GROUPING BY PROXIMITY AND MULTISTABILITY IN DOT LATTICES:

Abstract— Gestalt phenomena have long resisted quantification. In the spirit of Gestalt field theory, we propose a theory that predicts the probability of grouping by proximity in the six kinds of dot lattices (hexagonal, rhombic, square, rectangular, centered rectangular, and oblique). We claim that the unstable perceptual organization of dot lattices is caused by competing forces that attract each dot to other dots in its neighborhood. We model the decline of these forces as a function of distance with an exponential decay function. This attraction function has one parameter, the attraction constant Simple assumptions allow us to predict the entropy of the perceptual organization of different dot lattices. We showed dot lattices tachistoscopically to 7 subjects, and from the probabilities of the perceived organisations, we calculated the entropy of each lattice for each subject. The model fit the data exceedingly well. The attraction constant did not vary much over subjects     

On the surprising salience of curvature in grouping by proximity

The authors conducted 3 experiments to explore the roles of curvature, density, and relative proximity in the perceptual organization of ambiguous dot patterns. To this end, they developed a new family of regular dot patterns that tend to be perceptually grouped into parallel contours, dot-sampled structured grids (DSGs). DSGs are similar to the dot lattices used to study grouping by proximity, except that only one of the potential organizations is rectilinear; the others are curvilinear. The authors used the method of M. Kubovy and J. Wagemans (1995) to study grouping by proximity in DSGs. They found that in the competition between the most likely organizations, one rectilinear and the other curvilinear, the latter is more salient. This phenomenon cannot be explained by contemporary accounts of grouping by proximity or contour integration.     

The whole is equal to the sum of its parts: a probabilistic model of grouping by proximity and similarity in regular patterns

The authors investigated whether the gestalt grouping principles can be quantified and whether the conjoint effects of two grouping principles operating at the same time on the same stimuli differ from the sum of their individual effects. After reviewing earlier attempts to discover how grouping principles interact, they developed a probabilistic model of grouping by proximity, which allows measurement of strength on a ratio scale. Then, in 3 experiments using dot lattices, they showed that the strength of the conjoint effect of 2 grouping principles--grouping by proximity and grouping by similarity--is equal to the sum of their separate effects. They propose a physiologically plausible model of this law.     

Judgments of perceptual groups: Reliability and sensitivity to stimulus transformation

The reliability of subjects’ judgments of the groups present in dot patterns and the sensitivity of those judgments to stimulus transformation were assessed. The subjects indicated the groups that they saw within random dot patterns, and each judgment was compared with those of other subjects and with their own judgments for related presentations. Within subjects, each pattern appeared in an initial presentation, an identical repetition, and a transformed state (a rotation or a change in scale). Witfiin-subjects judgments were more reliable than between-subjects judgments. An interpretation of within-subjects results was made in relation to predictions made by a formal algorithm of grouping by proximity (the CODE algorithm), which assumes that grouping by proximity is invariant over transformations such as rotations or changes in scale. A slight cost to transforming the patterns was found. The implications for CODE and for using grouping judgments as data are discussed.     

Evaluating a computational model of perceptual grouping by proximity

A formal approach to the phenomenon of perceptual grouping by proximity was investigated. Grouping judgments of random dot patterns were made by the CODE algorithm (van Oeffelen & Vos, 1982) and several related algorithms, and these judgments were compared with subjects’ grouping judgments for the same stimuli. Each algorithm predicted significantly more subject judgments than would be expected by chance. The more subjects agreed on how a given dot pattern should be grouped, the more successful was the algorithms’ ability to match the judgments for that pattern. CODE predicted significantly fewer subject judgments than did some of the other algorithms, largely because of its overemphasis on the extent of interactivity among dots as they are being grouped.     

Configurational effects on the enumeration of dots: Counting by groups

The processing time for quantifying numerosity of two-dimensional dot patterns was investigated as a function of both number of dots and relative proximity between dots. A cluster algorithm (CODE) was first developed as a formal model of how human subjects organize neighboring dots into groups. CODE-based predictions of grouping effects on number processing latencies were then tested with patterns consisting of n dots (range n = 13–23). The results largely confirmed CODE-based predictions and thereby indicated that large collections of dots are preferably counted by groups. Small (n ≤ 5) groups are subitized and their partial results are summed to a running total. Based on criteria other than dot proximity, large (n > 5), proximity-based groups are subdivided into smaller groups of two or three dots, which are again subitized.     

Judgments of perceptual groups: reliability and sensitivity to stimulus transformation

The reliability of subjects' judgments of the groups present in dot patterns and the sensitivity of those judgments to stimulus transformation were assessed. The subjects indicated the groups that they saw within random dot patterns, and each judgment was compared with those of other subjects and with their own judgments for related presentations. Within subjects, each pattern appeared in an initial presentation, an identical repetition, and a transformed state (a rotation or a change in scale). Within-subjects judgments were more reliable than between-subjects judgments. An interpretation of within-subjects results was made in relation to predictions made by a formal algorithm of grouping by proximity (the CODE algorithm), which assumes that grouping by proximity is invariant over transformations such as rotations or changes in scale. A slight cost to transforming the patterns was found. The implications for CODE and for using grouping judgments as data are discussed.     

Simple kinetic information for transparent depth

The present paper reports three investigations of new kinetic information for transparent depth using computer-generated dot patterns. An initial demonstration showed that separation in depth could be obtained by translating rectangular lattices of dots through one another like intersecting columns of marching soldiers. The first two experiments showed that diagonal interactions between lattices created significantly stronger separation than did horizontal or vertical interactions (horizontal was, in turn, stronger than vertical) and that patterns which translated through one another without any of the individual elements intersecting were better separated than those whose rows or columns intersected in register. The third experiment showed that random patterns interacting in any direction created the strongest separations of all the patterns observed. Results were taken to indicate that a unified theory of depth information, developed in the context of James Gibson’s ecological optics, must incorporate both spatial and kinetic structure in its specification of necessary and sufficient stimulus conditions.     

视知觉组织在整体知觉中的作用--脑损伤病人的实验研究

本实验研究大脑损伤如何影响复合图形的整体知觉。三例病人脑损伤部位分别在大脑枕区、顶区、颞区、额区及基底节和豆状核。复合图形被呈现给病人和正常对照被试。强迫选择识别等任务表明,当空间相邻性决定局部图形的知觉组织时,病人识别整体性质的正确率高于(ZD和FL)或略底于(GK)识别局部性质的正确率;当形状相似性决定局部图形的知觉组织时,病人识别整体性质的正确率显著降低,而识别局部性质的正确率受到的影响较小。在同样的任务中正常被试识别整体和局部性质的正确率受知觉组织因素的影响很小。这些结果提示大脑损伤对整体知觉的破坏可能主要通过影响基于形状相似性的知觉组织实现。     

The relation between proximity and brightness similarity in dot patterns

The Gestalt studies demonstrated the tendency to visually organize dots on the basis of similarity, proximity, and global properties such as closure, good continuation, and symmetry. The particular organization imposed on a collection of dots is thus determined by many factors, some local, some global. We discuss computational reasons for expecting the initial stages of grouping to be achieved by processes with purely local support. In the case of dot patterns, the expectation is that neighboring dots are grouped as a function of proximity and similarity of contrast, by processes that are independent of the overall organization and the various global factors. We describe experiments that suggest a purely local relationship between proximity and brightness similarity in perceptual grouping.     

Symmetry and selective attention: A dissociation between effortless perception and serial search

It is widely assumed that symmetry is an important visual primitive, probably encoded without the need for attention. Julesz’s (1981) definition ofeffortless perception, which states that any stimulus property perceived for exposure durations of 160 msec or less is detected preattentively, contributed greatly to this belief.Single pattern studies confirm that symmetry is detected within this limit. In the present study, however, Julesz’s operationalization is compared with themultiple pattern visual search task, to see whether symmetry as a wholistic property is detected in parallel. The results show that symmetry detection times are highly dependent on the number of distractor patterns. The findings are similar for dot patterns, wire polygons, solid block shapes, and simple parentheses. We conclude that symmetry detection per se requires selective attention, but that some related grouping or segmentation mechanism may operate preattentively.     

Intuitive knowledge

In this paper I assume that we have some intuitive knowledge—i.e. beliefs that amount to knowledge because they are based on intuitions. The question I take up is this: given that some intuition makes a belief based on it amount to knowledge, in virtue of what does it do so? We can ask a similar question about perception. That is: given that some perception makes a belief based on it amount to knowledge, in virtue of what does it do so? A natural idea about perception is that a perception makes a belief amount to knowledge in part by making you sensorily aware of the concrete objects it is about. The analogous idea about intuition is that an intuition makes a belief amount to knowledge in part by making you intellectually aware of the abstract objects it is about. I expand both ideas into fuller accounts of perceptual and intuitive knowledge, explain the main challenge to this sort of account of intuitive knowledge (i.e. the challenge of making sense of intellectual awareness), and develop a response to it.     

Combined effects of perceptual grouping cues on object representation: Evidence from motion-induced blindness

We investigated the combined effects of perceptual grouping cues (proximity and contour closure/proximity and orientation similarity) on object representation, using motion-induced blindness, a phenomenon in which salient visual stimuli perceptually disappear when surrounded by moving patterns. We presented as visual targets two stimuli in which a solid square was embedded in an outlined square. Participants reported whether the targets disappeared independently or simultaneously. The results showed that a relatively high proximity cue (with a 0.2-deg separation between the targets) modulated the perceptions of the independent or simultaneous disappearances of targets, regardless of other grouping cues. The contour closure cue modulated these disappearances in the 0.4- to 0.8-deg separations. Finally, the orientation similarity cue began to modulate these disappearances in the 0.6- to 0.8-deg separations. We suggest that the separation between the visual stimuli modulates the combined effects of perceptual grouping cues on complete object representation.     

The effects of global grouping laws on surface lightness perception

Previous studies of lightness perception have shown that local surface grouping laws such as proximity and T junction were powerful determinants of target surface lightness. Recent lightness theories also emphasize the importance of local grouping of surfaces. In this study, we further examined the effects of three global grouping laws--symmetry, repetition, and alternation--on lightness perception. Local surface grouping laws such as proximity and good continuation were controlled across all of our stimulus displays. Participants' lightness perception consistently depended on a given surface's belongingness as determined by these laws--that is, global grouping laws affected a target surface's lightness perception. Our results indicate that global grouping laws determine a target surface's lightness when local surface grouping does not produce any distinct surface belongingness. Implications of our basic results are discussed in terms of a recent lightness theory.     

Figure-ground perception and random geometry

Constructs of random geometry were applied to the problem of figure-ground perception. Random-dot images of black and white dots with various area fractions and tesselations (square and triangular lattices) were used as stimuli. The constructs of random geometry are correlation functions of n-th order and some functionals defined on them. The only parameter which is independent of the tesselation used is the first-order correlation which is the area fraction. It was first conjectured and then experimentally verified that figureground perception is not affected by the various tesselations used. Thus, figure-ground phenomena depend only on the area fraction of the white and black dots in the stimulus. There is a perceptual bias for white, that is, figure-ground reversal is easiest at 40 percent white-black area fraction. It was also experimentally shown that size-constancy prevails in figure-ground perception, but brightnes s-constancy does not.     

Figure-ground perception and random geometry

Constructs of random geometry were applied to the problem of figure-ground perception. Random-dot images of black and white dots with various area fractions and tesselations (square and triangular lattices) were used as stimuli. The constructs of random geometry are correlation functions of n-th order and some functionals defined on them. The only parameter which is independent of the tesselation used is the first-order correlation which is the area fraction. It was first conjectured and then experimentally verified that figure-ground perception is not affected by the various tesselations used. Thus, figure-ground phenomena depend only on the area fraction of the white and black dots in the stimulus. There is a perceptual bias for white, that is, figure-ground reversal is easiest at 40 percent white-black area fraction. It was also experimentally shown that size-constancy prevails in figure-ground perception, but brightness-constancy does not.     

Effects of grouping and attention on the perception of causality

Beyond perceiving patterns of motion in simple dynamic displays, we can also perceive higher level properties, such as causality, as when we see one object collide with another object. Although causality is a seemingly high-level property, its perception--like the perception of faces or speech--often appears to be automatic, irresistible, and driven by highly constrained and stimulus-driven rules. Here, in an exploration of such rules, we demonstrate that perceptual grouping and attention can influence the both perception of causality in ambiguous displays. We first report several types of grouping effects, based on connectedness, proximity, and common motion. We further suggest that such grouping effects are mediated by the allocation of attention, and we directly demonstrate that causal perception can be strengthened or attenuated on the basis of where observers are attending, independent of fixation. Like Michotte, we find that the perception of causality is mediated by strict visual rules. Beyond Michotte, we find that these rules operate not only over discrete objects, but also over perceptual groups, constrained by the allocation of attention.     

Perceptual grouping between successively presented stimuli and its relation to visual simultaneity and masking

Summary A 4×4 matrix of dots was presented by a tachistoscope. The first and the third columns of the stimulus pattern were presented first for 20 ms and then the second and the fourth columns were presented for 20 ms with SOAs of 0 to 170 ms. Luminous dots on a dark background, black dots on a white background, and black dots and small outline circles on a white background were used in Experiments I, II, and III, respectively. In each experiment, 5 Ss were asked to report whether the stimulus dots were seen as 4 horizontal rows or 4 vertical columns, and whether they were seen simultaneously or successively. The experimental results showed that the time range of successive grouping was nearly the same as that of perceptual simultaneity in Experiments I and II, but was much greater than the latter in Experiment III where the similarity factor favored successive grouping. Successive grouping generally occurred in the same time range with visual masking of dot patterns by random dots, temporal organization of patterns from successive stimulus elements. But the time range was generally wider than those of contrast reduction caused by temporal luminance summation, metacontrast, and apparent movement.A part of this study was conducted during the junior author's stay at Chiba University and presented by him at the 20th International Congress of Psychology at Tokyo, August 13–19, 1972 (Yamada and Oyama, 1972)     

Motion structure in five-dot patterns as a determinant of perceptual grouping

The effect of basic motion structures on perceptual grouping was studied with five-dot motion patterns. Four basic motion structures were identified in terms of proximal common and relative motion vectors. In a forced-choice situation, the observers had to decide to which of two pairs of dots a fifth critical dot seemed to belong. Thus, one of two possible three-dot units was chosen by the observers. The two possible three-dot units defined different motion structures, and the chosen motion structure was considered to have stronger grouping power than the alternative structure had. It was found that parallel common motions (perceived translation in the plane) had the strongest grouping power; these were followed by circular common motions (perceived rotation in the plane), concurrent relative motions (perceived translation in depth), and, finally, parallel relative motions (perceived rotation in depth). The results also suggested effects of proximity and orientation of axis of rotation. It is further argued that the relative grouping power of the motion structures could not solely be interpreted in terms of changes of directions and distances between the dots. Instead it is suggested that vector analysis is a fundamental perceptual activity and that basic motion structures determine grouping power.