P. C. Dodwell

The Lie transformation group model of visual perception.

The Lie transformation group model of neuropsychology (LTG/NP) purports to represent and explain how the locally smooth processes observed in the visual field, and their integration into the global field of visual phenomena, are consequences of special properties of the underlying neuronal complex. These properties are modeled by a specific set of mathematical structures that account both for local (infinitesimal) operations and for their generation of the “integral curves” that are visual contours. The purpose of this tutorial paper is to expound, as nontechnically as possible, the mathematical basis for LTG/NP, and to evaluate that model against a reasonable set of criteria for a neuropsychological theory. It is shown that this approach to spatial vision is closer to the mainstream of current theoretical work than might be assumed; recent experimental support for LTG/NP is described.

Infants' Orientation to Lateral Sounds from Birth to Three Months.

Head turning to off-centered sound was videotaped monthly in a group of infants during their first 3 months of life. Infants turned reliably toward the sound at birth and at 1 and 3 months of age. They failed to respond reliably at 2 months due to an increase in no-turn responses. Potential explanations for the temporary decline in orientation responses to sound are discussed.

Reaching in very young infants.

It has been claimed that reaching to visually presented targets is a valid indicator of perceptual capacity in very young infants. In a previous report we failed to replicate the findings on which that claim is based. Here we reanalyze some of the tapes of the first report, using a less restricted criterion for what constitutes a reach, and a much more detailed analysis of the various components of reaching behaviour. A number of components are readily distinguished and reliably observed. Infants of seven to twenty-one days show great individual variation in their reaching, from no such behaviour to a great deal. Certain clusters of the components of reaching can be used to define different reaching ‘styles’. The infants who reached most frequently in our sample all showed a dominant pattern of reaching, which in certain respects appears to be more mature than that of other babies. The finer analysis revealed no differences in the reaching behaviour to objects and pictures of objects, even among the most active reachers.

Global factors generate the McCollough effect.

It has recently been demonstrated that certain globally orthogonal pattern pairs derived from Hoffmans Lie Transformation Group Model of Neuropsychology (LTG/NP) are sufficient to generate McCollough effects (pattern-contingent colour aftereffects: PCCAES). We now provide evidence that the global factors postulated to generate these particular PCCAEs are also necessary. In Experiment 1 observers made controlled eye movements over the induction patterns and subsequently showed PCCAEs which were as strong as those obtained under central fixation. The induction process therefore did not depend on selectively adapting local oriented and colour-specific edge detectors. The global structure of the inducing patterns appears to be a necessary component of the generation of such aftereffects. In Experiment 2, a number of pattern pairs having various degrees of global organization were used as induction patterns, but in every case there was an equal degree of local orthogonality. Local orthogonality was shown not to be sufficient to induce PCCAEs, but global orthogonality was. These results lend strong support to the notion that McCollough-type PCCAEs are generated in a structure of the visual system somewhat above the level of strictly local operations, whether defined as edge and bar detectors or, equivalently, as units selectively tuned to different spatial frequencies and orientations. The global nature of the effects, and the particular pattern structures involved, lead us to suggest that Hoffmans LTG/NP provides a sound basis for explaining our findings.

Angular frequency filtering: A basis for pattern decomposition

Much insight has been gained into the nature of early vision by postulating that the system encodes patterns by means of channels, or filters, tuned to specific orientations and spatial frequencies. We argue that a different decomposition, in terms of radially and rotationally symmetrical filters, is equally plausible, both in terms of the geometry of the eye and the ecology of visual pattern recognition. We demonstrate experimentally some of the properties of angular frequency filtering.

Colored aftereffects contingent on patterns generated by Lie transformation groups.

Two experiments are described which make a preliminary test of the power of the Lie transformation group model of neuropsychology (LTG/NP) in predicting pattern-specificity of visual aftereffects of color. In Experiment 1, each of three groups of eight subjects reported contingent aftereffects (CAEs) of color following induction with one of the three pairs of static representations of first-order Lie orbits, these patterns having been presented alternately (one in red light and one in green) every 9.5 sec during a 10-min adaptation period. This result demonstrates that CAEs can be subserved by each of the three pairs of elementary patterns generated by the LTG/NP. In Experiment 2, induction occurred to all three pairs of elementary Lie patterns in sequence. Eleven of the 12 subjects reported color aftereffects, five subjects on patterns from all three pairs, indicating that several pattern-specific aftereffects of color can coexist in an individual observer. Together, these results suggest that the LTG/NP is of value in describing the mechanism of CAEs, which are taken here to be subserved not by visual “molecules,” such as edges or dipoles, but rather by global vectorfield properties of patterns.

The discrimination of structure in vectorgraphs: Local and global effects

Many recent electrophysiological studies have demonstrated specificity for orientation and position tuning in single units of the visual system. Psychophysical investigations have produced complementary evidence for orientation and position coding in vision which is usually interpreted in terms of the underlying neuronal properties. To date, no studies have endeavored to relate such “local” receptive field response profiles to more “global” or field-specific aspects of the input signal. In a series of experiments, we have investigated orientation/position sensitivity as a function of general orientation and position rules governing line element, or “vectorgraph,” displays. We have discovered with such vectorgraph images that individual element acuities are determined by the field structures present. These results show that there are specific “top-down” components even to basic orientation/position coding in the visual system

Pattern perception in infants: Effects of structure and transformation

Four experiments on pattern perception in 4-month-old infants are reported. The first two experiments examined the perception of pattern structure as defined by Garner (1974). Although the infants did not show an immediate preference for well-structured patterns (Experiment 1), during habituation they showed a reliable decrement in looking only to well-structured patterns (Experiment 2). On recovery trials in Experiment 2 infants were presented with two types of pattern change: a new configuration of the habituation pattern and a change in the orientation of the habituation pattern. The infants recovered looking to the orientation change, but generally not to the changes in configuration. It is argued that the results of Experiment 2 highlight the role of symmetry, especially vertical symmetry, in infant pattern perception. Recovery of looking to changes in the orientation, size, and position of the habituation pattern was examined in Experiments 3 and 4 where it was demonstrated that such changes are salient to the infant, arguably because of the presence of a surrounding, external frame.

The roles of pattern orthogonality and color contrast in the generation of pattern-contingent color aftereffects

A previous report (Emerson, Humphrey, & Dodwell, 1985) presented evidence that several pattern-contingent color aftereffects could be established simultaneously in individual observers, using as induction patterns the three basic orthogonal pattern pairs of Hoffman’s (1966) Lie transformation group theory of neuropsychology. Contingent aftereffects (CAEs) generated with these patterns show little interference between pattern pairs. The present experiments explored the induction and test conditions that are sufficient and]or necessary for generating single and multiple CAEs. The data indicated that, for CAE generation to occur, it is necessary that two orthogonal inducing patterns not be viewed in light of the same color. It is sufficient to induce with two distinct patterns in different colors, but more CAEs are reported if these two patterns are orthogonal than if they are nonorthogonal. The scheduling of the inducing conditions is relatively unimportant. In testing, the probability of obtaining a CAE report is greatly increased by presenting the subject with a test pattern designed to elicit two CAEs of different hues; orthogonality of test pattern quadrants has little influence. The results support the view that pattern “channels” bounded by orthogonal pairmates exist in the human visual system and that operations in one channel are relatively independent of operations in another.

Pattern-contingent color aftereffects on noninduced patterns

In a series of experiments, we found that in addition to expected reports of color aftereffects on patterns viewed during induction, reliable and predictable reports of color were given by subjects to patterns they did not view during induction. These reports to noninduced patterns were generally to patterns that were orthogonal to the patterns seen during induction. Induction with, for example, a red vertical grating led to appropriate aftereffects (i.e., green) on that vertical pat. tern and to the complementary aftereffect (i.e., pink) on a horizontal grating. We suggest that such color aftereffects on noninduced patterns are based on a shift in the activity of orientation coding mechanisms as a result of viewing the inducing patterns. We further propose that the results are consistent with the Lie transformation group theory of neuropsychology and that they add to a growing body of research demonstrating the applicability of this theory to the understanding of pattern-contingent color aftereffects.