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

Abstract

Radial frequency patterns describe a small and perceptually distinct subset of all possible planar shapes.Schmidtmann, GThe 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.

An image-computable model of human visual shape similarity

“…Despite this, the representation of shape in the PLOS COMPUTATIONAL BIOLOGY human visual system remains elusive, and the basis for shape similarity judgments remains unclear. In part, this is due to the numerous potential shape descriptors proposed in the past, including simple metrics, like solidity [36], and contour curvature [39], and more complex metrics like shape context [38], part-based ones [1,85], Fourier descriptors [41,100,101], radial frequency components [82,102], shape skeletons [40,46,98,99,[103][104][105][106][107], linearity [108] convexity [109][110][111][112], triangularity [113], rectilinearity [114], information content [115,116] and models based on generalized cylinders for describing 3D animal-like objects [117]. While it is widely believed that human shape representations are multidimensional, to date there has been no comprehensive attempt to implement this idea in a concrete image-computable model.…”

Eccentricity Effect of Deformation Detection for Radial Frequency Patterns With Their Centers at Fixation Point

“…However, Wilkinson et al (1998) explained the mathematical limitations of RF patterns and stressed their differences from Fourier shape descriptors, which can in principle be used to create any kind of closed, two-dimensional shape. The representational and perceptual limitations of RF patterns were pointed out by Schmidtmann and Fruend (2019), who demonstrated that only a very small subset of natural and synthetic shapes can be reliably represented by RF compound patterns and that this subset is perceptually distinct. However, despite these limitations, the visual performances of RF patterns that have been observed in a wide range of stimulus conditions have provided deep insight into the shape processing mechanism of the visual system.…”

Effect of Shape on the Magnitude of the Delboeuf Illusion

“…In the present experiments, the participants were familiar with the circle, and thus, may have paid more attention to evaluating illusion magnitude (Shulman, 1992). The other explanation may be that neurons sensitive to curvature importantly for processing visual form (Salmela, Henriksson & Vanni, 2016;Schmidtmann & Fruend, 2019). Consequently, the size of the test gure would more accurately re ect the target, and hence, the magnitude of the quasi-Delboeuf illusion would be smaller for circles than for regular octagons or regular hexagons.…”