Psychophysical studies of shape with Fourier descriptor stimuli

Radial frequency patterns describe a small and perceptually distinct subset of all possible planar shapes

The visual system is exposed to a vast number of shapes and objects. Yet, human object recognition is effortless, fast and largely independent of naturally occurring transformations such as position and scale. The precise mechanisms of shape encoding are still largely unknown. Radial frequency (RF) patterns are a special class of closed contours defined by modulation of a circle's radius. These patterns have been frequently and successfully used as stimuli in vision science to investigate aspects of shape processing. Given their mathematical properties, RF patterns can not represent any arbitrary shape, but the ability to generate more complex, biologically relevant, shapes depicting the outlines of objects such as fruits or human heads raises the possibility that RF patterns span a representative subset of possible shapes. However, this assumption has not been tested before. Here we show that only a small fraction of all possible shapes can be represented by RF patterns and that this small fraction is perceptually distinct from the general class of all possible shapes. Specifically, we derive a general measure for the distance of a given shape's outline from the set of RF patterns, allowing us to scan large numbers of object outlines automatically. We find that only between 1% and 6% of naturally smooth outlines can be exactly represented by RF patterns. We present results from a visual search experiment, which revealed that searching an RF pattern among non-radial frequency patterns is efficient, whereas searching an RF pattern among other RF patterns is inefficient (and vice versa). These results suggest that RF patterns represent only a restricted subset of possible planar shapes and that results obtained with this special class of stimuli can not simply be expected to generalise to any arbitrary planar shape.

Creating Noisy Stimuli

A method for creating a variety of pseudo-random ‘noisy’ stimuli that possess several useful statistical and phenomenal features for psychophysical experimentation is outlined. These stimuli are derived from a pseudo-periodic function known as multidimensional noise. This class of function has the desirable property that it is periodic, defined on a fixed domain, is roughly symmetric, and is stochastic, yet consistent and repeatable. The stimuli that can be created from these functions have a controllable amount of complexity and self-similarity properties that are further useful when generating naturalistic looking objects and surfaces for investigation. The paper addresses the creation and manipulation of stimuli with the use of noise, including an overview of this particular implementation. Stimuli derived from these procedures have been used successfully in several shape and surface perception experiments and are presented here for use by others and further discussion as to their utility.

Discrete fixed-resolution representations in visual working memory

Limits on the storage capacity of working memory significantly affect cognitive abilities in a wide range of domains, but the nature of these capacity limits has been elusive. Some researchers have proposed that working memory stores a limited set of discrete, fixed-resolution representations, whereas others have proposed that working memory consists of a pool of resources that can be allocated flexibly to provide either a small number of high-resolution representations or a large number of low-resolution representations. Here we resolve this controversy by providing independent measures of capacity and resolution. We show that, when presented with more than a few simple objects, human observers store a high-resolution representation of a subset of the objects and retain no information about the others. Memory resolution varied over a narrow range that cannot be explained in terms of a general resource pool but can be well explained by a small set of discrete, fixed-resolution representations.

Detection of shape in radial frequency contours: independence of local and global form information

Radial frequency (RF) patterns have been used to study the processes involved in shape perception. The psychophysical literature suggests that there are distinct global and local shape detection processes for low and high radial frequency patterns, but this has not been tested in a combined contour pattern, such as would be needed to describe the contours of most natural objects. Here, we combined frequencies from the local and global range onto a compound RF structure. Observers' ability to detect a single RF component on the compound pattern was measured. Results show that sensitivity to high frequency local deviations in shape was not affected by the presence of a globally perceived low frequency pattern. In the reverse condition, detection of global form was not influenced by adding local deviations onto the structure. This suggests that local and global shape information can be detected independently within the human visual system.

Evaluating shape after-effects with radial frequency patterns

Mechanisms selective for complex shape are vulnerable to adaptation techniques historically used to probe those underlying performance in lower-level visual tasks. We explored the nature of these shape after-effects using radial frequency patterns. Adapting to a radial frequency pattern resulted in a strong and systematic after-effect of a pattern that was 180 degrees out of phase with the adapting pattern. This after-effect was characterized as both a shift in the point of subjective equality and an increase in response uncertainty. The after-effect transferred across adapting pattern contrast and adaptor amplitude, suggesting an involvement from shape-specific mechanisms located at higher processing stages along the visual pathway. Moreover, our results suggested that the shift in the point of subjective equality was guided by global processing mechanisms, whereas the increase in uncertainty reflected activity from local processing mechanisms. Together, these results suggest that shape-specific after-effects reflect gain control processes at various stages of processing along the ventral pathway.

Dynamics of shape interaction in human vision

Spatial context can alter perceived shape, and temporal context can influence the perception of a stimulus. We sought to determine the time course of shape interactions by using a paradigm in which closed shape contours are laterally displaced over space and time. Target and masks are separated by various stimulus onset asynchrony (SOA) values, yielding forward, backward, and simultaneous masking conditions. Results indicate that spatial lateral interactions of shape are amplified by temporal asynchrony, reaching a peak at SOAs of 80-110 ms. Mask amplitude scales all effects and masking is shape specific. When a single mask follows the target, both spatial configuration and mask onset transient are critical in determining depth of masking. When the target is followed by two sequential masks, the possibility of apparent motion determines whether one or both masks drive masking. These findings suggest that temporal interactions of shape are dependent on an interactive combination of shape specificity and transients, that apparent motion plays a modulatory role, and that target shape is determined after a temporal window, not at its onset.

Symmetry perception: a novel approach for biological shapes

The majority of quantitative studies on symmetry perception have employed random dot patterns, yet symmetrical random patterns are not common in nature. Here we explore symmetry perception utilizing sums of radial frequency (RF) patterns to define complex shapes. When a pair of RF patterns with different frequencies are added, the relative phase of the two components provides a precise measure of the degree of deviation from bilateral symmetry. Sums of RF2-RF7 define such diverse biological shapes as human heads, animal heads, torsos, and many fruit, so discrimination of symmetries defined by these patterns is highly relevant to biological vision. Here we show that symmetry discrimination during brief presentations is best for RF2+RF3 but becomes impossible for RF2+RF7. Further experiments demonstrate that the underlying neural mechanisms differ from those involved in random dot symmetry detection. These results were used to predict symmetry thresholds for deviations from bilateral symmetry of head shapes based on a principal components analysis of 30 female heads. Human V4 is hypothesized to be the site for symmetry discrimination of RF patterns but not of random dot patterns.