The topological approach to perceptual organization

To address the fundamental question of “what are the primitives of visual perception”, a theory of topological structure and functional hierarchy in visual perception has been proposed. This holds that the global nature of perceptual organization can be described in terms of topological invariants, global topological perception is prior to the perception of other featural properties, and the primitives of visual form perception are geometric invariants at different levels of structural stability. In Part I of this paper, I will illustrate why and how the topological approach to perceptual organization has been advanced. In Part II, I will provide empirical evidence supporting the early topological perception, while answering some commonly considered counteraccounts. In Part III, to complete the theory, I will apply the mathematics of tolerance spaces to describe global properties in discrete sets. In Part IV, I will further present experimental data to demonstrate the global-to-local functional hierarchy in form perception, which is stratified with respect to structural stability defined by Klein's Erlangen Program. Finally, in Part V, I will discuss relations of the global-to-local topological model to other theories: The topological approach reformulates both classical Gestalt holism and Gibson's direct perception of invariance, while providing a challenge to computational approaches to vision based on the local-to-global assumption.     

Orientation relative to the retina determines perceptual organization

Two experiments are reported which show that perceptual unit formation, as measured by Gillam’s method of using common reversals of ambiguous lines as an index of their coherence, depends strongly on the orientation of the configuration. Measurements under conditions of 90° head and body tilt show that the critical orientation is retinal, not physical. The results are discussed in relation to other findings and to possible explanations.     

Heterosocial perceptual organization: application of the choice model to sexual coercion

Luce's (1959, 1963) choice model was used to characterize individual differences in men's perception of women's affect as friendly, sexually interested, sad, or rejecting. Women's clothing styles were associated with differences in the model's parameters. Sensitivity to sadness, rejection, and friendliness declined when women were dressed provocatively, whereas sensitivity to sexual interest increased. Provocative clothing was also associated with an increased bias to assume that positive affect was sexual interest rather than friendliness. Men at risk for perpetrating sexual aggression were less sensitive to women's affect than low-risk men were. They were also more likely than low-risk men to associate provocative clothing with sexual interest, and conservative clothing with friendliness. Results indicate that heterosocial perception may help to predict sexually coercive behavior and may be an important target for intervention.     

Checkerboard-specific color aftereffects: A failure to find effects of perceptual organization

Two experiments investigated the effects of differing perceptual organizations of reversible figures on McCollough aftereffects. Experiment 1 used colored checkerboard inducing stimuli and achromatic grating test stimuli. While some subjects tended to organize the checkerboards into rows and/or columns and others to organize them into obliques, these variations did not result in differences in aftereffect direction or magnitude. Experiment 2 induced an aftereffect with colored gratings and tested with checkerboards, gratings, and a reversible concentric octagon pattern. Perceptual organization had no effect on results for checkerboards, but was related to aftereffect strength for the octagon pattern. Indirect evidence suggests that, in the latter case, differences in aftereffect strength may have influenced the perceived organization, rather than vice versa. Finally, regardless of the specific organization perceived, spontaneous viewing of all test stimuli produced stronger aftereffects than were found when subjects reorganized the pattern. This may have resulted from a viewing strategy associated with reorganization, since similarly small aftereffects were found when subjects concentrated their attention on a single pattern element.     

Learning perceptual organization in infancy

It has been demonstrated that older infants (6- to 7-month-olds), but not younger infants (3- to 4-month-olds), use form similarity to organize stimuli consisting of X and O elements. We investigated whether utilization of form similarity is governed by maturation or experience by contrasting how infants perform when familiarized with a single exemplar versus multiple exemplars depicting a particular organization. In Experiment 1, 3- to 4-month-olds failed to organize alternating columns or rows of squares and diamonds or Hs and Is, respectively. In Experiment 2, same-aged infants familiarized with all three patterns (X-O, square-diamond, H-I) displayed evidence of organization. The results suggest that 3- to 4-month-olds can use form similarity to organize visual patterns in a concept-formation task. The findings imply that perceptual organization based on form similarity is learned through experience with multiple patterns depicting a common arrangement, rather than immediately apprehended in an individual pattern.     

Rethinking perceptual organization: The role of uniform connectedness

A principle of perceptual organization, calleduniform connectedness (UC), is described, and a theoretical approach to perceptual organization is proposed in which this principle plays a fundamental role. The principle of UC states that closed regions of homogeneous properties—such as lightness, chromatic color, texture, and so forth—tend to be perceived initially as single units. We demonstrate its effects and show that they occur even when opposed by powerful grouping principles such as proximity and similarity. We argue that UC cannot be reduced to such grouping principles, because it is not a form of grouping at all. We then propose a theoretical framework within which UC accounts for the initial (orentry level) organization of the visual field into primitive units. Classical principles of grouping operate after UC, creating superordinate units consisting of two or more basic-level units. Parsing processes also operate after UC, dividing basic-level units into subordinate parts. UC in the retinal image is proposed to be a necessary, but not a sufficient, condition for unit formation, since connected elements on the retina that are perceived to lie in separate depth planes fail to be perceived as units. This fact, together with other evidence that the Gestalt principles of grouping are based onperceived (rather than retinal) relations, suggests that the organization of visual stimulation into UC objects is ultimately achieved within a relatively late, postconstancy representation of environmental surfaces. The implications of this possibility are discussed in light of present theories of visual perception.     

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.     

Predicting brain organization from dichotic listening performance: Cortical and subcortical functional asymmetries contribute to perceptual asymmetries

The patterns of perceptual asymmetry elicited by dichotic speech and complex pitch stimuli were evaluated in a group of 28 normal, right-handed subjects. As in previous studies, between 70 and 75% of the subjects showed a right-ear advantage for speech and left-ear advantage for pitch. However, less than half of the subjects (46%) showed the expected pattern on both tests. It is argued that the assumption of symmetrical, contralateral auditory pathway superiority during dichotic stimulation is only appropriate in roughly half of the dextral population. In the remaining half, significant subcortical asymmetries and/or a lack of contralateral advantage appear to be present. The assessment of complementary cortical functions should provide a way to reduce the confounding of cortical and subcortical contributions to auditory perceptual asymmetries, and thus provide a more accurate behavioral index of brain organization.     

Goodness takes effort: perceptual organization in dual-task settings

We adopted the Psychological Refractoriness Paradigm to study whether perceptual Goodness affects the load of central processing resources. In three dual-task experiments, 2-Alternative Forced Choice auditory classification was followed by a same-different task in which Garner's classical five-dot patterns were presented. Goodness of these patterns and stimulus-onset asynchrony (SOA) between the first and second task were varied between trials. These factors had additive effects on response latencies and accuracy, indicating that pattern Goodness determines central processing load in performing the same-different task. In a fourth experiment, same-different judgment with Garner patterns was the single task. SOA between the first and second pattern was varied. Over-additive effects of Goodness with decreasing SOA were obtained, indicating sharing of central resources between consolidation of the first Garner pattern and performing the same-different task. Whereas, the resources needed for the latter, again, depend on Goodness, those needed for consolidation are independent of it.     

Multielement visual tracking: attention and perceptual organization.

Two types of theories have been advanced to account for how attention is allocated in performing goal-directed visual tasks. According to location-based theories, visual attention is allocated to spatial locations in the image; according to object-based theories, attention is allocated to perceptual objects. Evidence for the latter view comes from experiments demonstrating the importance of perceptual grouping in selective-attention tasks. This article provides further evidence concerning the importance of perceptual organization in attending to objects. In seven experiments, observers tracked multiple randomly moving visual elements under a variety of conditions. Ten elements moved continuously about the display for several seconds; one to five of them were designated as targets before movement initiation. At the end of movement, one element was highlighted, and subjects indicated whether or not it was a target. The ease with which the elements in the target set could be perceptually grouped was systematically manipulated. In Experiments 1-3, factors that influenced the initial formation of a perceptual group were manipulated; this affected performance, but only early in practice. In Experiments 4-7, factors that influenced the maintenance of a perceptual group during motion were manipulated; this affected performance throughout practice. The results suggest that observers spontaneously grouped the target elements and directed attention toward this coherent but nonrigid virtual object. This supports object-based theories of attention and demonstrates that perceptual grouping, which is usually conceived of as a purely stimulus-driven process, can also be governed by goal-directed mechanisms.     

Asymmetry in 3-D perceptual organization: ground-like surface superior to ceiling-like surface

Attneave (1954) and Barlow (1961) proposed that the visual system might increase efficiency of representation by preferentially encoding spatiotemporally redundant patterns of the external world. The present experiments tested the application of this principle to three-dimensional (3-D) perceptual organization, capitalizing on the ecological constraint that human observers must frequently interact with objects arranged on the ground or on a surface parallel to it (Gibson, 1950). Observers performed a task that required them to perceptually segregate and search multiple items distributed in depth and embedded within a larger, 3-D array of distractors. Stimulus displays were organized to globally recede top-away in depth, as if attached to an underlying ground-like surface, or bottom-away, as if attached to an overhanging ceiling-like surface; ground-like and ceiling-like displays differed only in the direction of disparity gradient within the displays. Primary findings revealed superior performance with ground-like displays, suggesting that spatially and stereoscopically distributed items are more easily organized to represent an ecologically representative pattern, even when no inherent physical regularities favor that pattern.     

Optical defocusing reverses perceptual organization.

At a certain point during the defocusing of a reversible figure, the organization of the figure reversed unexpectedly, and the reversal seemed more abrupt than a spontaneous reversal. The critical point is approximately constant over time for a given subject, and a similar point occurs during refocusing. This phenomenon is discussed in terms of inhibition between competing neural structures.     

Color aftereffects contingent on perceptual organization

The present experiment demonstrated that (a) cognitive organizational factors influence an orientation-contingent color (McCollugh) aftereffect, and (b) adaptation to colored gratings affected the perceptual organization of a reversible figure. Following adaptation to colored gratings, color aftereffects were reported in only one of two organizations of a reversible figure, and the colors conformed to the subjective contours of the test pattern rather than exclusively to the regions defined by horizontal and vertical pattern elements. In addition, an organization of the reversible figure that segregated vertical and horizontal pattern elements was dominant subsequent to adaptation.     

Sequential priming of 3-D perceptual organization

In four experiments, the effects of sequential priming on the perceptual organization of complex three-dimensional (3-D) displays were examined. Observers were asked to view stereoscopic arrays and to search an embedded subset of items for an odd-colored target while 3-D orientation of the stimuli was varied randomly between trials. Search times decreased reliably when 3-D stimulus orientation was unchanged on consecutive trials, indicating substantial sequential priming by 3-D stimulus layout. The priming was nonsensory and was independent of priming by additional stimulus characteristics. Finally, priming by 3-D layout was unaffected by observers' foreknowledge of display orientation. Results indicate that perceptual organization of 3-D stimuli is guided by a short-term trace of 3-D spatial relationships between stimuli.     

Cognitive advantage in sport: the nature of perceptual structures

To extend and clarify the nature of the perceptual processes used by sport experts to perceive schematic sport information, two experiments used schematic football diagrams that varied in structure (structured vs. unstructured) and complexity (complex vs. easy). The primary objective was to examine and characterize the nature of the perceptual structures (chunks) that are initially encoded, stored, and subsequently retrieved. In Experiment 1, compared with nonexperts, experts recalled larger perceptual structures following the initial stimulus presentation of structured stimuli only, replicating the recall findings of previous research in other skill domains. Experiment 2 used a long-term memory recognition task and a sorting task. Experts had superior recall and recognition of structured stimuli only, along with more discriminating sorting criteria of perceptual structures within long-term memory. This suggests that experts possess a highly refined semantic network or organized, structured schematic information. This research extends and clarifies the similarities between the perceptual processes of experts in sport (i.e., football) and experts in skill domains that require obvious cognitive involvement (i.e., chess). The results are discussed with reference to the perceptual and conceptual chunking hypotheses. It is proposed that sport experts' knowledge of a conceptual category enables them to retrieve elements using a "generate-and-test process."