Spatiotemporal Form Integration: sequentially presented inducers can lead to representations of stationary and rigidly rotating objects

Abstract

Objects in the world often are occluded and in motion. The visible fragments of such objects are revealed at different times and locations in space. To form coherent representations of the surfaces of these objects, the visual system must integrate local form information over space and time. We introduce a new illusion in which a rigidly rotating square is perceived on the basis of sequentially presented Pacman inducers. The illusion highlights two fundamental processes that allow us to perceive objects whose form features are revealed over time: Spatiotemporal Form Integration (STFI) and Position Updating. STFI refers to the spatial integration of persistent representations of local form features across time. Position updating of these persistent form representations allows them to be integrated into a rigid global motion percept. We describe three psychophysical experiments designed to identify spatial and temporal constraints that underlie these two processes and a fourth experiment that extends these findings to more ecologically valid stimuli. Our results indicate that although STFI can occur across relatively long delays between successive inducers (i.e., greater than 500 ms), position updating is limited to a more restricted temporal window (i.e., ~300 ms or less), and to a confined range of spatial (mis)alignment. These findings lend insight into the limits of mechanisms underlying the visual system's capacity to integrate transient, piecemeal form information, and support coherent object representations in the ever-changing environment.

Keywords: Form perception; Form-motion interactions; Illusory contours; Motion perception; Surface perception.

Figure 1

Examples of spatial integration and Spatiotemporal Form Integration (STFI). A) Examples of a Kanizsa square and triangle (Kanizsa, 1955, 1979). Local form information provided by the inducers is spatially integrated to generate the percept of an occluding shape. B) Sequentially presented inducers are spatiotemporally integrated to generate the percept of an illusory square. C) STFI and Position Updating supporting motion perception. Inducers are presented sequentially and the occluding square is rotated between each successive inducer. The explicit features defined by the inducers are accumulated and spatiotemporally integrated and position updated to generate the percept of a rigidly rotating square. The above example illustrates a 7° clockwise rotation between each inducer.

Figure 2

A sample trial and the results for experiment 1. A) Inducers are presented sequentially in random order for ~150 ms with variable IIIs and observers report the orientation of the occluding rectangle via a key press (this example shows a vertical rectangle with an aspect ratio of 1.25 as indicated by the black dotted rectangle). The orientation of the occluding rectangle was randomly determined on each trial. B) Results of experiment 1. Gray bars indicate the average orientation discrimination across participants for simultaneous trials in which all four inducers are presented at once for the duration of a single inducer (~150 ms) or the duration of four sequential inducers (600 ms). The points on the solid black line indicate the average orientation discrimination across participants for the sequential condition with various IIIs. The dashed line indicates chance performance across participants in which they made orientation judgments when no occluding rectangle was present in the display. Lines with asterisks indicate main effects of trial type (simultaneous vs. sequential; left) and IIIs at which participants performed significantly better than chance (right). Error bars indicate standard error of the mean.

Figure 3

Two alternative hypotheses of how STFI leads to object representations. A) Corners defined by each inducer persist and are integrated with form information at a different location and time to support object representations. B) Corners defined by each inducer generate illusory contours extending beyond the explicitly defined region linking form information at a different location and time to support object representations.

Figure 4

Stimuli and results for experiment 2. A) The size of the inducers was varied so that, on average, they provided full spatial support for the contour to be spatiotemporally completed (left) or half spatial support (right). The centers of the inducers were jittered in the actual experiment to prevent participants from making orientation judgments based solely on local cues provided by the inducers. B) Results of experiment 2. The black line indicates the average orientation discrimination across participants for the full spatial support condition. The grey line indicates the average orientation discrimination across participants for the half spatial support condition. The line with the asterisk indicates a main effect of III. Error bars indicate standard error of the mean.

Figure 5

Task and results for experiment 3. Observers first indicated whether they perceived rigid rotation and if so, the direction of rotation (clockwise or counterclockwise) for the spatiotemporally integrated square. Stimuli were generated as illustrated in Figure 2. B) Rotational thresholds for each III. Points on the lines indicate the maximum angle of displacement the occluding square could undergo between successive inducers before participants could no longer determine the direction of rotation or the percept of a rigidly rotating square was no longer perceived. The black line illustrates ~150 ms inducer duration condition and the gray line indicates the ~60 ms inducer duration condition. C) Peak angular velocity for each III. Points on the lines indicate the maximum average angular velocity at which a rigidly rotating square was perceived. The black line illustrates ~150 ms inducer duration condition and the gray line indicates the ~60 ms inducer duration condition. Error bars indicate standard error of the mean.

Figure 6

Stimuli and results for experiment 4. A) Silhouettes used as occluding surfaces in the experiment. B) Average rotational thresholds that supported a rigid motion percept for all silhouettes. C) Average peak angular velocity that supported a rigid motion percept for all silhouettes. D) Sensitivity indexes for upright vs. inverted conditions. The left panel shows the index of the difference between participants’ ability to discriminate the direction of rotation for upright and inverted silhouettes. The right panel shows the index of the difference between participants reporting seeing a rigidly rotating object for upright and inverted silhouettes. Error bars indicate standard error of the mean.

Figure 7

A schematic of the conditions necessary for STFI to support rigidly rotating objects. The representation of an explicit form feature provided by an inducer at a given moment in time (first row) persists perceptually (second row). If the subsequent inducer provides information about another form feature that is geometrically relatable (third row) and this occurs within a critical time window, the position of the previously represented feature is updated and integrated with the current form information that is explicitly available (fourth row). These newly integrated form features are again accumulated perceptually and continue to be position updated with subsequent form information so long as this new information is geometrically relatable and is revealed within the critical duration under which position updating occurs (less than ~300 ms). These features become integrated together over space and time to support the percept of a rigidly rotating square (last row). If either of these conditions is violated, position updating does not occur and rigid motion is no longer perceived. The above example illustrates the maximal degree of rotational displacement allowed between successive inducers (7°) under which STFI can support rigidly rotating object representations.