statistical results for experiment 3

 Area\Stats F score P value Effect size (ηp2) V1 F1,11 = 0.121 >0.73 0.011 V2v F1,11 = 0.772 >0.41 0.062 V2d F1,11 = 0.088 >0.77 0.008 V3v F1,11 = 0.35 >0.56 0.031 V3d F1,11 = 0.014 >0.90 0.001 V3A F1,11 = 14.252 <0.003 0.564 V4v F1,11 = 0.561 >0.46 0.048 hMT+ F1,8 = 4.19 >0.07 0.344 LOC F1,8 = 4.11 >0.077 0.34
 Area\Stats F score P value Effect size (ηp2) V1 F1,11 = 0.121 >0.73 0.011 V2v F1,11 = 0.772 >0.41 0.062 V2d F1,11 = 0.088 >0.77 0.008 V3v F1,11 = 0.35 >0.56 0.031 V3d F1,11 = 0.014 >0.90 0.001 V3A F1,11 = 14.252 <0.003 0.564 V4v F1,11 = 0.561 >0.46 0.048 hMT+ F1,8 = 4.19 >0.07 0.344 LOC F1,8 = 4.11 >0.077 0.34

Note: For each of the individually identified ROIs, F scores, P values, and effect sizes are shown for the repeated-measures ANOVA with linear contrast. ROIs in which a significant amount of variance was accounted for by the linear contrast are shown in bold font (V3A).

Interestingly, however, the BOLD signal in both hMT+ and LOC appears to have some parametric relationship (albeit statistically insignificant P > 0.07) with CC. Directly interpreting “near-significant” results can be very difficult; however, it would be imprudent to neglect such results without first attempting to eliminate potential sources of confounding noise. One possible source of noise can arise from the threshold criterion for determining the hMT+ and LOC masks. For example, too liberal a criterion could include voxels not directly responsive to our stimuli. Because all the voxels within the localized masks are averaged together, these “extra” voxels would only serve to reduce the signal to noise ratio. In order to investigate this possibility, a second set of hMT+ and LOC masks was created using a stricter threshold criterion. Using these masks, the analysis was repeated and revealed that LOC was indeed parametrically modulated (F1,8 = 5.48, P < 0.047, ηp2 = 0.407), whereas hMT+ was not (F1,8 = 2.07, P > 0.18, ηp2 = 0.206). From this, we conclude that in addition to V3A, the LOC is more likely than hMT+ to process CC as a cue for rotational motion.

The results of this experiment indicate that the parametric modulation of BOLD signal observed in area V3A was not due to the perceived speed of rotation. Based on the results of experiments 1, 2, and 3, we can conclude that the percent BOLD signals observed in V3A, and possibly the LOC among the areas tested, vary parametrically with the CC of the stimuli. Figure 5 illustrates as an example the GLM activation map in a given subject for parametric modulations as a function of CC for each of the 3 experiments.

Figure 4.

Individual ROI analysis. Based on a voxel by voxel GLM analysis performed in each subject individually, mean beta weights were computed within each ROI and then averaged across hemisphere. (A) The mean beta weights for each stimulus condition for area hMT+ across subject. (B) The raw beta weights for each subject converted to Z scores to eliminate between-subject magnitude variance. (C) A repeated-measures ANOVA with a linear contrast incorporating the data from all subjects performed on the Z scores to determine the degree of parametric percent BOLD signal change across stimulus condition.

Figure 4.

Individual ROI analysis. Based on a voxel by voxel GLM analysis performed in each subject individually, mean beta weights were computed within each ROI and then averaged across hemisphere. (A) The mean beta weights for each stimulus condition for area hMT+ across subject. (B) The raw beta weights for each subject converted to Z scores to eliminate between-subject magnitude variance. (C) A repeated-measures ANOVA with a linear contrast incorporating the data from all subjects performed on the Z scores to determine the degree of parametric percent BOLD signal change across stimulus condition.

Figure 5.

Single-subject activation maps. Activation map based on a single-subject GLM (fixed effects) showing parametric BOLD variation as a function of CC in a single exemplar subject (left hemisphere). The activation maps for (A) experiment 1, (B) experiment 2, and (C) experiment 3 are shown overlaid with this subject's ROIs outlined in black.

Figure 5.

Single-subject activation maps. Activation map based on a single-subject GLM (fixed effects) showing parametric BOLD variation as a function of CC in a single exemplar subject (left hemisphere). The activation maps for (A) experiment 1, (B) experiment 2, and (C) experiment 3 are shown overlaid with this subject's ROIs outlined in black.

Experiment 4: Monitoring Eye Movements

In any fMRI study investigating neuronal activations within the retinotopic areas of the visual cortex, one has to take into consideration the role of eye movements (both voluntary and involuntary fixational microsaccades) as a potential source of confounding retinal stimulation. Due to technological limitations, we were unable to record eye movements during the fMRI scans. However, in order to determine whether or not a systematic relationship between our stimulus conditions and eye movements existed, we monitored the eye movements of a subset of subjects who participated in the fMRI experiments outside the scanner.

Methods

Twelve subjects (the 2 authors and 10 naïve Dartmouth students) participated in this control experiment conducted outside the scanner. Each subject was presented with one stimulus run like those presented in experiment 1 while simultaneously having their eye movements monitored using the presentation and eye-tracking system described in the psychophysics portion of experiment 3. As in the scanner, subjects were instructed to maintain fixation and press a button whenever the fixation square changed color.

The detection of microsaccades was performed in MATLAB using detection algorithms developed by Engbert and Kliegl (2002). The number and amplitude of microsaccades were computed for each stimulus condition. A repeated-measures ANOVA with linear contrast was performed to determine if there was a parametric relationship between eye movements and the CC of the stimulus groups.

Results

There was no statistically significant parametric variation in the number (F1,11 = 0.316, P > 0.58, ηp2 = 0.028) or amplitude (F1,11 = 1.26, P > 0.28, ηp2 = 0.103) of microsaccades across stimulus condition. Importantly, the effect sizes for the 2 ANOVAs were quite small relative to the effect sizes observed in the fMRI portions of the study. Subjects were nearly perfect (98% hit rate) in successfully responding to the fixation color changes. All responses to fixation color changes occurred within 1 s of the actual color change.

Discussion of Eye Movements

Although eye movements were not recorded during the fMRI runs, the above results indicate little or no correlation between the stimulus groups and the rate or magnitude of eye movements. For this reason, we conclude that eye movements and the confounding retinal stimulation they produce are unlikely to be the source of the parametric BOLD activations we see studying our fMRI experiments. Further evidence against the role of eye movements can be found in the fMRI data themselves in which BOLD modulations in V1 are not observed, as one would expect with systematic variations of eye movements.

General Discussion

Past research on smoothly moving contours has suggested that contour relationships contribute to motion analysis. Wallach (1935, 1976; Wuerger and others 1996) found that the perceived direction of motion of a straight line drifting smoothly behind an aperture depends on the shape of that aperture, even though such a line does not possess a mathematically well-defined direction of motion. Rather than being constructed from the ill-defined motion of the line itself, the motion percept followed the well-defined direction of motion of the line terminators defined by the aperture. In doing so, Wallach presaged what many years later would be called the aperture problem (Marr and Ullman 1981; Marr 1982; Hildreth 1984; Movshon and others 1985).

More recent work has shown how such terminator motions influence processes such as amodal completion and global integration of local motion signals (Lorenceau and Shiffrar 1992; Shiffrar and others 1995). However, the interactions of form and motion are not limited to local contour terminators. For example, there are several illusions where a 3D shape appears to change its direction of rotation depending on the 3D form interpretation one places over the moving object (e.g., Ames' rotating trapezoidal window illusion, Ames 1951; the rotating mask illusion, e.g., Klopfer 1991; motion from structure, e.g., Ullman 1979). Others (Dosher and others 1986) have noted that when a Necker stimulus is continuously rotated from a stationary position, it appears to rotate in a direction consistent with the 3D interpretation it had when stationary.

Similarly, Sinha and Poggio (1996) have shown that the representation of the 3D form of an ambiguous “rotating” wire silhouette determines whether rigid rotation or deformation is seen. They rotated a computer-generated wire silhouette. Although an infinity of 3D motions are consistent with the silhouette motion, an assumption of object rigidity allows the perception of a single rigidly rotating 3D shape. When a new wire is rotated from an initial position that happens to cast the same silhouette as the final position of the first wire, observers tend to see the wire deform, as the silhouette takes on shapes inconsistent with the shape inferred from the first rotating silhouette. Interestingly, observers who do not receive training with the first wire do not see deformation in the second stimulus but instead see rigid rotation. This demonstrates both the existence of an object rigidity assumption and the existence of an internal 3D model that can bias perceived motions toward paths involving rigid rotation or deformation. These studies demonstrate that global form analysis plays a role in the perception of continuous rotational motion.

The purpose of the experiments conducted in this study was to identify where in the brain such global form–motion processing takes place specifically in the context of 2D rotational motion. Each of the 3 studies controlled for a different aspect of the visual stimulus and together isolated CC as the sole form cue that varied across stimulus conditions. The convergent results of the 3 fMRI experiments identify visual area V3A and possibly the LOC as potential locations for neuronal activity underlying the processing of CC as a TF for the perception of continuous rotational motion.

Human V3A has been shown to be motion selective using neuroimaging techniques (fMRI: Tootell and others 1997; Braddick and others 2000, 2001; Vanduffel and others 2002; Vaina and others 2003; Lui and others 2004; Koyama and others 2005; Liu and Wandell 2005; Moutoussis and others 2005; magnetoencephalography: Schellart and others 2004; Aspell and others 2005). While anatomical investigations on the brain of nonhuman primates have revealed that V3A has direct reciprocal connections with primate area MT (for review of primate MT, see Born and Bradley 2005), it has been shown that V3A in humans is much more sensitive to motion than in nonhuman primates (Tootell and others 1997; Vanduffel and others 2001; Orban and others 2003). That we find activity in V3A to be parametrically modulated by CC is consistent with the work of Schira and others (2004) who demonstrated that percent BOLD signal in V3A is correlated with contour and figural processing, even in the absence of conscious perception. Figural processing is central to the TFs argument as the motion signal derived from the TF must be generalized to the rest of the contour. Whereas their findings demonstrated that V3A responded to figural contours, our findings extend and go beyond these by demonstrating that the percent BOLD signal in V3A is parametrically modulated by CC specifically in the context of continuous rotational motion. Unlike previous work, we provide a functional role for the processing of contours in V3A, namely, regions of high curvature can serve as a form-based TF that can be used by the visual system to solve the aperture problem.

Our findings are also consistent with recent imaging work that has investigated the neural correlates of form–motion interactions. Several groups (Braddick and others 2000, 2001; Vaina and others 2003; Moutoussis and others 2005) have shown that percent BOLD signal change in V3A was greater for coherent than for random motion. Koyama and others (2005) showed that V3A is more responsive to radial than to translational motion, at least in the central portion of the visual field. These findings suggest a role for V3A in the generation of global motion percepts. Our findings expand upon this work by suggesting a specific mechanism concerning how form and motion may interact to construct global motion percepts. Namely, we hypothesize that neural activity within V3A serves to extract reliable motion information from regions of high CC. Such TF motion information may then be propagated to the entire moving object, resulting in the global motion percept. The convergent evidence from these studies, as well as our own, leads to the hypothesis that V3A contains neural populations that process form, not to solve the “ventral problem” of determining object shape, but in order to solve the “dorsal problem” of what is going where. The form analysis that we hypothesize takes place here involves the specification and tracking of key TFs, such as CC.

Trackable Features

Motion perception is beset with the problem that many of the motion signals generated by early detectors in the visual system are ambiguous. There are many motions in the world that can give rise to any particular motion observed at the level of the retina or later. This ambiguity, known as the aperture problem, arises because of the receptive field properties of neurons in the early stages of visual processing.

The receptive fields of early motion detectors are small and tuned for orientation. Because of this, motion can only be detected by these neurons in the direction perpendicular to a neuron's orientation. Many authors have argued that the aperture problem can be solved by integrating component motion signals along the contour (Bonnet 1981; Burt and Sperling 1981; Adelson and Movshon 1982; Watson and Ahumada 1985). These models are based on the assertion that ambiguous motion signals can, via integration, be disambiguated. However, certain locations along a contour such as corners, terminators, and junctions do not move ambiguously when they are intrinsically part of the moving object. An alternative solution to the aperture problem lies in exploiting such TFs in order to disambiguate ambiguous component motion signals that arise along portions of contour distant from TFs (Ullman 1979).

Recent neurophysiological data have shown that neurons in MT in the macaque respond more to terminator motion in a barber pole stimulus than to the ambiguous signals generated by portions of the contour away from terminators. Furthermore, they respond more to intrinsically owned terminators than to extrinsic terminators (Pack and others 2004). It has also been shown that neurons in MT in the macaque will initially respond to the direction of motion that is perpendicular (component direction) to a moving line independent of the actual direction of motion (Pack and Born 2001). These same neurons will, over a period of ∼60 ms, shift their response properties so that they respond to the true motion of the line independent of its orientation, suggesting that the unambiguously moving endpoints of the line are quickly but not instantaneously exploited to generate a veridical motion solution. The response properties of these neurons match behavioral data that show that initial pursuit eye movements will be in the direction perpendicular to the moving line and then rapidly adapt to follow the direction of veridical motion as defined by the line terminators (Pack and Born 2001). There is also neurophysiological evidence of end-stopped neurons in V1 that respond to the motion of line terminators independently of the line's orientation (Pack and others 2003), suggesting that form-based TFs such as line terminators can be directly extracted from the image as early as V1. Such cells are largely immune to the aperture problem.

In line with this view, features to which such end-stopped cells would respond have been shown psychophysically to be processed both rapidly and in parallel across the visual scene. Visual search studies have found several form-based “features,” including certain types of contour junctions (Enns and Rensink 1991), contour concavities (Hulleman and others 2000), corners (Humphreys and others 1994), CC (Wolfe and others 1992), and CC discontinuities (Kristjansson and Tse 2001), that will pop out among a set of distracters. It is commonly believed that features that exhibit pop out during visual search are processed rapidly and in parallel across the visual field (Treisman and Gelade 1980), suggesting the existence of hardwired contour discontinuity detectors. Indeed, contour discontinuity information may begin to be extracted even before V1 because circular center-surround receptive fields will respond more to corners than to edges and more to bar terminators than corners (Troncoso and others 2005).

Perceptual Phenomenology of Rotational Motion

Caplovitz and others (2006) characterized the relationship between the degree of curvature along the contour of an ellipse and the speed at which it is perceived to rotate. They found that as the degree of CC increases, so does the perceived speed of rotation. Thus, a skinny ellipse will be perceived to rotate faster than a “fat” ellipse. This observation served as the basis for the design of experiment 3 of the current study, in which the perceived rotational speed of the bumps was shown to parametrically modulate with CC. Indeed, we hypothesize that this illusory percept results from the processing of motion signals generated by the regions of high curvature (TFs) and that the modulation of percent BOLD signal observed in V3A, hMT+, and LOC may reflect this processing.

It is important to note, however, that both the illusory percept of rotational speed as well as the TFs hypothesis only apply to percepts of rigid rotation. It has been shown (Wallach and others 1956; Weiss and Adelson 2000) that a low-aspect ratio ellipse rotating continuously in the 2D plane can be perceived to deform as though its contour were made out of jelly. This nonrigid percept can be influenced by many factors including the presence of satellites (Weiss and Adelson 2000) but most importantly depends on the aspect ratio of the ellipse being low (i.e., close to 1). In the case of nonrigid motion, the question of rotational speed no longer applies because the object is not perceived to rotate at all, but to deform. Similarly, because the shape of the nonrigid object is continuously changing, the concept of a shape-defined TF for a gelatinous ellipse is ill-defined. Based on the verbal reports of the participants (both authors and naives), we are confident that all the stimuli used in the current study were indeed perceived to rotate rigidly at all times by all observers.

Psychophysical evidence examining other forms of motion perception has demonstrated a critical link between form-defined features and the perception of rigid motion. An example can be found in the kinetic depth effect (Wallach and O'Connell 1953) in which the projected 2D image of a rotating, backlit, 3D bent wire will appear to pop out into a 3D rotating object. Importantly, the kinetic depth effect will only occur if the 3D bent wire object has regions of high or discontinuous curvature. Similarly, the phenomenon of anorthoscopic projection (Zollner 1862; von Helmholtz 1867/1925; Parks 1965), in which an object moving behind a narrow slit can be recognized, is also heavily dependent upon the presence of highly salient contour features. In the absence of corners or regions of high curvature, nonrigid motion is perceived through the slit, and object recognition does not occur. Based on these findings, one can speculate that the degree of CC or the presence of other TFs may play a critical role in determining whether a rotating object is perceived as rigid or nonrigid.

Conclusions

Based on the results of these experiments, we conclude that neuronal processing in area V3A and possibly the LOC serves to analyze CC as a TF for the perception of rotational motion. This raises the possibility that these areas contain neural populations that process form, not to solve the ventral problem of determining object shape but in order to solve the dorsal problem of what is going where. We predict that neurons in V3A and possibly in the LOC will respond to the continuous motion of other TFs defined by contour discontinuities, such as junctions, corners, and terminators.

We thank Melissa Henley for assistance in collecting and analyzing data. This project was funded by NIH R03 MH0609660-01 grant to PUT and NSF fellowship 2005031192 to GPC. Conflict of Interest: None declared.

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