2D Geometry Predicts Perceived Visual Curvature in Context-Free Viewing

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.

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