The perceptual organization of dot lattices

Bravais (1850/1949) demonstrated that there are five types of periodic dot patterns (or lattices): oblique, rectangular, centered rectangular, square, and hexagonal. Gestalt psychologists studied grouping by proximity in rectangular and square dot patterns. In the first part of the present paper, I (1) describe the geometry of the five types of lattices, and (2) explain why, for the study of perception, centered rectangular lattices must be divided into two classes (centered rectangular andrhombic). I also show how all lattices can be located in a two-dimensional space. In the second part of the paper, I show how the geometry of these lattices determines their grouping and their multistability. I introduce the notion ofdegree of instability and explain how to order lattices from most stable to least stable (hexagonal). In the third part of the paper, I explore the effect of replacing the dots in a lattice with less symmetric motifs, thus creating wallpaper patterns. When a dot pattern is turned into a wallpaper pattern, its perceptual organization can be altered radically, overcoming grouping by proximity. I conclude the paper with an introduction to the implications of motif selection and placement for the perception of the ensuing patterns.     

Toward a Psychophysics of Perceptual Organization Using Multistable Stimuli and Phenomenal Reports

We explore experimental methods used to study the phenomena of perceptual organization, first studied by the Gestalt psychologists. We describe an application of traditional psychophysics to perceptual organization and offer alternative methods. Among these, we distinguish two approaches that use multistable stimuli: (1) phenomenological psychophysics, in which the observer's response is assumed to accurately and directly reflect perceptual experience; and (2) the interference paradigm, in which an observer's response is evaluated as correct or incorrect because it pertains to a corrigible task, but does not directly reflect the observer's experience. We show that phenomenological psychophysics can yield valuable information about perceptual organization and lends itself to the development of quantitative theory. We discuss some criticisms of the method and argue that the two approaches that use multistable stimuli are complementary. We also compare each of the approaches with traditional psychophysics. We conclude that the several methods are convergent.     

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.     

Dynamics of perceptual grouping: Similarities in the organization of visual and auditory groups

In vision, the Gestalt principles of perceptual organization are generally well understood and remain a subject of detailed analysis. However, the possibility for a unified theory of grouping across visual and auditory modalities remains largely unexplored. Here we present examples of auditory and visual Gestalt grouping, which share important organizational properties. In particular, similarities are revealed between grouping processes in apparent motion, auditory streaming, and static 2-D displays. Given the substantial difference in the context, within which the phenomena in question occur (auditory vs. visual, static vs. dynamic), these similarities suggest that the dynamics of perceptual organization could be associated with a common (possibly central) mechanism. If the relevance of supramodal invariants of grouping is granted, the question arises as to whether they can be studied empirically. We propose that a “force-field” theory, based on a differential-geometric interpretation of perceptual space, could provide a suitable starting point for a systematic exploration of the subjective properties of certain classes of auditory and visual grouping phenomena.     

Relative importance of perceptual and mnemonic variance in human temporal bisection

We investigated the relative contributions of perception and reference memory to behavioural variability in a temporal discrimination with human subjects. We used two temporal bisection tasks. In both tasks each trial consisted of a sequential presentation of three intervals, two standards, and a probe, and subjects were asked to judge the similarity of each probe against the two standards. In a "single bisection", the standards' duration was constant across trials. In a "roving bisection", the two standards were trial unique. We compared our results with the predictions from a model related to Scalar Expectancy Theory, with the added assumption that the decision process minimizes the expected number of errors given the information available. The model shows that if errors in reference memory were dominant the psychometric function should be identical for single and roving tasks, and if perceptual errors were dominant the psychometric function should be steeper for the single than for the roving bisection. As we found that psychometric functions were steeper for the single than for the roving tasks, we concluded that perceptual errors are dominant.     

Goodness of regularity in dot patterns: global symmetry, local symmetry, and their interactions

Goodness is a classic Gestalt notion defined as salience or perceptual strength of a given pattern. All operational models of goodness have assigned a central role to mirror symmetry but not much attention has been paid to the distinction between global and local mirror symmetry, and their possible interactions. We designed eight different types of dot patterns (all consisting of 80 dots), combining different numbers (0, 1, and 2) and relative orientations (parallel or orthogonal to each other) of local and global axes of symmetry (affecting 50% or 100% of the dots, respectively) at different absolute orientations (vertical and horizontal). Each of 640 trials consisted of a short presentation of a new dot pattern, which subjects had to classify as regular or random. We hypothesised that the overall goodness of patterns is not the simple sum of the amount of regularity present in them but depends on the cooperation and competition between symmetries. The results confirmed our hypothesis, showing that performance in this regularity-detection task did not increase in a linear way when some symmetries were added to other symmetries.     

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.     

Subliminal Gestalt grouping: Evidence of perceptual grouping by proximity and similarity in absence of conscious perception

Previous studies making use of indirect processing measures have shown that perceptual grouping can occur outside the focus of attention. However, no previous study has examined the possibility of subliminal processing of perceptual grouping. The present work steps forward in the study of perceptual organization, reporting direct evidence of subliminal processing of Gestalt patterns. In two masked priming experiments, Gestalt patterns grouped by proximity or similarity that induced either a horizontal or vertical global orientation of the stimuli were presented as masked primes and followed by visible targets that could be congruent or incongruent with the orientation of the primes. The results showed a reliable priming effect in the complete absence of prime awareness for both proximity and similarity grouping principles. These findings suggest that a phenomenal report of the Gestalt pattern is not mandatory to observe an effect on the response based on the global properties of Gestalt stimuli.     

A dynamic model for anomalous figures: the shape of line-induced brightness modifications.

It is recognized that a fundamental role in the perception of anomalous figures is played by the intensity and shape of brightness modifications induced by line ends. The aim of this work was to study the structure of these modifications experimentally, by using variously arranged dots as probes. It was thus assumed that dots can measure activations generated inside abrupt line ends. The results show distribution of activation which differs according to dot distance and angle with respect to the continuation of the line near its end. These data do not agree with the predictions of information processing models in the literature on anomalous figures, which are based on perceptually postulated figures accounting for unlikely gaps. However, they do agree with the dynamic model proposed here, which is based on the idea that certain figure characteristics, eg the differential brightness of anomalous figures, depend on activation distribution which in turn depends on the organization of the forces in play. This idea is rooted in Gestalt theory. Another model supported by our experimental data is Grossberg's neural dynamic approach. In this case too, the basic idea is that of activation distribution which depends on the interaction of complex neural networks functioning according to special algorithms.     

Structural salience and the nonaccidentality of a gestalt

We perceive structure through a process of perceptual organization. Here we report a new perceptual organization phenomenon-the facilitation of visual grouping by global curvature. Observers viewed patterns that they perceived as organized into collections of curves. The patterns were perceptually ambiguous such that the perceived orientation of the patterns varied from trial to trial. When patterns were sufficiently dense and proximity was equated for the predominant perceptual alternatives, observers tended to perceive the organization with the greatest curvature. This effect is tantamount to visual grouping by maximal curvature and thus demonstrates an unprecedented effect of global structure on perceptual organization. We account for this result with a model that predicts the perceived organization of a pattern as function of its nonaccidentality, which we define as the probability that it could have occurred by chance. Our findings demonstrate a novel relationship between the geometry of a pattern and the visual salience of global structure.     

Visual attention and perceptual grouping.

Perceptual organization is thought to involve an analysis of both textural discontinuities and perceptual grouping. In earlier work, we found that textural discontinuities were detected normally even when visual attention was engaged elsewhere. Here we report how perceptual grouping is affected when visual attention is engaged by a concurrent visual task. To elicit perceptual grouping, we used the Gestalt demonstrations of grouping on the basis of proximity and of similarity. Four tasks were investigated, some requiring the observer to discriminate between horizontal and vertical grouping, and some requiring the observer to merely detect the presence or absence of grouping. Visual attention was engaged at the center of the display by a form identification task. The detection of a textural discontinuity served as a control task. Concurrent form identification conflicted with all four grouping tasks, resulting in a significant reduction of grouping performance in each case. No performance reduction was observed when either form identification or grouping discrimination was combined with the detection of a textural discontinuity. These results suggest that perceptual grouping and form identification compete for visual attention, whereas the detection of a textural discontinuity does not.     

Languages for Gestalts of line patterns

Any formal model of visual Gestalt perception requires a language for representing possible perceptual structures of visual stimuli, as well as a decision criterion that selects the actually perceived structure of a stimulus among its possible alternatives. This paper discusses an existing model of visual Gestalt perception that is based on Structural Information Theory. We investigate two factors that determine the representational power of this model: the domain of visual stimuli that can be analyzed, and the class of perceptual structures that can be generated for these stimuli. We show that the representational power of the existing model of Structural Information Theory is limited, and that some of the generated structures are perceptually inadequate. We argue that these limitations do not imply the implausibility of the underlying ideas of Structural Information Theory and introduce alternative models based on the same ideas. For each of these models, the domain of visual stimuli that can be analyzed properly is formally defined. We show that the models are conservative modifications of the original model of Structural Information Theory: for cases that are adequately analyzed in the original model of Structural Information Theory, they yield the same results.     

Tests of parallel versus integrated structure in polyrhythmic tapping

Musically trained subjects tapped three beats with their right hand versus two beats with their left hand in synchrony with two corresponding tones. For independent groups of subjects, the pitch difference of the two tones was either small to encourage an integrated perceptual organization or large to encourage a streamed perceptual organization. Integrated versus parallel motor organization was tested by examining the pattern of covariances among intertap intervals. All subjects exhibited integrated motor organization. An integrated multiplicative hierarchical model of motor organization was superior to a serial chained model and to an independent hierarchical model in describing the pattern of covariances. The subjects who heard tones that encouraged an integrated percept performed with less variability than the subjects who heard tones that encouraged a streamed percept. This superior performance with an integrated motor organization and an integrated rather than a streamed perceptual organization is interpreted as evidence for temporal perceptual-motor compatibility.     

Trance and confusion in Gestalt therapy

This article introduces hypnotic principles of confusion and trance as fundamental operations in Gestalt therapy. A process is identified which utilizes perceptual shifts of reference as a method of organizing Gestalt techniques. The sequence of operations constituting the confusion process is outlined and developed in a psychotherapy session through the use of implication, dissociation, and embodiment. The development of this organization of Gestalt therapy is intended to enhance the strategic capacities of therapists.     

Gestalt Issues in Modern Neuroscience

We present select examples of how visual phenomena can serve as tools to uncoverbrain mechanisms. Specifically, receptive field organization is proposed as a Gestalt-like neural mechanism of perceptual organization. Appropriate phenomena, such as brightness and orientation contrast, subjective contours, filling-in, and aperture-viewed motion, allow for a quantitative comparison between receptive fields and their psychophysical counterparts, perceptive fields. Phenomenology might thus be extended from the study of perceptual qualities to their transphenomenal substrates, including memory functions. In conclusion, classic issues of Gestalt psychology can now be related to modern “Gestalt psychophysics” and neuroscience.     

Visual attention and perceptual grouping

Perceptual organization is thought to involve an analysis of bothtextural discontinuities andperceptual grouping. In earlier work, we found that textural discontinuities were detected normally even when visual attention was engaged elsewhere. Here we report how perceptual grouping is affected when visual attention is engaged by a concurrent visual task. To elicit perceptual grouping, we used the Gestalt demonstrations of grouping on the basis of proximity and of similarity. Four tasks were investigated, some requiring the observer to discriminate between horizontal and vertical grouping, and some requiring the observer to merely detect the presence or absence of grouping. Visual attention was engaged at the center of the display by a form identification task. The detection of a textural discontinuity served as a control task. Concurrent form identification conflicted with all four grouping tasks, resulting in a significant reduction of grouping performance in each case. No performance reduction was observed when either form identification or grouping discrimination was combined with the detection of a textural discontinuity. These results suggest that perceptual grouping and form identification compete for visual attention, whereas the detection of a textural discontinuity does not.     

Has the time come to rehabilitate Gestalt theory?

Summary The distinction is drawn between the metatheoretical commitments of Gestalt theory and their instantiations in explicit theory. It is argued that the metatheoretical commitments of Gestalt theory reflect important insights which might have served as the foundation of a theory of perception that avoids a number of the major difficulties associated with constructivism and the theory of direct perception. For this reason rehabilitation of the reputation of Gestalt theory is urged. In the concluding section certain similarities between the foundational premises of Gestalt theory and parallel distributed processing approaches are noted.The contents of this paper were presented initially at a symposium on perceptual theory in honor of Irvin Rock which convened in Washington, DC, on the occasion of the 1986 meetings of the American Psychological Association     

The role of perceptual organization in the depth perception of kinetic lattice displays

College student subjects were asked to judge perceived depth in computer-generated displays. In all displays, one lattice of points moved through a stationary lattice in either a rowwise or columnwise direction. No points of the two lattices ever touched. Two display variables, strain and shear, each had a significant effect on depth ratings. Shear, however, was only effective at the level of strain for which depth ratings were high. The results confirm earlier studies in which “topological breakage” information was found to affect depth perception. The outcome of this study suggests that principles of perceptual organization can influence the nature of effective breakage information.