When negotiating a narrow gap, honeybees tend to fly through the middle of the gap, balancing the distances to the boundary on either side. To investigate the basis of this “centering response,” bees were trained to fly through a tunnel on their way to a feeding site and back, while their flight trajectories were filmed from above. The wall on either side carried a visual pattern. When the patterns were stationary vertical gratings, bees tended to fly through the middle of the tunnel, i.e. along its longitudinal axis. However, when one of the gratings was in motion, bees flying in the same direction as the moving grating tended to fly closer to while bees flying in the opposite direction tended to fly closer to the stationary grating. This demonstrates, directly and unequivocally, that flying bees estimate the distances of surfaces in terms of the apparent motion of their images. A series of further experiments revealed that the distance to the gratings is gauged in terms of their apparent angular speeds, and that the visual system of the bee is capable of measuring angular speed largely independently of the spatial period, intensity profile, or contrast of the grating. Thus, the motion-sensitive mechanisms mediating range perception appear to be qualitatively different from those that mediate the well-known optomotor response in insects, or those involved in motion detection and ocular tracking in man.

Previous studies have shown that directionally selective (DS) retinal ganglion cells cannot only discriminate the direction of a moving object but they can also discriminate the sequence of two flashes of light at neighboring locations in the visual field: that is, the cells elicit a DS response to both real and apparent motion. This study examines whether a DS response can be elicited in DS ganglion cells by simply stimulating two neighboring areas of the retina with high external K+. Extracellular recordings were made from ON-OFF DS ganglion cells in superfused rabbit retinas, and the responses of these cells to focal applications of 100 mM KCl to the vitreal surface of the retina were measured. All cells produced a burst of spikes (typically lasting 50–200 ms) when a short pulse (10–50 ms duration) of KCl was ejected from the tip of a micropipette that was placed within the cell's receptive field. When KCl was ejected successively from the tips of two micropipettes that were aligned along the preferred-null axis of a cell, sequence-dependent responses were observed. The response to the second micropipette was suppressed when mimicking motion in the cell's null direction, whereas an enhancement during apparent motion in the opposite direction frequently occurred. Sequence discrimination in these cells was eliminated by the GABA antagonist picrotoxin and by the Ca2+-channel blocker ω-conotoxin MVIIC, two drugs that are known to abolish directional selectivity in these ganglion cells. The spatiotemporal properties of the K+-evoked sequence-dependent responses are described and compared with previous findings on apparent motion responses of ON-OFF DS ganglion cells.

Visual information is processed in a series of subsequent steps. The performance of each of these steps depends not only on the computations it performs itself but also on the representation of the visual surround on which it operates. Here we investigate the consequences of signal preprocessing for the performance of the motion-detection system of the fly. In particular, we analyze whether the retinal input signals are rectified and segregate into separate ON and OFF channels, which then feed independent parallel motion-detection pathways. We recorded the activity of an identified directionally selective interneuron (HI-cell) in response to apparent motion stimuli, i.e. sequential brightness changes at two neighboring locations in the visual field, as well as to brightness changes at only a single location. For apparent motion stimuli, the motion-dependent response component was determined by subtracting from the overall response the responses to the individual stimulus components when presented alone. The following conclusions could be derived: (1) Apparent motion consisting of a sequence of increased or decreased brightness at two locations in the visual field have the same optimum interstimulus time interval (Fig. 3). (2) Sequences of brightness steps of like polarity (either increments or decrements) elicit positive and negative motion-dependent response components when mimicking motion in the cell's preferred and null direction, respectively. The motion-dependent response components are inverted in sign when the brightness steps of a stimulus sequence have a different polarity (Fig. 7). (3) The responses to the beginning and the end of a brightness pulse depend on the pulse duration. For pulse durations of less than 2 s, both events interact with each other (Fig. 9). All of these results do not provide any indication that the fly processes motion information in independent ON and OFF motion detectors. Brightness changes of both signs are rather represented at the input of the same movement detectors, and interactions between signals resulting from both brightness increments and decrements take their sign into account. This type of preprocessing of the retinal input is argued to render a motion-detection system particularly robust against noise.

The phenomenon of apparent motion can arise when two spatially separated visual tokens are presented in temporal sequence. If tokens at opposite corners of a hypothetical square are presented simultaneously followed by simultaneous presentation of tokens at the remaining two corners, an apparent motion percept may occur along either the vertical or horizontal axis. The display is perceptually metastable since most observers will perceive motion along only one axis at a time. The metastable display, however, produces anisotropic results, in that with central fixation, vertical motion is seen more frequently than horizontal motion. The ratio of the vertical to horizontal length of the sides of a rectangle needed to achieve equal frequencies of motion judgments along the respective axes falls in the range of 1.18–1.92 for different observers in our experiments. It appears that signal transmission across the vertical midline is a major determinant of the vertical bias, since the anisotropic effects disappear when the fixation point is sufficiently offset along the horizontal meridian so as to cause a fully homonymous representation of all of the metastable tokens. One of the factors may be signal degradation or delay in callosal transmission which could reduce the strength of the motion signal along the horizontal axis. In addition, there appears to be a strip along the vertical midline with a width of 30–50 min are within which reduced levels of anisotropy are found. The possibility that this strip is a consequence of a zone of naso-temporal overlap in the projection of the retina to the brain along the vertical meridian will be discussed.

The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe – provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three-dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is canceled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily-shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum-entropy priors.

Roger Shepard's proposals and supporting experiments concerning evolutionary internalized regularities have been very influential in the study of vision and in other areas of psychology and cognitive science. This paper examines issues concerning the need, nature, explanatory role, and justification for postulating such internalized constraints. In particular, I seek further clarification from Shepard on how best to understand his claim that principles of kinematic geometry underlie phenomena of motion perception.

My primary focus is on the ecological validity of Shepard's kinematic constraint in the context of ordinary motion perception. First, I explore the analogy Shepard draws between internalized circadian rhythms and the supposed internalization of kinematic geometry. Next, questions are raised about how to interpret and justify applying results from his own and others' experimental studies of apparent motion to more everyday cases of motion perception in richer environments. Finally, some difficulties with Shepard's account of the evolutionary development of his kinematic constraint are considered.

Shepard has supposed that the mind is stocked with innate knowledge of the world and that this knowledge figures prominently in the way we see the world. According to him, this internal knowledge is the legacy of a process of internalization; a process of natural selection over the evolutionary history of the species. Shepard has developed his proposal most fully in his analysis of the relation between kinematic geometry and the shape of the motion path in apparent motion displays. We argue that Shepard has made a case for applying the principles of kinematic geometry to the perception of motion, but that he has not made the case for injecting these principles into the mind of the percipient. We offer a more modest interpretation of his important findings: that kinematic geometry may be a model of apparent motion. Inasmuch as our recommended interpretation does not lodge geometry in the mind of the percipient, the motivation of positing internalization, a process that moves kinematic geometry into the mind, is obviated. In our conclusion, we suggest that cognitive psychologists, in their embrace of internal mental universals and internalization may have been seduced by the siren call of metaphor.