A test of the minimum principle requires a perceptual coding system

A language of thought for the mental representation of geometric shapes

In various cultures and at all spatial scales, humans produce a rich complexity of geometric shapes such as lines, circles or spirals. Here, we propose that humans possess a language of thought for geometric shapes that can produce line drawings as recursive combinations of a minimal set of geometric primitives. We present a programming language, similar to Logo, that combines discrete numbers and continuous integration to form higher-level structures based on repetition, concatenation and embedding, and we show that the simplest programs in this language generate the fundamental geometric shapes observed in human cultures. On the perceptual side, we propose that shape perception in humans involves searching for the shortest program that correctly draws the image (program induction). A consequence of this framework is that the mental difficulty of remembering a shape should depend on its minimum description length (MDL) in the proposed language. In two experiments, we show that encoding and processing of geometric shapes is well predicted by MDL. Furthermore, our hypotheses predict additive laws for the psychological complexity of repeated, concatenated or embedded shapes, which we confirm experimentally.

Sensitivity to geometric shape regularity in humans and baboons: A putative signature of human singularity

Among primates, humans are special in their ability to create and manipulate highly elaborate structures of language, mathematics, and music. Here we show that this sensitivity to abstract structure is already present in a much simpler domain: the visual perception of regular geometric shapes such as squares, rectangles, and parallelograms. We asked human subjects to detect an intruder shape among six quadrilaterals. Although the intruder was always defined by an identical amount of displacement of a single vertex, the results revealed a geometric regularity effect: detection was considerably easier when either the base shape or the intruder was a regular figure comprising right angles, parallelism, or symmetry rather than a more irregular shape. This effect was replicated in several tasks and in all human populations tested, including uneducated Himba adults and French kindergartners. Baboons, however, showed no such geometric regularity effect, even after extensive training. Baboon behavior was captured by convolutional neural networks (CNNs), but neither CNNs nor a variational autoencoder captured the human geometric regularity effect. However, a symbolic model, based on exact properties of Euclidean geometry, closely fitted human behavior. Our results indicate that the human propensity for symbolic abstraction permeates even elementary shape perception. They suggest a putative signature of human singularity and provide a challenge for nonsymbolic models of human shape perception.

On Bayesian Simplicity in Human Visual Perceptual Organization

A returning idea among some Bayesians in research on human visual perceptual organization is that the surprisal of something (i.e., the negative logarithm of its probability) expresses its complexity (i.e., the length of its shortest description). Bayes' rule is a powerful modeling tool and descriptive simplicity is a rich concept, but this idea is wishful thinking at best: If true, it would unify the simplicity and likelihood principles, which reflect two traditionally opposed schools of thought on perceptual organization. Some rapprochement between the two principles can certainly be discerned, but the aforementioned idea lacks formal underpinning and confounds otherwise perfectly good ideas. Here, this idea is revisited and its latest version is debunked step by step. In addition, I argue that its likely origin lies, inadvertently, in a standard Bayesian textbook: The author made (a) a pivotal mistake and (b) a compelling argument that was overinterpreted by others.

The simplicity principle in perception and cognition

The simplicity principle, traditionally referred to as Occam's razor, is the idea that simpler explanations of observations should be preferred to more complex ones. In recent decades the principle has been clarified via the incorporation of modern notions of computation and probability, allowing a more precise understanding of how exactly complexity minimization facilitates inference. The simplicity principle has found many applications in modern cognitive science, in contexts as diverse as perception, categorization, reasoning, and neuroscience. In all these areas, the common idea is that the mind seeks the simplest available interpretation of observations- or, more precisely, that it balances a bias toward simplicity with a somewhat opposed constraint to choose models consistent with perceptual or cognitive observations. This brief tutorial surveys some of the uses of the simplicity principle across cognitive science, emphasizing how complexity minimization in a number of forms has been incorporated into probabilistic models of inference. WIREs Cogn Sci 2016, 7:330-340. doi: 10.1002/wcs.1406 For further resources related to this article, please visit the WIREs website.

Local and Global Processes in Visual Completion

In the natural environment, objects are frequently occluded, and people continuously complete partly occluded objects Do local processes or global processes control the completion of partly occluded objects? To answer this question, most previous studies simply asked subjects to draw the completions they “saw” Such drawing tasks are highly subjective, and they provide equivocal results Our studies are the first to use an objective, implicit paradigm (primed matching) to determine the extent to which local or global processes underlie the visual completion of partly occluded objects Our results suggest that global processes dominate perceptual completion, whereas local processes do not play a large role Therefore, local theories of completion, or theories in which local processes dominate, cannot be entirely correct

Bayesian confusions surrounding simplicity and likelihood in perceptual organization

In the study of perceptual organization, the Occamian simplicity principle (which promotes efficiency) and the Helmholtzian likelihood principle (which promotes veridicality) have been claimed to be equivalent. Proposed models of these principles may well yield similar outcomes (especially in everyday situations), but as argued here, claims that the principles are equivalent confused subjective probabilities (which are used in Bayesian models of the Occamian simplicity principle) and objective probabilities (which are needed in Bayesian models of the Helmholtzian likelihood principle). Furthermore, Occamian counterparts of Bayesian priors and conditionals have led to another confusion, which seems to have been triggered by a dual role of regularity in perception. This confusion is discussed by contrasting complete and incomplete Occamian approaches to perceptual organization.

Real space and represented space: Cross-cultural perspectives

This paper examines the contribution of cross-cultural studies to our understanding of the perception and representation of space. A cross-cultural survey of the basic difficulties in understanding pictures—ranging from the failure to recognise a picture as a representation to the inability to recognise the object represented in the picture— indicates that similar difficulties occur in pictorial and nonpictorial cultrues. The experimental work on pictorial space derives from two distinct traditions: the study of picture perception in “remote” populations and the study of the perceptual illusions. A comprison of the findings on pictorial space perception with those on real space perceptual illusions. A comparison of findings on pictorial space perception with those on real space perception and perceptual constancy suggersts that cross-cultural differences in the perception of both real and representational space involve two different types of skills: those related exclusively to either real space or representational space, and those related to both. Different cultural groups use different skills to perform the same perceptual tasks.

Contour curvature polarity and surface interpolation

Contour curvature polarity (i.e., concavity/convexity) is recognized as an important factor in shape perception. However, current interpolation models do not consider it among the factors that modulate the trajectory of amodally-completed contours. Two hypotheses generate opposite predictions about the effect of contour polarity on surface interpolation. Convexity advantage: if convexities are preferred over concavities, contours of convex portions should be more extrapolated than those of concave portions. Minimal area: if the area of amodally-completed surfaces tends to be minimized, contours of convex portions should be less extrapolated than contours of concave portions. We ran three experiments using two methods, simultaneous length comparison and probe localization, and different displays (pictures vs. random dot stereograms). Results indicate that contour polarity affects the amodally-completed angles of regular and irregular surfaces. As predicted by the minimal area hypothesis, image contours are less extrapolated when the amodal portion is convex rather than concave. The field model of interpolation [Fantoni, C., & Gerbino, W. (2003). Contour interpolation by vector-field combination. Journal of Vision, 3, 281-303. Available from http://journalofvision.org/3/4/4/] has been revised to take into account surface-level factors and to explain area minimization as an effect of surface support ratio.

Amodal completion of partly occluded figures: Effect of contour orientation

In present study the temporal dimension of amodal completion in visual occlusion was investigated. We supposed that the visual system prefers to complete normally (vertically-horizontally) oriented contours than the oblique ones. Using the prime-matching paradigm we investigated the strength of amodal primes effects on processing speed of relating test figures. Both, prime and test stimuli were presented in normal and oblique (45o) orientations. The primes were pairs of identical figures: CC (truncked squares), SS (hexagons) and AA (amodal patterns: circle occludes either amodal C or amodal S). Temporal distribution of stimuli: prime 400ms, ISIs 20ms and test figures until response. Test figures were the ?same? pairs, CC and SS, and the ?different? pairs, SC and CS. Each ?same? test figures had its identical prime (CC => CC or SS => SS) and its amodal prime (AA => CC and AA => SS). The subjects were asked to answer whether the figures in test stimuli were same or different. The ?same? RTs were analysed. The effect of amodal prime was systematically weaker (longer RT) than the effect of identical primes. Orientation was not significant factor. The significant partial interaction prime x orientation was obtained for C test figures: the effect of amodal prime was closer to effect of identical prime when the contour was normally oriented. In the case of S test figures the interaction was not obtained. We concluded that the more symmetric test figure (S) was resistant to the prime effect.

Simplicity versus likelihood in visual perception: from surprisals to precisals

The likelihood principle states that the visual system prefers the most likely interpretation of a stimulus, whereas the simplicity principle states that it prefers the most simple interpretation. This study investigates how close these seemingly very different principles are by combining findings from classical, algorithmic, and structural information theory. It is argued that, in visual perception, the two principles are perhaps very different with respect to the viewpoint-independent aspects of perception but probably very close with respect to the viewpoint-dependent aspects which, moreover, seem decisive in everyday perception. This implies that either principle may have guided the evolution of visual systems and that the simplicity paradigm may provide perception models with the necessary quantitative specifications of the often plausible but also intuitive ideas provided by the likelihood paradigm.

The role of objects in perceptual grouping

Perceptual organization can be viewed as the selection of the best or "most reasonable" parse of a given scene. However, the principles that determine which interpretation is most reasonable have resisted most attempts to define them formally. This paper summarizes a formal theory of human perceptual organization, called minimal model theory, in which the best interpretation of a given scene is expressed as the formally minimal interpretation in a well-defined space of possible interpretations. We then focus specifically on the role of types of grouping units, in particular the difficult notion of "object". Although grouping is often thought of as the process of dividing the image into objects, most research in perceptual grouping actually focuses on simpler types of units, such as contours and surfaces. Minimal model theory characterizes grouping units at a logical level, demonstrating how formal assumptions about units induce the observer to place a certain preference ranking on interpretations. The theory is then applied to the more subtle problem of objects, culminating in a definition for objects that is formally rigorous but at the same time captures some of the flexibility of human intuitions about objects.

Integrating global and local aspects of visual occlusion

The phenomenon of visual occlusion has frequently been studied by means of two-dimensional line drawings. These drawings may elicit various interpretations. Sometimes a mosaic of shapes is seen, sometimes a shape that partly occludes another shape. In the latter case, observers often have a clear idea about the form of the partly occluded shape. Local and global pattern aspects both seem to be decisive with respect to the preferred interpretation. An attempt is made to integrate these aspects by applying the global-minimum principle to the perceptual complexity of three distinct components of those pattern interpretations: (i) The internal structure, dealing with each of the shapes separately, (ii) the external structure, dealing with the positional relation between these shapes, and (iii) the virtual structure, dealing with the occluded parts of the shapes. The perceptual complexity of each of these three components can be expressed in terms of structural information. The hypothesis that the perceptually preferred interpretation is the one for which the total information load is minimal is tested on many patterns stemming from different studies on pattern completion.

From geons to structure. A note on object representation

Two models of object perception are compared: recognition by components (RBC), proposed by Biederman, and structural information theory (SIT), initially proposed by Leeuwenberg. According to RBC a complex object is decomposed into predefined elementary objects, called geons. According to SIT, the decomposition is guided by regularities in the object. It is assumed that the simplest of all possible interpretations of any object is perceptually preferred. The comparison deals with two aspects of the models. One is the representation of simple objects--various definitions of object axes are considered. It is shown that the more these definitions account for object regularity and thus the more they agree with SIT, the better the object representations predict object classification. Another topic concerns assumptions underlying the models: the identification of geons is mediated by cues which are supposed to be invariant under varying viewpoints of objects. It is argued that such cues are not based on this invariance but on the regularity of actual objects. The latter conclusion is in line with SIT. An advantage of RBC, however, is that it deals with the perceptual process from stimulus to interpretation, whereas SIT merely concerns the outcome of the process, not the process itself.

Local and global minima in visual completion: effects of symmetry and orientation

The visual information that specifies three-dimensional objects is often incomplete because objects occlude parts of themselves and other objects. Yet people rarely have difficulty perceiving complete, three-dimensional forms. Somehow the visual system seems to 'complete' partially specified objects. The perceptual processes underlying this seemingly effortless and immediate completion are poorly understood. Sekuler and Palmer designed in 1992 the primed-matching paradigm for the objective study of completion effects and their microgenesis. Results from the paradigm suggest that global processes may play a role early in perceptual completion, and that local processes dominate only under limited conditions of figural regularity and orientation. These results are not consistent with purely local or purely global theories of completion. The findings have implications for object perception and representation.

Local and global factors in visual occlusion

Although interest in the phenomenon of visual occlusion is of very long standing, only a small number of experimental studies have been reported, and available theories fail to give satisfactory explanations of the data. In this paper the efficacy of local factors in organising the perception of globally regular occlusion patterns is explored. Three experiments are reported in which the relative contribution of local and global factors to the salience of percepts is investigated. It is demonstrated that local factors play a very important role in the perception of these kinds of patterns.

Perceptual organisation and object recognition--POOR is the acronym, rich the notion

Instead of studying perceptual organisation and object recognition in relative isolation, they can be viewed as two highly related sets of processes performed by the visual system to achieve its goal of acquiring information about the world. Fifteen papers devoted to specific subproblems within this active area of research have been brought together in two successive issues of Perception. Collectively they demonstrate that focusing on the functional interrelationships between perceptual organisation and object recognition will enrich our understanding of each of the subprocesses involved. The editorial provides an overview of the papers together with a discussion on how they relate to one another. If a general message is to be extracted from this set of papers, it is that the reported findings and the speculations offered to explain them suggest that the visual system's processes cannot be characterised in general by simple dichotomies such as analytic versus wholistic, bottom-up versus top-down, local versus global, low-level versus high-level, parallel versus serial, etc. Instead, it appears that a wide variety of mechanisms is available to the visual system. Therefore, a complete understanding of its functioning will require careful examination of the circumstances within which one processing mechanism seems to be selected over another, depending on the available information, the task demands, and perhaps even the observer's individual characteristics.

A good-continuation model of some occlusion phenomena

Occlusion phenomena raise two questions: (1) When will an occluding and a partly occluded object be seen, as opposed to several nonoverlapping objects? (2) What is seen behind the occluding object? Available theories give no satisfactory description of occlusion data. In our view, this situation is at least partially due to the fact that patterns used in occlusion studies are always regular, whereas it is almost unknown which regularities are actually perceived in occlusion patterns. We have therefore collected a complete set of data for a restricted domain of patterns with minimal regularity. Starting from these data, we have developed a model of the perceptual organization of this class of patterns and tested it in a second experiment. The model is a specification of the Gestalt law of good continuation. It assumes that there is a tendency to describe a pattern by the smallest possible number of contour elements and with the smallest possible changes of direction within and between necessary contour elements. The results fit in well with the predictions of the model. It is further demonstrated that the model also describes the preferred interpretations of many regular patterns, published in other studies.

Unity and variety in visual form

Some stimuli are perceived as unitary patterns, and others as dual or plural patterns. Such 'unity-and-variety' phenomena are explained by various process approaches of perception, such as the global precedence hypothesis, the preattentive orientation detection assumption, and the recognition-by-components model. However, these three approaches, which will be discussed in this paper, each explain a different subset of these phenomena. It will be argued that not only these three subsets but also other unity-and-variety phenomena can be explained from just one point of view by adopting the descriptive minimum principle. This principle states that the preferred interpretation of a pattern is reflected by the simplest of all possible representations of that pattern. The highest hierarchical level in the simplest pattern-representation will be called the 'superstructure' of the pattern. The superstructure of a pattern neither refers necessarily to the largest or global pattern component, nor is assessed necessarily in a primary stage in the perception process. Yet, it will be argued that the superstructure is decisive in determining whether a shape is perceived either as unitary or as dual.

The minimum principle and visual pattern completion

The minimum principle states that a perceiver will see the simplest possible interpretation of a pattern. Some theorists of human perception take this principle as a core-explanatory concept. Others hold the view that a perceptual minimum principle is untenable. In two recent extensive surveys of the relevant literature a more differentiated position is taken: the minimum principle is not renounced in a definite way. In the research reported here, an intuitively appealing specification of a minimum principle is tested. An experiment on visual pattern completion was performed in which patterns were presented to subjects who traced the contours of the shapes they saw. It was predicted that there would be a preference for interpretations that describe a pattern as a set of separate shapes with minimal information load as computed by Leeuwenberg's coding language. However, only half of the responses given by the subjects were predicted by this specification of a minimum principle. It was further demonstrated that locally complex interpretations of junctions of contour elements are easily made, but not in order to attain globally minimal interpretations.

Necessary considerations for a theory of form perception: a theoretical and empirical reply to Boselie and Leeuwenberg (1986)

Boselie and Leeuwenberg (1986) recently defended their version of the minimum principle, called structural information theory or SIT, against a varied set of criticisms. Two of the most notable of these criticisms are (i) that perceptual organization can proceed as a piecemeal, rather than as a global, process (as demonstrated by partially-biased Necker cubes and 'impossible' figures), and (ii) that perceptual organization is influenced by subjective variables as well as by stimulus variables (Peterson and Hochberg 1983). The second criticism was acknowledged by Boselie and Leeuwenberg but not addressed. The first criticism was addressed by the introduction of two new variables into SIT in order to argue that the perceived organization of partially-biased Necker cubes and impossible figures can be predicted by a global coding scheme, thereby supporting rather than refuting global minimum principles. It is argued here that the criticisms cannot be dismissed by this rebuttal, which is focused narrowly on single examples rather than on the general principles embodied by the demonstrations. The implications of piecemeal perception and subjective mediation are spelled out, and both old and new data showing that the applicability of global minimum principles must be reexamined, not merely defended, are discussed. Finally, the argument for a richer, more interacting, theory of form perception is presented.