Illusory Optic Flow Transformation with Binocular Vision

We investigated the influence of stereoscopic vision on the perception of optic flow fields in psychophysical experiments based on the effect of an illusory transformation found by Duffy and Wurtz (1993 Vision Research33 1481 – 1490). Human subjects are not able to determine the centre of an expanding optic flow field correctly if the expansion is transparently superimposed on a unidirectional motion pattern. Its location is rather perceived shifted in the direction of the translational movement. Duffy and Wurtz proposed that this illusory shift is caused by the visual system taking the presented flow pattern as a flow field composed of linear self-motion and an eye rotation. As a consequence, the centre of the expansional movement is determined by compensating for the simulated eye rotation, like determining one's direction of heading (Lappe and Rauschecker, 1994 Vision Research35 1619 – 1631).

In our experiments we examined the dependence of the illusory transformation on differences in depth between the superimposed movements. We presented the expansional and translational stimuli with different relative binocular disparities. In the case of zero disparity, we could confirm the results of Duffy and Wurtz. For uncrossed disparities (ie translation behind expansion) we found a small and nonsignificant decrease of the illusory shift. In contrast, there was a strong decrease up to 80% in the case of crossed disparity (ie translation in front of expansion). These findings confirm the assumption that the motion pattern is interpreted as a self-motion flow field: only in the unrealistic case of a large rotational component present in front of an expansion are the superimposed movements interpreted separately by the visual system.

Impairment of saccade adaptation in a patient with a focal thalamic lesion

The frequent jumps of the eyeballs-called saccades-imply the need for a constant correction of motor errors. If systematic errors are detected in saccade landing, the saccade amplitude adapts to compensate for the error. In the laboratory, saccade adaptation can be studied by displacing the saccade target. Functional selectivity of adaptation for different saccade types suggests that adaptation occurs at multiple sites in the oculomotor system. Saccade motor learning might be the result of a comparison between a prediction of the saccade landing position and its actual postsaccadic location. To investigate whether a thalamic feedback pathway might carry such a prediction signal, we studied a patient with a lesion in the posterior ventrolateral thalamic nucleus. Saccade adaptation was tested for reactive saccades, which are performed to suddenly appearing targets, and for scanning saccades, which are performed to stationary targets. For reactive saccades, we found a clear impairment in adaptation retention ipsilateral to the lesioned side and a larger-than-normal adaptation on the contralesional side. For scanning saccades, adaptation was intact on both sides and not different from the control group. Our results provide the first lesion evidence that adaptation of reactive and scanning saccades relies on distinct feedback pathways from cerebellum to cortex. They further demonstrate that saccade adaptation in humans is not restricted to the cerebellum but also involves cortical areas. The paradoxically strong adaptation for outward target steps can be explained by stronger reliance on visual targeting errors when prediction error signaling is impaired.

A method for the estimation of functional brain connectivity from time-series data

A central issue in cognitive neuroscience is which cortical areas are involved in managing information processing in a cognitive task and to understand their temporal interactions. Since the transfer of information in the form of electrical activity from one cortical region will in turn evoke electrical activity in other regions, the analysis of temporal synchronization provides a tool to understand neuronal information processing between cortical regions. We adopt a method for revealing time-dependent functional connectivity. We apply statistical analyses of phases to recover the information flow and the functional connectivity between cortical regions for high temporal resolution data. We further develop an evaluation method for these techniques based on two kinds of model networks. These networks consist of coupled Rössler attractors or of coupled stochastic Ornstein-Uhlenbeck systems. The implemented time-dependent coupling includes uni- and bi-directional connectivities as well as time delayed feedback. The synchronization dynamics of these networks are analyzed using the mean phase coherence, based on averaging over phase-differences, and the general synchronization index. The latter is based on the Shannon entropy. The combination of these with a parametric time delay forms the basis of a connectivity pattern, which includes the temporal and time lagged dynamics of the synchronization between two sources. We model and discuss potential artifacts. We find that the general phase measures are remarkably stable. They produce highly comparable results for stochastic and periodic systems. Moreover, the methods proves useful for identifying brief periods of phase coupling and delays. Therefore, we propose that the method is useful as a basis for generating potential functional connective models.

Effects of saccadic adaptation on visual localization before and during saccades

Short-term saccadic adaptation is a mechanism that adjusts saccade amplitude to accurately reach an intended saccade target. Short-term saccadic adaptation induces a shift of perceived localization of objects flashed before the saccade. This shift, being detectable only before an adapted saccade, disappears at some time around saccade onset. Up to now, the exact time course of this effect has remained unknown. In previous experiments, the mislocalization caused by this adaptation-induced shift was overlapping with the mislocalization caused by a different, saccade-related localization error, the peri-saccadic compression. Due to peri-saccadic compression, objects flashed immediately at saccade onset appear compressed towards the saccade target. First, we tested whether the adaptation-induced shift and the peri-saccadic compression were either independent or related processes. We performed experiments with two different luminance-contrast conditions to separate the adaptation-induced shift and the peri-saccadic compression. Human participants had to indicate the perceived location of briefly presented stimuli before, during or after an adapted saccade. Adaptation-induced shift occurred similarly in either contrast condition, with or without peri-saccadic compression. Second, after validating the premise of both processes being independent and superimposing, we aimed at characterizing the time course of the adaptation-induced shift in more detail. Being present up to 1 s before an adapted saccade, the adaptation-induced shift begins to gradually decline from about 150 ms before saccade onset, and ceases during the saccade. A final experiment revealed that visual references make a major contribution to adaptation-induced mislocalization.

Perception of biological motion from limited-lifetime stimuli

The visual perception of human movement from sparse point-light walkers is often believed to rely on local motion analysis. We investigated the role of local motion in the perception of human walking, viewed from the side, in different tasks. The motion signal was manipulated by varying point lifetime. We found the task of coherence discrimination, commonly used in biological motion studies, to be inappropriate for testing the role of motion. A task requiring temporal information showed a strong performance drop when fewer points were used or when the image sequence was sampled and displayed at a reduced frame rate. Irrespective of the frame rate, performance did not vary with point lifetime. We concluded that local motion is not required for the perception of tested biological movements, suggesting that the analysis of biological motion does not benefit from examining local motion. The reliance of perception on the number of displayed points and frames supports the idea that biological motion is perceived from a sequence of spatiotemporally sampled forms.

Biologically motivated space-variant filtering for robust optic flow processing

We describe and test a biologically motivated space-variant filtering method for decreasing the noise in optic flow fields. Our filter model adopts certain properties of a particular motion-sensitive area of the brain (area MT), which averages the incoming motion signals over receptive fields, the sizes of which increase with the distance from the center of the projection. We use heading estimation from optic flow as a criterion to evaluate the improvement of the filtered flow field. The tests are conducted on flow fields calculated with a standard flow algorithm from image sequences. We use two different sets of image sequences. The first set is recorded by a camera which is installed in a moving car. The second set is derived from a database containing three dimensional data and reflectance information from natural scenes. The latter set guarantees full control of the camera motion and ground truth about the flow field and the heading. We test the space-variant filtering method by comparing heading estimation results between space-variant filtered flow, flow filtered by averaging over domains of the visual field with constant size (constant filtering) and raw unfiltered flow. Because of noise and the aperture problem the heading estimates obtained from the raw flows are often unreliable. Estimated heading differs widely for different sub-sampled calculations. In contrast, the results obtained from the filtered flows are much less variable and therefore more consistent. Furthermore, we find a significant improvement of the results obtained from the space-variant filtered flow compared to the constant filtered flow. We suggest extensions to the space-variant filtering procedure that take other properties of motion representation in area MT into account.

Local image structures and optic flow estimation

Different kinds of local image structures (such as homogeneous, edge-like and junction-like patches) can be distinguished by the intrinsic dimensionality of the local signals. Intrinsic dimensionality makes use of variance from a point and a line in spectral representation of the signal in order to classify it as homogeneous, edge-like or junction-like. The concept of intrinsic dimensionality has been mostly exercised using discrete formulations; however, recent work has introduced a continuous definition. The current study analyzes the distribution of local patches in natural images according to this continuous understanding of intrinsic dimensionality. This distribution reveals specific patterns than can be also associated to local image structures established in computer vision and which can be related to orientation and optic flow features. In particular, we link quantitative and qualitative properties of optic-flow error estimates to these patterns. In this way, we also introduce a new tool for better analysis of optic flow algorithms.

Algorithms for protein interaction networks

The functional characterization of all genes and their gene products is the main challenge of the postgenomic era. Recent experimental and computational techniques have enabled the study of interactions among all proteins on a large scale. In this paper, approaches will be presented to exploit interaction information for the inference of protein structure, function, signalling pathways and ultimately entire interactomes. Interaction networks can be modelled as graphs, showing the operation of gene function in terms of protein interactions. Since the architecture of biological networks differs distinctly from random networks, these functional maps contain a signal that can be used for predictive purposes. Protein function and structure can be predicted by matching interaction patterns, without the requirement of sequence similarity. Moving on to a higher level definition of protein function, the question arises how to decompose complex networks into meaningful subsets. An algorithm will be demonstrated, which extracts whole signal-transduction pathways from noisy graphs derived from text-mining the biological literature. Finally, an algorithmic strategy is formulated that enables the proteomics community to build a reliable scaffold of the interactome in a fraction of the time compared with uncoordinated efforts.

Measurement of generalization fields for the recognition of biological motion

The human visual system processes complex biological motion stimuli with high sensitivity and selectivity. The characterization of spatio-temporal generalization in the perception of biological motion is still a largely unresolved problem. We present an experiment that investigates how the visual system responds to motion stimuli that interpolate spatio-temporally between natural biological motion patterns. Inspired by analogous studies in stationary object recognition, we generated stimuli that interpolate between natural perceptual categories by morphing. Spatio-temporal morphs between natural movement patterns were obtained with a technique that allows to calculate linear combinations of spatio-temporal patterns. The weights of such linear combinations define a linear metric space over the set of generated movement patterns, so that the spatio-temporal similarity of the motion patterns can be quantified. In our experiments, we found smooth and continuous variation of the categorization probabilities with the weights of the prototypes in the morphs. For bipedal locomotion patterns we could accurately predict the perceived properties of the morphs by linear combinations of the perceived properties of the prototypes. Such predictions were not possible for morphs between locomotion and very dissimilar movements. We conclude that the visual system shows generalization within classes of motion patterns with similar basic structure, such as bipedal locomotion.

Perception of biological motion without local image motion

A vivid perception of the moving form of a human figure can be obtained from a few moving light points on the joints of the body. This is known as biological motion perception. It is commonly believed that the perception of biological motion rests on image motion signals. Curiously, however, some patients with lesions to motion processing areas of the dorsal stream are severely impaired in image motion perception but can easily perceive biological motion. Here we describe a biological motion stimulus based on a limited lifetime technique that tests the perception of a moving human figure in the absence of local image motion. We find that subjects can spontaneously recognize a moving human figure in displays without local image motion. Their performance is very similar to that for classic point-light displays. We also find that tasks involving the discrimination of walking direction or the coherence of a walking figure can be performed in the absence of image motion. Thus, although image motion may generally aid processes such as segmenting figure from background, we propose that it is not the basis for the precept of biological motion. Rather, we suggest biological motion is derived from dynamic form information on body posture evolving over time.

Generating protein interaction maps from incomplete data: application to fold assignment

MOTIVATION

We present a framework to generate comprehensive overviews of protein-protein interactions. In the post-genomic view of cellular function, each biological entity is seen in the context of a complex network of interactions. Accordingly, we model functional space by representing protein-protein-interaction data as undirected graphs. We suggest a general approach to generate interaction maps of cellular networks in the presence of huge amounts of fragmented and incomplete data, and to derive representations of large networks which hide clutter while keeping the essential architecture of the interaction space. This is achieved by contracting the graphs according to domain-specific hierarchical classifications. The key concept here is the notion of induced interaction, which allows the integration, comparison and analysis of interaction data from different sources and different organisms at a given level of abstraction.

RESULTS

We apply this approach to compute the overlap between the DIP compendium of interaction data and a dataset of yeast two-hybrid experiments. The architecture of this network is scale-free, as frequently seen in biological networks, and this property persists through many levels of abstraction. Connections in the network can be projected downwards from higher levels of abstraction down to the level of individual proteins. As an example, we describe an algorithm for fold assignment by network context. This method currently predicts protein folds at 30% accuracy without any requirement of detectable sequence similarity of the query protein to a protein of known structure. We used this algorithm to compile a list of structural assignments for previously unassigned genes from yeast. Finally we discuss ways forward to use interaction networks for the prediction of novel protein-protein interactions.

AVAILABILITY

http://www.ebi.ac.uk/~lappe/FoldPred/.

Prehospital sedation with intramuscular droperidol: a one-year pilot

OBJECTIVE

Combative patients pose a threat to themselves and prehospital personnel, and are at risk for sudden death. Droperidol is an antipsychotic and sedative agent that might be effectively utilized by paramedics to assist in the management of uncontrollably violent patients.

METHODS

A prospective observational study of patients requiring sedation was conducted in an urban third-service emergency medical services system (55,000 calls per year). Patients were scored by paramedics on a five-point agitation scale with 5 being extremely combative (continuous, vigorous fighting against restraints) and 1 being somnolent (sleeping or sleepy). Eligible (score 4-5) patients received 5 mg of intramuscular droperidol on direct physician order. Data including vital signs and agitation scores were recorded at 5-minute intervals until hospital arrival. Adverse effects were also recorded.

RESULTS

Fifty-three patients received droperidol (51 patients received 5 mg; two received 2.5 mg) during the study period. The average predrug agitation score was 4.7 (+/- 0.1 SD). The average 5-minute postdrug score was 3.9 (+/- 0.1 SD, 95% CI 3.7-4.1. The average 10-minute postdrug score was 3.3 (+/- 0.1 SD, 95% CI 3.1-3.6). The average hospital arrival score was 2.8 (+/- 0.1 SD, 95% CI 2.5-3.1). One patient became obtunded and required supplemental oxygen; no other patient experienced an adverse event after receiving droperidol. Sedation was ineffective in seven patients, three of whom had head injuries, and one of whom received 2.5 mg of droperidol per physician order. Paramedics sustained no needlestick exposures.

CONCLUSION

Intramuscular droperidol contributed to effective and rapid prehospital sedation in this observational series of 53 combative patients.

Neuronal latencies and the position of moving objects

Neuronal latencies delay the registration of the visual signal from a moving object. By the time the visual input reaches brain structures that encode its position, the object has already moved on. Do we perceive the position of a moving object with a delay because of neuronal latencies? Or is there a brain mechanism that compensates for latencies such that we perceive the true position of a moving object in real time? This question has been intensely debated in the context of the flash-lag illusion: a moving object and an object flashed in alignment with it appear to occupy different positions. The moving object is seen ahead of the flash. Does this show that the visual system extrapolates the position of moving objects into the future to compensate for neuronal latencies? Alternative accounts propose that it simply shows that moving and flashed objects are processed with different delays, or that it reflects temporal integration in brain areas that encode position and motion. The flash-lag illusion and the hypotheses put forward to explain it lead to interesting questions about the encoding of position in the brain. Where is the 'where' pathway and how does it work?

Mapping protein family interactions: intramolecular and intermolecular protein family interaction repertoires in the PDB and yeast

In the postgenomic era, one of the most interesting and important challenges is to understand protein interactions on a large scale. The physical interactions between protein domains are fundamental to the workings of a cell: in multi-domain polypeptide chains, in multi-subunit proteins and in transient complexes between proteins that also exist independently. To study the large-scale patterns and evolution of interactions between protein domains, we view interactions between protein domains in terms of the interactions between structural families of evolutionarily related domains. This allows us to classify 8151 interactions between individual domains in the Protein Data Bank and the yeast Saccharomyces cerevisiae in terms of 664 types of interactions, between protein families. At least 51 interactions do not occur in the Protein Data Bank and can only be derived from the yeast data. The map of interactions between protein families has the form of a scale-free network, meaning that most protein families only interact with one or two other families, while a few families are extremely versatile in their interactions and are connected to many families. We observe that almost half of all known families engage in interactions with domains from their own family. We also see that the repertoires of interactions of domains within and between polypeptide chains overlap mostly for two specific types of protein families: enzymes and same-family interactions. This suggests that different types of protein interaction repertoires exist for structural, functional and regulatory reasons.

A fully automatic evolutionary classification of protein folds: Dali Domain Dictionary version 3

The Dali Domain Dictionary (http://www.ebi.ac.uk/dali/domain) is a numerical taxonomy of all known structures in the Protein Data Bank (PDB). The taxonomy is derived fully automatically from measurements of structural, functional and sequence similarities. Here, we report the extension of the classification to match the traditional four hierarchical levels corresponding to: (i) supersecondary structural motifs (attractors in fold space), (ii) the topology of globular domains (fold types), (iii) remote homologues (functional families) and (iv) homologues with sequence identity above 25% (sequence families). The computational definitions of attractors and functional families are new. In September 2000, the Dali classification contained 10 531 PDB entries comprising 17 101 chains, which were partitioned into five attractor regions, 1375 fold types, 2582 functional families and 3724 domain sequence families. Sequence families were further associated with 99 582 unique homologous sequences in the HSSP database, which increases the number of effectively known structures several-fold. The resulting database contains the description of protein domain architecture, the definition of structural neighbours around each known structure, the definition of structurally conserved cores and a comprehensive library of explicit multiple alignments of distantly related protein families.

Perception of two-dimensional, simulated ego-motion trajectories from optic flow

A veridical percept of ego-motion is normally derived from a combination of visual, vestibular, and proprioceptive signals. A previous study showed that blindfolded subjects can accurately perceive passively travelled straight or curved trajectories provided that the orientation of the head remained constant along the trajectory. When they were turned (whole-body, head-fixed) relative to the trajectory, errors occurred. We ask whether vision allows for better path perception in that situation, to correct or complement vestibular perception. Seated, stationary subjects wore a head mounted display showing optic flow stimuli which simulated linear or curvilinear 2D trajectories over a horizontal ground plane. The observer's orientation was either fixed in space, fixed relative to the path, or changed relative to both. After presentation, subjects reproduced the perceived movement with a model vehicle, of which position and orientation were recorded. They tended to correctly perceive ego-rotation (yaw), but they perceive orientation as fixed relative to trajectory or (unlike in the vestibular study) to space. This caused trajectory misperception when body rotation was wrongly attributed to a rotation of the path. Visual perception was very similar to vestibular perception.

Responses to continuously changing optic flow in area MST

We studied the temporal behavior and tuning properties of medial superior temporal (MST) neurons in response to constant flow-field stimulation and continuously changing flow-field stimulation (transitions), which were obtained by morphing one flow field into another. During transitions, the flow fields resembled the motion pattern seen by an observer during changing ego-motion. Our aim was to explore the behavior of MST cells in response to changes in the flow-field pattern and to establish whether the responses of MST cells are temporally independent or if they are affected by contextual information from preceding stimulation. We first tested whether the responses obtained during transitions were linear with respect to the two stimuli defining the transition. In over half of the transitions, the cell response was nonlinear: the response during the transition could not be predicted by the linear interpolation between the stimulus before and after the transition. Nonlinearities in the responses could arise from a dependence on temporal context or from nonlinearities in the tuning to flow-field patterns. To distinguish between these two hypotheses, we fit the responses during transitions and during continuous stimuli to the predictions of a temporally independent model (temporal-independence test) and we compared the responses during transitions to the responses elicited by inverse transitions (temporal-symmetry test). The effect of temporal context was significant in only 7.2% and 5.5% of cells in the temporal-independence test and in the temporal-symmetry test, respectively. Most of the nonlinearities in the cell responses could be accounted for by nonlinearities in the tuning to flow-field stimuli (i.e., the responses to a restricted set of flow fields did not predict the responses to other flow fields). Tuning nonlinearities indicate that a complete characterization of the tuning properties of MST neurons cannot be obtained by testing only a small number of flow fields. Because the cells' responses do not depend on temporal context, continuously changing stimulation can be used to characterize the receptive field properties of cells more efficiently than constant stimulation. Temporal independence in the responses to transitions indicates that MST cells do not code for second-order temporal properties of flow-field stimuli, i.e., for changes in the flow field through time that can be construed as paths through the environment. Information about ego-motion three-dimensional paths through the environment may either be processed at the population level in MST or in other cortical areas.

A model of the perceived relative positions of moving objects based upon a slow averaging process

We extend the local energy model of position detection to cope with temporally varying position signals and the perception of relative position. The extension entails two main components. First, a form of persistence for the position signal based on the temporal impulse response function of the visual system. Secondly, we hypothesise that the perceived relative position of two objects is determined by a slow average of the difference of the objects' position signals. The model explains why briefly flashed static dots are perceived to lag behind continuously visible moving dots, without the need for a motion extrapolation process [Nijhawan, R. (1994). Nature, 370, 256-257]. The dependence of this illusion on parameters such as the velocity, duration, frequency and number of flashes of the motion trajectories is accurately captured by the model. Furthermore, the model makes two predictions. First, briefly flashed dots on a staircase trajectory should lead dots with a long duration. Secondly, it should be possible to abolish the lag-effect between continuously visible and stroboscopically moving objects by halting the continuously visible dots during the interflash interval of the stroboscopic dots. Both predictions are corroborated in experiments.

Postsaccadic visual references generate presaccadic compression of space

With every rapid gaze shift (saccade), our eyes experience a different view of the world. Stable perception of visual space requires that points in the new image are associated with corresponding points in the previous image. The brain may use an extraretinal eye position signal to compensate for gaze changes, or, alternatively, exploit the image contents to determine associated locations. Support for a uniform extraretinal signal comes from findings that the apparent position of objects briefly flashed around the time of a saccade is often shifted in the direction of the saccade. This view is challenged, however, by observations that the magnitude and direction of the displacement varies across the visual field. Led by the observation that non-uniform displacements typically occurred in studies conducted in slightly illuminated rooms, here we determine the dependence of perisaccadic mislocalization on the availability of visual spatial references at various times around a saccade. We find that presaccadic compression occurs only if visual references are available immediately after, rather than before or during, the saccade. Our findings indicate that the visual processes of transsaccadic spatial localization use mainly postsaccadic visual information.

How stereovision interacts with optic flow perception: neural mechanisms

Optic flow, the global visual motion experienced during self-movement, supplies important navigational information. Optic flow analysis in the visual system is aided by several other visual and non-visual signals. Recent psychophysical findings demonstrate an interaction of optic flow perception and stereoscopic depth vision. Retinal disparity strongly affects an optic flow illusion, which can be related to the mechanisms of visual self-motion detection. To investigate the neuronal basis of this interaction, we tested several hypotheses by introducing different disparity contributions in a detailed neurobiological model of optic flow processing in monkey cortex. The disparity-dependent modification, which accounted best for the data suggests a specific contribution of a subset of stereoscopically modulated cortical neurons present in areas MT and MST.

The position of moving objects

Moving objects occupy a range of positions during the period of integration of the visual system. Nevertheless, a unique position is usually observed. We investigate how the trajectory of a stimulus influences the position at which the object is seen. It has been shown before that moving objects are perceived ahead of static objects shown at the same place and time. We show here that this perceived position difference builds up over the first 500 ms of a visible trajectory. Discontinuities in the visual input reduce this buildup when the presentation frequency of a stimulus with a duration of 42 ms falls below 16 Hz. We interpret this relative mislocalization in terms of a spatiotemporal-filtering model. This model fits well with the data, given two assumptions. First, the position signal persists even though the objects are no longer visible and, second, the perceived distance is a 500 ms average of the difference of these position signals.

Dynamical use of different sources of information in heading judgments from retinal flow

The optic flow arising in the eyes of an observer during self-motion is influenced by the occurrence of eye movements. The determination of heading during eye movements may be based on the pattern of retinal image motion (the retinal flow) or on an additional use of an extraretinal eye-movement signal. Previous research has presented support for either of these hypotheses, depending on the movement geometry and the layout of the visual scene. A special situation in which all previous studies unequivocally have agreed that an extra-retinal signal is required occurs when the visual scene consists of a single frontoparallel plane. In this situation eye movements shift the center of expansion on the retina to a location that does not correspond to the direction of self-movement. Without extraretinal input, human observers confuse the center of expansion with their heading and show a systematical heading estimation error. We reexamined and further investigated this situation. We presented retinal flow stimuli on a large projection screen in the absence of extra-retinal input and varied stimulus size, presentation duration, and orientation of the plane. In contrast to previous studies we found that in the case of a perpendicular approach toward the plane, heading judgments can be accurate. Accurate judgments were observed when the field of view was large (90 degrees x 90 degrees) and the stimulus duration was short (< or = 0.5 s). For a small field of view or a prolonged stimulus presentation, a systematic and previously described error appeared that is related to the radial structure of the flow field and the location of the center of expansion. An oblique approach toward the plane results in an ambiguous flow field with two mathematically possible solutions for heading. In this situation, when the stimulus duration was short, subjects reported a perceived heading midway between these two solutions. For longer flow sequences, subjects again chose the center of expansion. Our results suggest a dynamical change in the analysis or interpretation of retinal flow during heading perception.