The Mechanism of Interaction between Visual Flow and Eye Velocity Signals for Heading Perception

Transcription

1 Neuron, Vol. 26, , June, 2000, Copyright 2000 by Cell Press The Mechanism of Interaction between Visual Flow and Eye Velocity Signals for Heading Perception Albert V. van den Berg* and Jaap A. Beintema Helmholtz School for Autonomous Systems Research Department of Physiology Faculty of Medicine Erasmus University Rotterdam P.O. Box DR Rotterdam The Netherlands Summary A translating eye receives a radial pattern of motion that is centered on the direction of heading. If the eye is rotating and translating, visual and extraretinal signals help to cancel the rotation and to perceive heading correctly. This involves (1) an interaction between visual and eye movement signals and (2) a motion template stage that analyzes the pattern of visual motion. Early interaction leads to motion templates that integrate head-centered motion signals in the visual field. Integration of retinal motion signals leads to late interaction. Here, we show that retinal flow limits precision of heading. This result argues against an early, vector subtraction type of interaction, but is consistent with a late, gain field type of interaction with eye velocity signals and neurophysiological findings in area MST of the monkey. Introduction Our eyes are placed on top of an array of mobile sup- ports like ankles, hips, torso, and the head. The rotation of these body parts as well as the rotation of the eyes complicates the perception of heading from the retinal flow. A translating eye receives a radial pattern of motion, or optic flow, that emanates from the direction of heading (Gibson, 1966). Any rotation of the eye, however, will shift the center of the flow on the retina in the direction of the eye rotation or it will obliterate the radial structure altogether. Thus, the direction of heading no longer corresponds to the center of the pattern of retinal motion. Yet, for eye pursuit (Royden et al., 1992, 1994; Banks et al., 1996; van den Berg, 1996) and self-generated head movement (Crowell et al., 1998), correct heading perception remains the rule. This performance results from visual analysis and the interplay between visual and extraretinal signals concerning eye and head rotation (Warren and Hannon, 1988; Royden et al., 1992; van den Berg, 1992). Monkey studies have identified areas in the temporal and parietal cortex that analyze the visual motion in a way that is relevant for heading perception. At these stages, cells have wide fields of view in which visual * To whom correspondence should be addressed ( vandenberg@ fys.fgg.eur.nl). motion signals are integrated spatially. Many units collect differently directed motion from different retinal regions. Hence, these units prefer certain patterns of motion (e.g., radial motion or circular motion) and behave like motion templates (Duffy and Wurtz, 1991; Graziano et al., 1994; Lappe et al., 1996). We call this the motion template stage of analysis. Psychophysically, the motion template stage is revealed by a clear performance increase for pattern of motion discrimination as the visible extent of the pattern grows (Morrone et al., 1995). We ask whether the motion templates integrate retinal motion signals or whether the integration involves motion signals that are corrected by an extraretinal signal for the rotation of the eye. Our question relates to the general problem of what kind of processing strategy the brain uses to blend streams of information that have widely different formats. This problem arises regularly in the context of multisensory information processing for example, the blending of eye-centered visual and head- centered auditory information on where an object is or the combination of a field of vertical disparity (that visually specifies binocular eye orientation [Gårding et al., 1995]) with rate-coded eye position signals for percep- tion of surface orientation. What difference in the formats of the eye velocity signals and visual flow compli- cates their interaction? Eye velocity signals specify information that is mathe- matically equivalent to a single vector that represents the spin of the eye (the components of rotation about a horizontal, a vertical, and a torsional axis). Visual infor- mation about the eye rotation, however, has an entirely different format. It consists of a map of angular motion vectors (one vector for each visual direction toward an object in the environment) that represents the image motion caused by the eye rotation. For a meaningful interaction, either the eye velocity signal needs to be transformed into a map of angular velocity vectors or an eye rotation like signal (i.e., a single vector) must be derived from the map of visual motion vectors. Our analysis focuses on the case of a head moving on a linear track through space combined with an eye rotation. For the more general case in which the head is also rotating, extraretinal signals (vestibular or efference copy) on the head s rotation should come into play. The priciples of interaction that will be discussed below pertain to that case also. Two models have been presented that take into ac- count the interaction between visual and extraretinal eye movement signals to explain the perception of heading during eye rotation. The vector subtraction scheme uses the extraretinal signal to subtract out at each retinal location the motion component that corresponds to the eye rotation (Royden et al., 1994). Essentially, that scheme proposes that the brain transforms the spin vector of the eye into a map of angular velocity vectors. This serves to recover the radial flow pattern relative to the head that would be seen by the nonrotating eye. Because the center of that radial pattern corresponds to the heading direction, an array of motion templates tuned to radial patterns of motion then suffices to identify the direction of self-motion. Thus, the motion templates of the vector subtraction model integrate local motion signals that represent the flow relative to the

2 Neuron 748 Figure 1. Example of a Pooling Unit in the Velocity Gain Field Scheme The unit prefers radial motion for a fixating eye as shown in the upper panel ( 0 /s). If the eye rotates ( 3 /s), the retinal flow changes and the activity of the retinal unit drops from the maximum activity (open circles) to a lower level (closed circle). The drop is approximated by the product of the eye velocity and the tangent to the tuning curve ( O/ R). This tangent can be derived from a visual unit that is sensitive to the component of local direction change of the flow due to eye rotation. The flow pattern preferred by such a unit is shown in the rightmost panel. Eye rotation adds a parallel component to the retinal flow. For approach of a wall, this results in a shift of the center of the radial pattern on the retina in the direction of the eye rotation. Because of the aperture, the radial pattern of flow on the screen may thus become nearly parallel flow on the retina (Figure 2c) or vice versa (Figure 2d). This begs the question of whether the precision of heading is limited by the pattern of retinal flow or the pattern of flow on the screen. If retinal motion signals are spatially integrated first, the precision of heading perception is limited by the structure of the retinal flow, because the extraretinal signal cannot remedy the loss of information for conditions of nearly parallel retinal flow. This would be pre- dicted by the velocity gain field scheme. For vector subtraction, precision should be limited by the pattern of flow on the screen because that scheme removes the effect of the eye rotation prior to spatial integration and recovers the flow relative to the head, which equals the flow on the screen, if the head is stationary. Thus, most precise heading percepts should occur for radial patterns of flow on the screen if vector subtraction applies, but for radial patterns of flow on the retina if the velocity gain field applies. head (or relative to the world if head velocity were also accounted for). Alternatively, no attempt is made to recover the radial flow. In the velocity gain field scheme (Beintema and van den Berg, 1998), the retinal motion signals are integrated in the template stage. The change of the retinal flow due to eye rotation will now cause a change in activity of any motion template that prefers a pattern of radial motion on the retina (Figure 1). The gain field scheme computes such a unit s change in activity in order to cancel that change. This cancellation results in a signal that is the same as if the eye were fixating. To first order, the change in activity equals the derivative of the unit s tuning curve to rotational flow (represented by the activity of a different kind of motion template) multiplied by the extraretinal eye velocity signal (the eye velocity gain field; van den Berg and Beintema, 1997; Beintema and van den Berg, 1998). The derivative signal is proportional to the eye velocity for a range that is limited by the tuning properties of that visual unit. Thus, the gain field scheme proposes that the brain uses the alternate strategy for meaningful interaction: an eye rotation estimate is derived from the visual map of motion signals. Thus, both models integrate motion signals, but of a different kind: retinocentric in case of the gain field scheme, head-centric in case of vector subtraction. An important structural difference between the models (possibly open to further anatomical or physiological analysis) is that the spatial integration of visual motion signals precedes (velocity gain field) or follows (vector subtraction) the interaction with the extraretinal signal. We aimed to investigate whether the functional architecture of human heading perception corresponds more to one or the other scheme. We exploited a geometric constraint on heading perception to distinguish between these two possibilities. When the visible flow is limited to a small aperture, the center of the radial pattern may become difficult to localize if it is placed outside the aperture (Figure 2b, ). This holds because the nearly parallel flow within the aperture transforms small error in the local velocity signal (Figure 2b, red circle surrounding local motion vectors) into much larger error in the inferred center of flow (red shaded zone; Koenderink and van Doorn, 1987). A radial pattern within the aperture, however, supplies a robust estimate of the center of the flow (Figure 2a). Indeed, for fixation the variability in perceived heading is much higher when the center is located outside the aperture than within (Crowell and Banks, 1993). Results We simulated the head s approach of a wall (average speed, 1.5 m/s; distance, 8.5 m) in various directions. The subject pursued a point target moving horizontally at 3 /s or fixated a stationary target. The head was stabi- lized by supports. The wall was visible only through a10 diameter aperture at the center of the screen. Horizontal heading direction was varied over a 56 range symmetric with respect to the aperture. At the end of the motion sequence, subjects moved a pointer on the screen to indicate their perceived heading direction. Each condition of eye movement and simulated ap- proach direction was repeated to obtain mean and SD of the perceived heading direction. We were particularly interested in the SD of perceived heading as a measure of its precision. Mean perceived heading varied over a smaller range than simulated heading. Thus, subjects in general un- derestimated the heading s eccentricity. This deviation depended little on the eye s rotation (Figures 3a and 3b, left). Mean perceived heading was biased by about 6 (Figure 3b) in the direction of the eye rotation (red and green lines are offset relative to the blue line). For our experimental conditions, 3 /s eye rotation shifts the cen- ter of the radial pattern on the retina (the retinal focus) 18

3 Interaction of Visual Flow and Pursuit Signals 749 Figure 2. The Experimental Paradigm Shown are patterns of flow on the screen and on the back of the eye during fixation and pursuit to the left for two directions of heading (green ) toward a wall. Only a small part (diameter, 10 ) of the wall is visible. If simulated heading is straight ahead (a and c), the radial structure of the flow on the screen causes nearly parallel retinal flow during pursuit (c). For rightward heading (b and d), pursuit to the left can transform the nearly parallel flow on the screen into radial flow on the retina (d). The precision by which the center of the flow can be localized depends on the structure of the flow within the aperture. Uncertainty in the local motion measurement (indicated by the circular patch around two randomly chosen flow vectors in [a] and [b]) leads to much larger horizontal uncertainty for the implied center (the red elliptical zone on the screen) if heading is outside (b) the aperture than if inside (a). For fixation one cannot tell whether the flow on the retina or the screen limits precision because their structures are the same. During pursuit one can, because the flow on the retina in condition 2d allows more precise heading percepts, but the flow on the screen allows higher precision for condition 2c. The areas of uncertainty of the heading direction are smaller if more than two flow vectors are taken into account. Nevertheless, the advantage for radial flow within the aperture remains. of flow. Conversely, if heading percepts are equally pre- cise for parallel and radial flow, then the local motions must have been measured more precisely for the parallel flow (Koenderink and van Doorn, 1987). Our results show that most precise heading percepts occur consistently for a radial pattern of motion on the retina. On the screen the pattern is then also radial for fixation but much more parallel for pursuit. This result can be interpreted in two different ways. Either highest precision for the analysis of heading requires a radial pattern of flow on the retina irrespective of the eye s movement, or the brain analyzes the pattern of motion on the screen in such a way that nearly parallel local motion vectors on the screen are measured more precisely during pursuit than during fix- ation. To distinguish between these possibilities, we per- formed a control experiment. If during pursuit the local motion vectors on the screen are measured more pre- cisely, any perceptual task that depends on the local motion measurement should improve. A straightforward prediction would therefore be that subjects should be able to determine the direction of uniform motion on the screen more precisely during pursuit than during fixation. Thus, we compared the perceived direction of parallel flow during horizontal pursuit and during fixation. Subjects pursued or fixated a point target while observing a stationary reference line on the screen. Sub- jects had to judge the direction of motion on the screen of subsequently presented (500 ms) parallel flow (Figure 4a). The premotion reference line on the screen served to help subjects to judge motion relative to the head. Direction of motion on the screen was 22.5, 45, or 67.5 off the horizontal. Importantly, the horizontal component of the flow on the screen was fixed at 3 /s away from the heading direction. Apparently, subjects perceived directions of heading that did not correspond to the retinal focus. This shows that the extraretinal signal compensated for part of the 18 shift. The SD of the perceived heading direction was a V-shaped curve with a clear minimum. For fixation, SD was lowest at simulated headings of 4 (Figures 3a and 3b, right, ). Thus, heading was most precise if the center of the radial pattern was visible within the aperture, in line with previous observations (Crowell and Banks, 1993). For opposite directions of eye rotations (open circles, closed circles), the minima of SD were located at heading directions (center of radial flow on the screen) that were about 32 apart. Now, the minimum of each SD curve was obtained when simulated heading was outside the aperture. As a function of the retinal focus (shifing the curves for pursuit by 18 in the pursuit direction), the SD curves match much better (Figure 3c), and the highest precision was found when the center of the radial pattern was visible on the retina. The most precise heading occurred when a radial pattern of flow was visible on the retina. Yet, the SD curves did not match precisely for all eye rotations (Fig- ure 3c). The computed retinal focus locations were based on perfect pursuit. The mismatch agrees with a 10% 20% smaller shift of the retinal focus relative to the heading direction during pursuit, possibly due to lower eye pursuit than target speed. In independent experiments using comparable stimuli we found eye pursuit gain that ranged from 0.8 to close to 1.0. For fixation we know from theoretical (Koenderink and van Doorn, 1987) and experimental (Crowell and Banks, 1993) analysis that if the local motion vectors are mea- sured with equal precision, more precise heading percepts occur for radial than for nearly parallel patterns

4 Neuron 750 flow on the screen. This, in turn, leads us to conclude that the spatial integration of local motion signals pre- cedes the interaction with an eye movement signal. Thus, the human brain appears to derive a visual esti- mate of eye rotation from the retinal flow rather than converting the eye velocity signals into a field of retinal motion vectors. This argues against vector subtraction types of models. There are, however, some potential pitfalls that we discuss below. First, the compensation by the extrareti- nal signal was not complete, because some bias of per- ceived heading was found. Does this support a partial vector subtraction scheme? We believe not. Vector subtraction aims to recover the flow relative to the head. If the eye movement is underestimated, this will result in recovered flow that contains a remainder of the rotation, and its center will be shifted relative to the simulated heading direction. Because according to this model the recovered pattern forms the basis for the heading percept, the bias and the precision of heading will be the same as if a shifted pattern was shown on the screen to a fixating eye. Thus, for partial vector subtraction, Figure 3. Effect of Eye Rotation on the Perceived Heading and Its Precision for Apertured Flow (a) Shown are mean and SD of perceived heading direction as a function of the simulated heading and the eye s rotation for subject JD. Each datapoint is based on 16 settings. Point lifetime equaled presentation time. The dashed diagonal line in the left graph indicates perfect heading perception. (b) Across subject averages of mean and SD for different eye rotations and simulated heading. Error bars plot the SE of the mean. Data are based on five subjects and two conditions of simulated approach of a wall. Pursuit to the left, closed red circles; pursuit to the right, open green circles; fixation, blue crosses. For certain simulated heading directions and directions of pursuit, a drop of the SD of perceived heading of about 2 occurs (arrows). For these conditions, the nearly parallel flow on the screen is accompanied by radial flow on the retina. (c) The SD of heading as a function of the retinal focus location. Symbols are as in (b). The horizontal bar in (b) and (c) denotes the width of the aperture. for all flow directions. Thus, horizontal pursuit reduced the retinal velocity by 24% 65%, closely matching the retinal speed ratios for pursuit versus fixation in the heading experiment. The SD of the perceived motion direction was the same during pursuit (Figure 4b). This shows that local motion vectors on the screen are not measured more precisely during pursuit. Discussion We have observed that heading judgments are limited by the pattern of retinal flow, not by the structure of the Figure 4. The Precision of Perceived Direction of Uniform Motion (a) The sequence of events during a trial. Initially, the subject pursues a horizontally moving target (red circle) on a background that consists of a stationary reference line. The line disappears during the uniform motion on the screen (blue arrows), while pursuit continues. Finally, the line reappears and is aligned by the subject with the remembered flow direction. (b) The SD of the perceived flow direction for different simulated directions of parallel motion on the screen. Each data point is based on 16 settings by a single subject for a single pursuit direction (or fixation) and flow direction. Data of all (4) subjects are pooled in this figure. The motion directions were characterized by a 180 range, because the horizontal component of motion on the screen always matched the direction of pursuit. Horizontal flow corresponds to 0. Upward motion on the screen corresponds to 90 for rightward pursuit and 90 for leftward pursuit. In a single session, one pursuit and one fixation condition were measured, using the same stimuli and convention of angular orientation on the screen.

5 Interaction of Visual Flow and Pursuit Signals 751 equal shifts for the perceived heading and for the locus Thus, the site of interaction between extraretinal and of most precise heading should occur. However, the visual motion signals seems to be located in area MST, shift in perceived heading (between left- and rightward rather than MT. pursuit) was about 12, whereas the shift of the SD This by itself does not permit one to distinguish be- curves was 32. tween the two proposed models as the shift could result We initially focused on the question of whether the from a vector subtraction like interaction with an eye SD of heading was consistent with the structure of the velocity signal at the dendritic input stage of MST units retinal flow or with the structure of the flow relative to (Lappe, 1998) as well as by a multiplicative interaction the head, using eye pursuit as a tool to dissociate the at the output stage of units. A subset of cells in MST patterns of retinal and head-centric flow. Our observations shows modulation of the response to radial flow on the indicate that the structure of the retinal flow retina by eye velocity, but these cells do not shift their determines the precision of heading direction, arguing preferred locus for the center of the radial pattern (Brad- against the vector subtraction scheme. This assumes, ley et al., 1996). This would seem to be more consistent however, that pursuit does not improve the local flow with the velocity gain field scheme. We do not know, measurement. Could this assumption be false? however whether these cells contribute to the monkey s We found for simulated approach at 20 to the left heading percept as required by the gain field model. that the SD of perceived heading dropped about 2 for Thus, strong neurophysiological evidence for either rightward pursuit compared to fixation (left arrow in Figure scheme is lacking. 3b, right). A similar observation holds for leftward To our knowledge, models on the interaction between pursuit and heading 20 to the right (right arrow). Let s visual and extraretinal signals fall into the classes of assume that vector subtraction is correct. If so, more gain field like or vector subtraction like. Our results are precise heading during pursuit than during fixation of consistent with the velocity gain field account of heading the same pattern means that the head-centric flow was perception (Beintema and van den Berg, 1998) and provide measured more precisely during pursuit. This could be human-based data to discriminate between the two the case, because for these simulated headings and models of interaction between visual and extraretinals directions of pursuit the retinal speed was reduced from signals. Modulation of motion templates by extraretinal about 3 /s (during fixation) to values below 1.0 /s. (Reti- signals was also proposed in two other schemes to nal speed discrimination is known to improve for lower explain heading perception (Perrone and Stone, 1994; base speed.) The increase in precision of the retinal Bradley et al., 1996). We remark, though, that direct signals during pursuit might have boosted the precision support for a gain field type of interaction is not supplied of recovered head-centric flow. We tested this idea in by our data. the control experiment. Because vector subtraction is a In the case of the vector subtraction scheme, no model of interaction between local visual motion signals match to the extraretinal signal is derived from the visual and an extraretinal signal, it should apply equally to flow. The gain field model does derive an estimate of radial patterns of flow and to parallel patterns of flow the eye s rotation from the visual flow that can be compared on the screen. Thus, to rescue the vector subtraction to the extraretinal signal. Thus, visual and extraon model, we must conclude from our heading experiment retinal sources of information on the eye s rotation can that pursuit makes the measurement of the head-centric be compared, which might be useful for long-term cali- flow vectors more precise if it reduces the retinal motion. bration, for distinguishing self-generated from imposed But then we also predict that pursuit improves the precision rotation, and for the purpose of finding the center of of perceived direction of parallel flow on the screen. rotation (in the eye, in the neck, or in- or outside the We found, however, no change in precision in that case. body). Our results, then, show that the structure of the retinal A key feature of the velocity gain field model is the flow, not the recovered flow on the screen, limits the multiplicative modulation by an eye velocity signal of precision of heading. Moreover, they show that the ex- units that are sensitive to complex flow patterns. traretinal signal cannot counter the loss of information Through this interaction, the model can compensate for for parallel retinal flow. This implies that the site of inter- the change in activity of retinal flow sensitive units due action between visual and extraretinal signals is placed to eye rotation. The outcome of this compensation is a after the motion template stage. set of signals that are invariant under eye rotation. In Neurophysiological studies in the monkey have indicated other words, the units that carry such signals are now area MST as an important site for motion integra- dynamically tuned to retinal flow; the preferred flow on tion. Units in this area collect motion signals in a large the retina of such units is dependent on the eye part of the visual field and are selective to patterns of movement. rotational, radial, or linear flow or their combinations Current accounts of how the brain transforms retinal (Duffy and Wurtz, 1991; Graziano et al., 1994; Lappe et direction to head-centric or arm-centric reference frames al., 1996). Cells have also been reported to modulate rely on a multiplicative modulation of visual activity by their response with eye position (Bremmer et al., 1997) an eye position signal (Andersen et al., 1990). The underlying or eye velocity (Bradley et al., 1996), indicating effects mathematical principle (van den Berg and Beinor of an extraretinal signal. Moreover, some cells appear tema, 1997) is that a shift of a receptive field is equivalent to adjust their preferred location for the center of a radial to addition of a weighted sum of spatial derivatives of pattern depending on the direction of eye movement that receptive field. The weights should depend on the (Bradley et al., 1996; Paige and Duffy, 1999). required shift according to Taylor s expansion formula. Microstimulation of this area leads to shifts in per- Because for transformation between eye- and headcentered ceived heading in the monkey (Britten and van Wezel, coordinate systems the required shift is equal 1998). In contrast, area MT, which feeds directly into and opposite to the eye deviation, this principle neatly MST and which processes local motion signals, does leads to the requirement of multiplicative modulation of not appear to carry nonvisual signals (Wurtz et al., 1990). a receptive field by an eye position signal. Treating a

6 Neuron 752 tuning curve to rotational flow as a receptive field in the Banks, M.S., Ehrlich, S.M., Backus, B.T., and Crowell, J.A. (1996). abstract flow space of possible eye rotations, one can Estimating heading during real and simulated eye movements. Vi- apply the same principle to understand compensation sion Res. 36, for eye movements. Thus, multiplication between rateusing Beintema, J.A., and van den Berg, A.V. (1998). Heading detection coded extraretinal signals and map-based visual signals motion templates and eye velocity gain fields. Vision Res. 38, may be the common principle for transformations be tween reference frames for visual motion and visual di- Bradley, D.C., Maxwell, M., Andersen, R.A., Banks, M.S., and rection. Shenoy, K.V. (1996). Mechanisms of heading perception in primate visual cortex. Science 273, Experimental Procedures Bremmer, F., Ilg, U.J., Thiele, A., Distler, C., and Hoffman, K.-P. (1997). Eye position effects in monkey cortex. I. Visual and pursuit- In both experiments, the same four subjects participated. A fifth related activity in extrastriate areas MT and MST. J. Neurophysiol. subject participated only in the first experiment. All conditions of 77, heading direction and eye movement were presented in randomized Britten, K.H., and van Wezel, R.J.A. (1998). Electrical microstimulaorder. tion of cortical area MST biases heading perception in monkeys. In the first experiment, subjects pursued a moving red dot to the Nat. Neurosci. 1, right or left (3 /s) for 3 s or fixated a stationary dot on a dark screen. Pursuit always ended at the center of the screen. The flow was Crowell, J.A., and Banks, M.S. (1993). Perceiving heading with differshown during the last 0.5 s. The fixation dot was clearly discernible ent retinal regions and types of optic flow. Percept. Psychophys. from the dots in the flow, because of its 3 size. Flow was presented 53, within a 10 diameter aperture on the screen. The aperture and the Crowell, J.A., Banks, M.S., Shenoy, K.V., and Andersen, R.A. (1998). target were always concentric. Thus, the aperture moved 1.5 during Visual self-motion perception during head turns. Nat. Neurosci. 1, pursuit. We simulated linear approach (speed varied randomly be tween 1.0 and 2.0 m/s) of a wall covered with dots (distance, 9 m Duffy, C.J., and Wurtz, R.H. (1991). Sensitivity of MST neurons to at the onset of the flow presentation). optic flow stimuli. II. A continuum of response selectivity to large- Simulated heading varied in 8 steps from 28 left to 28 right of field stimuli. J. Neurophysiol. 65, the screen s center. Each condition was repeated 16 times. We collected data in two sessions that used the same set of heading Gårding, J., Porrill, J., Mayhew, J.E.W., and Frisby, J.P. (1995). Stere- directions and pursuit speeds but varied in the lifetime of the dots opsis, vertical disparity and relief transformations. Vision Res. 35, (as long as the flow duration or randomly limited lifetime up to ms). In the latter condition, new points appeared at 9 m distance Gibson, J.J. (1966). The Perception of the Visual World (Boston: throughout the trial, whereas in the former condition the entire set Houghton Mifflin). of dots approached. The dots approached no more than 1.0 m in Graziano, M.S.A., Andersen, R.A., and Snowden, R.J. (1994). Tuning any of the reported conditions. In the final frame, more than 20 dots of MST neurons to spiral motions. J. Neurosci. 14, were visible in each condition. The distances of the points in the final frame varied slightly across conditions (range, 8 9 m). Koenderink, J.J., and van Doorn, A.J. (1987). Facts on optic flow. The shift (S) of the center of radial flow on the retina relative to Biol. Cybernet. 56, the center of flow on the screen is computed as: S distance Lappe, M. (1998). A model of the combination of optic flow and target rotation/speed. Because the speed varied across trials, we extraretinal eye movement signals in primate extrastriate visual cor- computed for all trials the shift S halfway during the 0.5 s flow tex. Neural Networks 11, interval. We found an average shift of 18 (SD 4 ). The variation in Lappe, M., Bremmer, F., Pekel, M., Thiele, A., and Hoffman, K.-P. the shift will cause a broadened minimum for the SD of the perceived (1996). Optic flow processing in monkey STS: A theoretical and heading if precision is limited by the retinal flow. A shift of 18 experimental approach. J. Neurosci. 16, was used to plot SD as a function of the retinal focus. Morrone, M.C., Burr, D.C., and Vaina, L.M. (1995). Two stages of As the lifetime had little effect on the results, we averaged across these conditions. Thus, average and standard deviation of perceived visual processing for radial and circular motion. Nature 376, heading direction was based on 32 settings for each subject In the second experiment, uniform motion on the screen was Paige, W.K., and Duffy, C.J. (1999). MST neuronal responses to shown in the final 0.5 s of pursuit (3 /s left- or rightward). Approxi- heading direction during pursuit eye movements. J. Neurophysiol. mately 130 points were visible within the aperture. Dots were not 81, refreshed. The horizontal component of flow on the screen always Perrone, J.A., and Stone, L.S. (1994). A model of self-motion estimamatched the speed of the pursuit target. Following the motion se- tion within primate extrastriate visual cortex. Vision Res. 34, 2917 quence, subjects adjusted a rotatable line to indicate the perceived motion direction. Each pursuit block of stimuli was combined with Royden, C.S., Banks, M.S., and Crowell, J.A. (1992). The perception a fixation block of the same motion stimuli. Each of the 24 conditions (12 directions of motion for fixation and 6 directions of motion for of heading during eye movements. Nature 360, each direction of eye pursuit) was presented 16 times. For each Royden, C.S., Crowell, J.A., and Banks, M.S. (1994). Estimating condition, the precision of the perceived direction of motion on the heading during eye movements. Vision Res. 34, screen was determined from the SD of the angular settings of the van den Berg, A.V. (1992). Robustness of perception of heading postmotion line. from optic flow. Vision Res. 32, Acknowledgments van den Berg, A.V. (1996). Judgements of heading. Vision Res. 36, This work was supported by a Netherlands Organization for Scienwith van den Berg, A.V., and Beintema, J.A. (1997). Motion templates tific Research grant (SLW-NWO P) and Human Frontiers eye velocity gain fields for transformation of retinal to head- grants (RG 34/96B and RG 71/2000B). centric flow. Neuroreport 8, Warren, W.H., and Hannon, D.J. (1988). Direction of self-motion is Received January 11, 2000; revised April 21, perceived from optical flow. Nature 336, Wurtz, R.H., Komatsu, H., Dürsteler, M.R., and Yamasaki, D.S. (1990). References Motion to movement: cerebral cortical visual processing for pursuit eye movements. In Signal and Sense: Local and Global Order in Andersen, R.A., Bracewell, R.M., Barash, S., Gnadt, J.W., and Fo- Perceptual Maps, G. Edelman, W.E. Gall, and W.M. Cowan, eds. gassi, L. (1990). Eye position effects on visual, memory, and sac- (New York: John Wiley), pp cade-related activity in areas LIP and 7a of macaque. J. Neurosci. 10,