Abstract
Planar geometry was exploited for the computation of symmetric visual curves in the image plane, with consistent variations in local parameters such as sagitta, chordlength, and the curves' height-to-width ratio, an indicator of the visual area covered by the curve, also called aspect ratio. Image representations of single curves (no local image context) were presented to human observers to measure their visual sensation of curvature magnitude elicited by a given curve. Nonlinear regression analysis was performed on both the individual and the average data using two types of model: (1) a power function where y (sensation) tends towards infinity as a function of x (stimulus input), most frequently used to model sensory scaling data for sensory continua, and (2) an “exponential rise to maximum” function, which converges towards an asymptotically stable level of y as a function of x. Both models provide satisfactory fits to subjective curvature magnitude as a function of the height-to-width ratio of single curves. The findings are consistent with an in-built sensitivity of the human visual system to local curve geometry, a potentially essential ground condition for the perception of concave and convex objects in the real world.
Highlights
The question whether the human brain may have an inbuilt sense of geometry has led to the emergence of new approaches to visual cognition (e.g., [1])
Objects represented in the two-dimensional image plane cover spaces with a roughly elliptic geometry (Figure 1)
Global shape representation is enabled by local stimulus biases favouring symmetry and other 2D structural regularities [14, 18]
Summary
The question whether the human brain may have an inbuilt sense of geometry has led to the emergence of new approaches to visual cognition (e.g., [1]). Local two-dimensional (2D) curvature is a highly informative visual cue for global shape perception, object recognition, and image interpretation (e.g., [2,3,4,5,6,7,8]). Nonconscious brain representations of local stimulus geometry may enable conscious knowledge about object properties and associations between specific two-dimensional projections and their correlated threedimensional structures in the real world (e.g., [1, 9,10,11,12,13,14]). Objects represented in the two-dimensional image plane cover spaces with a roughly elliptic geometry (Figure 1). The receptive field structures of visual cortical neurons (curvature detectors) in the primate brain, sensitive to local 2D properties of curve stimuli, are roughly elliptic (e.g., [15,16,17]). Neurons of the same coding population, responding optimally to deviations from a single straight line (Figure 2), constitute a whole curvature-processing network in the primate brain [19]
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