paraafPeter A. van der Helm Demo link
About Teaching Research Publications Presentations


Research



The core of my research concerns perceptual organization. It comprises theoretical research into formal descriptions of visual structures and empirical research triggered by such formal descriptions. This research is performed by means of mathematical formalizations, computer implementations, cognitive models, and psychophysical experiments.

For an empirically oriented book on perceptual organization, see Structural Information Theory
For a theoretically oriented book on perceptual organization, see Simplicity in Vision

For a positioning of my specific research field in the general research field, see Levels of vision
For methodological principles guiding my research, see Marr's levels, Research cycles, and Metaphors of cognition

For a class of "arresting" motion and velocity illusions I found, see Kaleidoscope
For a number of novel concepts I introduced, see Glossary
For a pdf-presentation on my theoretical work, see Visual regularity or its printable handout

My specific research topics include:
  • Structural information theory
    		•  ---   A competitive theory of perceptual organization
  • Information measurement
    		•  ---   From probabilistic to descriptive information
  • Simplicity versus likelihood
    		•  ---   Assessing the veridicality of vision
  • Transparant holographic regularity
    		•  ---   The nature of visual regularity
  • The holographic approach to goodness
    		• ---   A comprehensive model of symmetry perception
  • Transparallel processing by hyperstrings
    		•  ---   Going beyond parallel distributed processing
  • Human cognitive architecture
    		•  ---   From neurons to gnosons



    Structural information theory

    My research on perceptual organization starts from the conglomerate of ideas in structural information theory (SIT). SIT began as a coding model of visual pattern classification which, in interaction with empirical research, developed into a competitive theory of perceptual organization.

    Central to SIT is the simplicity principle, which implies that the visual system is assumed to prefer the simplest interpretation among all possible interpretations of a stimulus. To make quantifiable and verifiable predictions, the interpretations are represented by symbol strings, and the symbol string with the overall simplest code is taken to specify the preferred interpretation. A simplest code enables the reproduction of the stimulus by means of a minimum number of descriptive parameters. It is obtained by capturing a maximum amount of regularity, and it implies a hierarchical stimulus organization in terms of wholes and parts. These wholes and parts then are predicted to be the perceived objects.

    My work on SIT focuses on the foundations of its conglomerate of ideas, and it includes:
    Further reading:
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    Information measurement

    The Morse Code marks the beginning of the Information Age, in the mid 19th century. Since that time, an on-going problem has been the quantification of the amount of information in objects --- where an object may be anything, including messages and perceptual interpretations. In communication theory, this problem was addressed to minimize the long-term burden on transmission channels. Shannon (1948) came with a ground-breaking solution to minimize this burden. Following Nyquist (1924) and Hartley (1928), this solution involves a measure of probabilistic information which implies: The more often an object occurs, the less information it contains.

    In many domains, however, probabilities of occurrence are unknown, if not unknowable. This drawback triggered a rethinking about information, both in mathematics (most prominently by Kolmogorov, 1965) and in perception research (most prominently by Garner, 1962). In mathematics, this rethinking led to algorithmic information theory (AIT) and, in perception research, it led to structural information theory (SIT). Both AIT and SIT define the complexity of an object by the length of its shortest reconstruction recipe. This involves a measure of descriptive information which implies: The more regularity an object exhibits, the less information it contains.

    In contrast to AIT, SIT quantifies information to differentiate between perceptual organizations, makes a distinction between metrical and structural information (following MacKay, 1950, taking the structural information to be decisive in perception), and does not consider any imaginable regularity but only visual regularities. At first, SIT used a complexity metric that performed well empirically but that was not very compelling theoretically. The mathematical characterization of visual regularities as being transparant holographic regularities (see below), however, paved the way for an improved metric which not only is theoretically compelling but also performs better empirically. Since 1990, this improved metric is the standard in SIT.

    Further reading:
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    Simplicity versus likelihood

    Usually, vision is sufficiently reliable (i.e., veridical, or truthful) to guide action. But what makes vision so reliable? Around 1900, Helmholtz proposed the likelihood principle which suggests that the visual system selects interpretations most likely to be true, that is, with the highest probability of occurrence in the world. This sounds attractive but the, thus far unsolved, question then is: How can vision scientists, or the visual system for that matter, acquire knowledge about these probabilities? After all, the tool to assess these probabilities can be nothing else than the visual system itself, so that one would measure still-to-be-explained perceptual preferences rather than probabilities of occurrence in the world.

    In the early 20th century, the Gestaltists argued conversely that the visual system follows its own internal rules of perceptual organization. Hochberg and McAlister (1953) proposed that one of these internal rules is the simplicity principle which suggests that the visual system selects interpretations with the lowest descriptive complexity (see above). Findings in mathematics and psychology show that descriptive simplicity has a stable quantification. Furthermore, SIT's empirically successful model of amodal completion (van Lier et al., 1994) shows that it is possible to integrate viewpoint-independent factors and viewpoint-dependent factors, quantified both in terms of complexities.

    A Bayesian translation of this integration, combined with findings in mathematics, suggests that simplicity and likelihood may be far apart for viewpoint-independent factors (Bayesian priors), but also that they are close for viewpoint-dependent factors (Bayesian conditionals) which seem decisive in the everyday perception by a moving observer. This implies that either principle may have guided the evolution of vision: the likelihood principle is a special-purpose principle in that it is highly adapted to one specific world, whereas the simplicity principle is a general-purpose principle in that it is fairly adaptive to many different worlds.

    Further reading: Spin-off:


    Transparant holographic regularity

    During the past century, formal descriptions of visual regularity relied on the transformational approach, which defines visual regularities as configurations that are invariant under motion (i.e., under rotations or translations). This traditional definition is adequate for object recognition but not for object perception. Therefore, a new formalization was developed, defining visual regularities as transparent holographic configurations; this refers to the following concepts: The three transparent holographic regularities are symmetry, repetition, and so-called alternation. Alternation covers, among others, so-called Glass patterns which consist of randomly positioned but coherently oriented dot pairs.

    Further reading:
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    The holographic approach to goodness

    My empirical research focuses on the perceptual goodness (i.e., detectability) of visual regularities such as symmetry, repetition, and Glass patterns. The literature contains many empirical studies into symmetry, which indeed forms a perfect case to investigate general perceptual processes -- but more so if it is contrasted with other visual regularities as is done in the holographic approach.

    The holographic approach was introduced in the mid 1990s. It adheres the idea that insight in the actual detection process starts with insight in the structures to be detected. To this end, it builds on the mathematical characterization of visual regularities as being transparant holographic regularities (see above). This shared property implies that symmetry, repetition, and Glass patterns have different visual structures, namely, a point structure, a block structure, and a dipole structure, respectively.

    This unique structural differentiation forms the heart of a quantitative model of the detectability of single, perturbed, and nested regularities. A faithful translation into a qualitative process model relates this quantitative model to general perceptual processes. The two models explain a wide range of phenomena; for instance, thus far, these are the only models explaining the key phenomenon that mirror symmetries and Glass patterns are about equally good and better than repetitions. This research line also extends to the role of visual regularities in perceptual organization, that is, in the formation of perceived objects.

    Further reading: Spin-off:


    Transparallel processing by hyperstrings

    A serious problem to SIT's simplicity principle (see above) was the computation of simplest codes of symbol strings. This problem seemed unsolvable, because such a simplest code has to be selected from among a superexponential number of possible codes. Hence, even parallel processing of all possible codes would not be a realistic option. The mathematical characterization of visual regularities as being transparant holographic regularities (see above), however, paved the way for a previously uncharacterized form of processing, namely, transparallel processing: Simultaneous processing of many items as if only one item were concerned.

    In general, items can be processed serially by one processor or in parallel by many processors. Compared to serial processing, parallel processing reduces the time to finish a job but not the amount of work to be done. The amount of work can be reduced substantially if the items can be gathered in a distributed representation, which is a data-structure that exploits the fact that many items share item parts (think of routes as represented in a road map). Then, to select an item that satisfies certain criteria, for instance, it may suffice to process (serially or in parallel) only all different item parts. This form of processing is called distributed processing.

    Transparallel processing goes one step further, by using special distributed representations called hyperstrings. This graph-theoretical concept refers to a collection of strings that can be searched for regularities as if only one string were concerned. Transparent holographic regularities group by nature into hyperstrings, which enables a hierarchically recursive regularity search using hyperstrings. This has been implemented in an algorithm that computes guaranteed simplest codes of symbol strings.

    Further reading:
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    Human cognitive architecture

    The brain is typically assumed to be attuned to relevant regularities in the world. Transparent holographic regularities are visually relevant regularities that lend themselves for transparallel processing (see above). Hence, just as parallel distributed processing, transparallel processing might well be a form of cognitive processing. This idea has been elaborated into a concrete picture of flexible representational cognitive architecture implemented in the relatively rigid neural architecture of the brain.

    To give a gist, in neuroscience, transient neural assemblies in the visual hierarchy in the brain -- which signal their presence by way of firing synchronization of the neurons involved -- are believed to bind similar features in an incoming stimulus. Because binding of similar features is also what hyperstrings do, and because hyperstrings allow for transparallel processing of these similar features, it might well be that the neuronal synchronization in those transient neural assemblies is a manifestation of transparallel feature processing mediated by those assemblies.

    Hence, those temporarily synchronized neural assemblies can be conceived of as neural counterparts of hyperstrings or, in other words, as cognitive information processors which mediate transparallel processing of similar features. This suggests that they are the constituents of flexible self-organizing cognitive architecture in between the relatively rigid level of neurons and the still elusive level of consciousness. They are therefore proposed to be called "gnosons", that is, fundamental particles of cognition.

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