Set-size effects for sampled shapes: experiments and model

Abstract

The location of imperfections or heterogeneities in shapes and contours often correlates with points of interest in a visual scene. Investigating the detection of such heterogeneities provides clues as to the mechanisms processing simple shapes and contours. We determined set-size effects (e.g., sensitivity to single target detection as distractor number increases) for sampled contours to investigate how the visual system combines information across space. Stimuli were shapes sampled by oriented Gabor patches: circles and high-amplitude RF4 and RF8 radial frequency patterns with Gabor orientations tangential to the shape. Subjects had to detect a deviation in orientation of one element (“heterogeneity”). Heterogeneity detection sensitivity was measured for a range (7–40) of equally spaced (2.3–0.4°) elements. In a second condition, performance was measured when elements sampled a part of the shapes. We either varied partial contour length for a fixed (7) set-size, co-varying inter-element spacing, or set-size for a fixed spacing (0.7°), co-varying partial contour length. Surprisingly, set-size effects (poorer performance with more elements) are rarely seen. Set-size effects only occur for shapes containing concavities (RF4 and RF8) and when spacing is fixed. When elements are regularly spaced, detection performance improves with set-size for all shapes. When set-size is fixed and spacing varied, performance improves with decreasing spacing. Thus, when an increase in set-size and a decrease in spacing co-occur, the effect of spacing dominates, suggesting that inter-element spacing, not set-size, is the critical parameter for sampled shapes. We propose a model for the processing of simple shapes based on V4 curvature units with late noise, incorporating spacing, average shape curvature, and the number of segments with constant sign of curvature contained in the shape, which accurately accounts for our experimental results, making testable predictions for a variety of simple shapes.

Detecting shapes in noise: tuning characteristics of global shape mechanisms

“…For a frequency of RF5, the critical amplitude A crit = 0.038. Both values are close to the data points where coherence thresholds relative to a circle start to increase (ω ≤ 4; A ≤ 0.05; Figure 3), suggesting that the transition from convex to concave may be an important factor in the processing of RF shapes (Kempgens et al, 2013). …”

Aging and the integration of orientation and position in shape perception

“…Interestingly, similar to the current results, the effect of interelement spacing on contour grouping was the same in younger and older subjects (Hadad, 2012;Roudaia et al, 2013), even though overall ability to detect and discriminate contours in noise declines with aging (Del Viva & Agostini, 2007;Roudaia et al, 2011Roudaia et al, , 2013. Although Day and Loffler (2009) speculated that the shape illusion is generated by integration by a global pooling mechanism, as opposed to local contour integration mechanisms thought to underlie detection of elongated contours in noise (e.g., Field, Hayes, & Hess, 1993), there is growing evidence suggesting that global shape mechanisms do not operate directly on individual contour elements, but instead pool information from intermediate-stage mechanisms that integrate local orientation information to encode curved contour segments and inflection points (e.g., Bell et al, 2011;Bell, Hancock, Kingdom, & Peirce, 2010;Kempgens et al, 2013;Schmidtmann et al, 2012). To the extent that there may be shared, overlapping mechanisms that contribute to performance in different tasks that involve the integration of orientation information in sampled contours, the current results are consistent with previous studies (Hadad, 2012;McKendrick et al, 2010;Roudaia et al, 2013) in finding no differential effect of interelement spacing on performance with aging.…”

“…Furthermore, several studies have shown that the inputs to the global pooling stage are themselves outputs of intermediate stage curvature detectors that integrate local orientation information to encode curvature and inflection points along the contour (Bell et al, , 2010(Bell et al, , 2011. A biologicallyplausible model developed by Kempgens et al (2013), based on an earlier model by Poirier and Wilson (2006), consists of five stages: In the first three stages, local contour information, the size and center of the shape are determined and, in the fourth stage, multiple local curvature units integrate information from local orientation channels in a nonlinear fashion, and outputs of one or more of these curvature units are combined with the earlier stages of the model to represent the curvature signals in relation to the center of the shape. In the final stage, a global mechanism pools the inputs of the various arc units from the fourth stage and a population code of these convexities and concavities in different locations around the shape combine to represent different shape types.…”

Probing intermediate stages of shape processing

“…Based on these behavioral results, models have been devised for shape processing that incorporate a population code strategy (Kempgens, Loffler, & Orbach, 2013;Poirier & Wilson, 2006;Wilson & Wilkinson, 2015). This follows cell recordings from V4, which have been shown to be consistent with a population code for complex curved shapes (Pasupathy & Connor, 2001.…”

“…One model (Kempgens et al, 2013) arose from a psychophysical investigation into the ability to detect local changes in sampled RF contours. Observers were required to detect a deviation in orientation of one element from tangential to the sampled shape.…”