Two dimensionality of the correspondence process in apparent motion

Easy, bias-free Bayesian hierarchical modeling of the psychometric function using the Palamedes Toolbox

A hierarchical Bayesian method is proposed that can be used to fit multiple psychometric functions (PFs) simultaneously across conditions and subjects. The method incorporates the generalized linear model and allows easy reparameterization of the parameters of the PFs, for example, to constrain parameter values across conditions or to code for experimental effects (e.g., main effects and interactions in a factorial design). Simulations indicate that fitting PFs for multiple conditions and observers simultaneously using the hierarchical structure effectively eliminates bias and improves precision in parameter estimates relative to fitting PFs individually in each condition. The method is further validated by analyzing human psychophysical data obtained in an experiment investigating the effect of attention on correspondence matching in an ambiguous long-range motion display. The method converges successfully, even for experiments that use a low number of trials per subject, without the need for fine-tuning by the user and while using the default essentially uninformative priors. The latter may make the method more acceptable to those critical of applying informative priors. The method is implemented in the freely downloadable Palamedes Toolbox, which also includes routines that graphically display the fitted psychometric functions alongside the data, and derive and display posterior distributions of parameters, summary statistics, and diagnostic measures. Overall, these features make hierarchical Bayesian modeling of PFs easily available to researchers who wish to use Bayesian statistics but lack the expertise to implement these methods themselves.

Suppressive Traveling Waves Shape Representations of Illusory Motion in Primary Visual Cortex of Awake Primate

How does the brain link visual stimuli across space and time? Visual illusions provide an experimental paradigm to study these processes. When two stationary dots are flashed in close spatial and temporal succession, human observers experience a percept of apparent motion. Large spatiotemporal separation challenges the visual system to keep track of object identity along the apparent motion path, the so-called "correspondence problem." Here, we use voltage-sensitive dye imaging in primary visual cortex (V1) of awake monkeys to show that intracortical connections within V1 can solve this issue by shaping cortical dynamics to represent the illusory motion. We find that the appearance of the second stimulus in V1 creates a systematic suppressive wave traveling toward the retinotopic representation of the first. Using a computational model, we show that the suppressive wave is the emergent property of a recurrent gain control fed by the intracortical network. This suppressive wave acts to explain away ambiguous correspondence problems and contributes to precisely encode the expected motion velocity at the surface of V1. Together, these results demonstrate that the nonlinear dynamics within retinotopic maps can shape cortical representations of illusory motion. Understanding these dynamics will shed light on how the brain links sensory stimuli across space and time, by preformatting population responses for a straightforward read-out by downstream areas.SIGNIFICANCE STATEMENT Traveling waves have recently been observed in different animal species, brain areas, and behavioral states. However, it is still unclear what are their functional roles. In the case of cortical visual processing, waves propagate across retinotopic maps and can hereby generate interactions between spatially and temporally separated instances of feedforward driven activity. Such interactions could participate in processing long-range apparent motion stimuli, an illusion for which no clear neuronal mechanisms have yet been proposed. Using this paradigm in awake monkeys, we show that suppressive traveling waves produce a spatiotemporal normalization of apparent motion stimuli. Our study suggests that cortical waves shape the representation of illusory moving stimulus within retinotopic maps for a straightforward read-out by downstream areas.

Motion perception induced by dynamic grouping: a probe for the compositional structure of objects

A new method is described for determining how the visual system resolves ambiguities in the compositional structure of multi-surface objects; i.e., how the surfaces of objects are grouped together to form a hierarchical structure. The method entails dynamic grouping motion, a high level process in which changes in a surface (e.g., increases or decreases in its luminance, hue or texture) transiently perturb its affinity with adjacent surfaces. Affinity is determined by the combined effects of Gestalt and other grouping variables in indicating that a pair of surfaces forms a subunit within an object's compositional structure. Such pre-perturbation surface groupings are indicated by the perception of characteristic motions across the changing surface. When the affinity of adjacent surfaces is increased by a dynamic grouping variable, their grouping is transiently strengthened; the perceived motion is away from their boundary. When the affinity of adjacent surfaces is decreased, their grouping is transiently weakened; the perceived motion is toward the surfaces' boundary. It is shown that the affinity of adjacent surfaces depends on the nonlinear, super-additive combination of affinity values ascribable to individual grouping variables, and the effect of dynamic grouping variables on motion perception depends on the prior, pre-perturbation affinity state of the surfaces. It is proposed that affinity-based grouping of an object's surfaces must be consistent with the activation of primitive three-dimensional object components in order for the object to be recognized. Also discussed is the potential use of dynamic grouping for determining the compositional structure of multi-object scenes.

Tuning properties of the auditory frequency-shift detectors

Demany and Ramos [(2005). J. Acoust. Soc. Am. 117, 833-841] found that it is possible to hear an upward or downward pitch change between two successive pure tones differing in frequency even when the first tone is informationally masked by other tones, preventing a conscious perception of its pitch. This provides evidence for the existence of automatic frequency-shift detectors (FSDs) in the auditory system. The present study was intended to estimate the magnitude of the frequency shifts optimally detected by the FSDs. Listeners were presented with sound sequences consisting of (1) a 300-ms or 100-ms random "chord" of synchronous pure tones, separated by constant intervals of either 650 cents or 1000 cents; (2) an interstimulus interval (ISI) varying from 100 to 900 ms; (3) a single pure tone at a variable frequency distance (Delta) from a randomly selected component of the chord. The task was to indicate if the final pure tone was higher or lower than the nearest component of the chord. Irrespective of the chord's properties and of the ISI, performance was best when Delta was equal to about 120 cents (1/10 octave). Therefore, this interval seems to be the frequency shift optimally detected by the FSDs.

Depth Representation of Moving 3-D Objects in Apparent-Motion Path

Apparent motion is perceived when two objects are presented alternately at different positions. The internal representations of apparently moving objects are formed in an apparent-motion path which lacks physical inputs. We investigated the depth information contained in the representation of 3-D moving objects in an apparent-motion path. We examined how probe objects—briefly placed in the motion path—affected the perceived smoothness of apparent motion. The probe objects comprised 3-D objects which were defined by being shaded or by disparity (convex/concave) or 2-D (flat) objects, while the moving objects were convex/concave objects. We found that flat probe objects induced a significantly smoother motion perception than concave probe objects only in the case of the convex moving objects. However, convex probe objects did not lead to smoother motion as the flat objects did, although the convex probe objects contained the same depth information for the moving objects. Moreover, the difference between probe objects was reduced when the moving objects were concave. These counterintuitive results were consistent in conditions when both depth cues were used. The results suggest that internal representations contain incomplete depth information that is intermediate between that of 2-D and 3-D objects.

The duration of 3-d form analysis in transformational apparent motion

Transformational apparent motion (TAM) occurs when a figure changes discretely from one configuration to another overlapping configuration. Rather than an abrupt shape change, the initial shape is perceived to transform smoothly into the final shape as if animated by a series of intermediate shapes. We find that TAM follows an analysis of form that takes 80-140 msec. Form analysis can function both at and away from equiluminance and can occur over contours defined by uniform regions as well as outlines. Moreover, the forms analyzed can be 3-D, resulting in motion paths that appear to smoothly project out from or into the stimulus plane. The perceived transformation is generally the one that involves the least change in the shape or location of the initial figure in a 3-D sense. We conclude that perception of TAM follows an analysis of 3-D form that takes approximately 100 msec. This stage of form analysis may be common to both TAM and second-order motion.

Unilateral right parietal damage leads to bilateral deficit for high-level motion

Patients with right parietal damage demonstrate a variety of attentional deficits in their left visual field contralateral to their lesion. We now report that patients with right lesions also show a severe loss in the perception of apparent motion in their "good" right visual field ipsilateral to their lesion. Three tests of attention were conducted, and losses were found only in the contralesional fields for a selective attention and a multiple object tracking task. Losses in apparent motion, however, were bilateral in all cases. The deficit in apparent motion in the parietal patients supports previous claims that this relatively effortless percept is mediated by attention. However, the bilateral deficit suggests that the disruption is due to a bilateral loss in the temporal resolution of attention to transient events that drive the apparent motion percept.

Relative roles of 3-D and 2-D coordinate systems in solving the correspondence problem in apparent motion

There has been a controversy in the apparent motion literature regarding the influence of 3-D distances between motion tokens on correspondence matching. The current series of experiments indicates that this discrepancy results because the effect of three-dimensional distance is too small to be detected unless the retinal coordinates of the motion tokens are carefully chosen so as to lead to ambiguous correspondence matches on identical trials. It is also shown that, even when the retinal coordinates of motion tokens are equated, such that the different solutions to the correspondence problem are generated with equal probability, the effect of 3-D distances obtained is relatively small when compared to the effect of the retinal coordinates of motion tokens.

Object-based apparent motion

The interpretation of a dynamic visual scene requires integrating information within frames (grouping and completion) and across frames (correspondence matching). Fragmentary views of objects were used in five experiments. These views could not be matched with each other by any similarity transformation on the basis of their explicit visual features, but their completed versions were related by a rotational transformation. When the fragmentary images were successively presented to observers, it was found that they produced apparent motion in the picture plane and in depth. Thus, apparent motion is capable of establishing correspondence at the level of perceptually recovered objects in three-dimensional space.

Spatial scale dependent in-phase and anti-phase directional biases in the perception of self-organized motion patterns

A long row of evenly spaced dots is displaced on successive frames by half the distance between the dots. Although these stimuli are directionally ambiguous, spatially and temporally coherent unidirectional and oscillatory motion patterns are perceived as a result of the temporal persistence of competing in-phase and anti-phase directional biases, respectively. The perceiver's spatial scale is critical is determining whether dots are near enough to favor an in-phase bias or far enough apart to favor an anti-phase bias. The results are explained by a differential-gradient model of cooperative interaction, which specifies that the strength of facilitating (excitatory) interactions among motion detectors with similar directional selectivity falls off with distance at a greater rate than the strength of competing inhibiting interactions.

Static depth cues do affect the perceived direction of motion

Models of motion perception usually assume that the visual system references spatial displacements to retinal coordinates, and not to three-dimensional coordinates recovered by a parallel process. The present studies investigated whether moving elements viewed in the context of a static random-dot stereogram could lead to the appearance of motion in depth. Observers judged the velocity of a monocular element translating horizontally in the stereo context as 'same as' or 'different to' that of a standard. Based on velocity constancy, if there was apparent motion in depth, the relative velocity judgments would yield a predictable pattern of errors. The first experiment compared two stereo contexts: a sloped surface versus a fronto-parallel plane at zero disparity. The results indicated an overall increase in the perceived velocity of the element moving in the sloped surface context. A similar pattern of results was found when surfaces differing in incline were compared. Experiment 2 explored the case of fronto-parallel planes at crossed and uncrossed disparities. Here depth differences did not systematically affect observers' judgments. It was concluded that in some cases motion analysis can be affected by three-dimensional disparity information and not by angular displacement alone.

Effects of element orientation on apparent motion perception

We present an ambiguous motion paradigm that allows us to quantify the influence of aspects of form relevant to the perception of apparent motion. We report on the role of bar element orientation in motion paths. The effect of orientation differences between bar elements in a motion path is small with respect to the crucial role of the orientation of bar elements relative to motion direction. Motion perception between elements oriented along the motion direction dominates motion perception between elements oriented perpendicularly to motion direction. The perception of apparent motion is affected by bar length and width and is anisotropic.

The representation of uniform motion in vision

For veridical detection of object motion any moving detecting system must allocate motion appropriately between itself and objects in space. A model for such allocation is developed for simplified situations (points of light in uniform motion in a frontoparallel plane). It is proposed that motion of objects is registered and represented successively at four levels within frames of reference that are defined by the detectors themselves or by their movements. The four levels are referred to as retinocentric, orbitocentric, egocentric, and geocentric. Thus the retinocentric signal is combined with that for eye rotation to give an orbitocentric signal, and the left and right orbitocentric signals are combined to give an egocentric representation. Up to the egocentric level, motion representation is angular rather than three-dimensional. The egocentric signal is combined with signals for head and body movement and for egocentric distance to give a geocentric representation. It is argued that although motion perception is always geocentric, relevant registrations also occur at the three earlier levels. The model is applied to various veridical and nonveridical motion phenomena.

Moving contexts do affect the perceived direction of apparent motion in motion competition displays

Three experiments were performed to test Ullman's [The Interpretation of Visual Motion. MIT Press, Cambridge, Mass. (1979)] independence hypothesis, used in the minimal mapping theory of motion correspondence. Subjects were required to detect the direction of motion (left vs right) of an element in a motion competition display. In control conditions, threshold interelement distances were obtained for this task in the absence of any moving context. In experimental conditions, context elements that moved either to the left or to the right were added to the display. This resulted in changes in thresholds (relative to the control condition) that indicated that a context moving in one direction increased the probability of seeing the competition element move in the same direction. The magnitude of the context effect was shown to be related to the proximity of the context to the competition display, as well as to the number of elements in the context. These results are in conflict with Ullman's independence hypothesis. An alternative model of the motion correspondence process, which uses information about interdependencies between element movements, is briefly discussed.

Correspondence matching in apparent motion: evidence for three-dimensional spatial representation

The path of an object in apparent motion depends on correspondence matching, the decision that images seen at different places and at different times represent the same object. One determinant of correspondence is proximity. Still debated, however, is whether proximity is defined in a two- or three-dimensional spatial representation. Observers judged the motion path taken by an object with two neighbors of different apparent depth. Given similar two-dimensional distances, objects moved toward the neighbor of the same apparent depth. This is evidence that correspondence operates in a three-dimensional spatial representation.

Measurements of the Pulfrich effect over days of exposure

Mean depth settings and subjective reports appear to confirm previous subjective reports from users of the X-Chrom prescription lens that Pulfrich Effect depth distortions decrease with continued exposure to light intensity disparity. Depth setting variability across Days of exposure indicates a rapid increase in depth judgment errors which persists without decrement across Days. This increased variability, the apparent depth decrements, and color discrimination improvements shed light on the visual processing underlying the Pulfrich Effect and reveal a potentially dangerous illusion.

The effect of two-dimensional and three-dimensional distance on apparent motion

The problem of how the visual system matches corresponding inputs from one instant to the next to produce the perception of motion has been experimentally examined. The specific concern was whether this correspondence problem is solved prior to the interpretation of three-dimensional distance. Observers judged the degree of apparent motion between pairs of lights in a conflicting motion display. Spatial separation of the lights was varied in two and three dimensions in order to assess whether retinal distance, actual depth, or some combination of these provided critical information for correspondence. The results support Ullman's contention that only two-dimensional (retinal) distances are used in establishing correspondence in motion perception.

The effect of similarity between line segments on the correspondence strength in apparent motion

The correspondence between line segments in apparent motion is shown to be affected by the similarity between them. Increase in orientation difference or in length ratio between lines in a competing motion configuration decreases the probability of perceived apparent motion between them. The results suggest the existence of a built-in preference metric that may reflect a measure of matching likelihood between elements in three-dimensional space.