#### Keywords

Symmetry, Scene Perception, Medial Axis Transform

#### Abstract

Symmetry has been shown to be an important principle that guides the grouping of scene information. Previously, we have described a method for measuring the local, ribbon symmetry content of line-drawings of real-world scenes (Rezanejad, et al., MODVIS 2017), and we demonstrated that this information has important behavioral consequences (Wilder, et al., MODIVS 2017). Here, we describe a continuous, local version of the symmetry measure, that allows for both ribbon and taper symmetry to be captured. Our original method looked at the difference in the radius between successive maximal discs along a symmetric axis. The number of radii differences in a local region that exceeded a threshold, normalized by the number of total differences, was used as the symmetry score at an axis point. We now use the derivative of the radius function along the symmetric axis between two contours, which allows for a continuous method of estimating the score which does not need a threshold. By replacing the first derivative with a second derivative, we can generalize this method to allow pairs of contours which taper with respect to one another, to express high symmetry. Such situations arise, for example, when parallel lines in the 3D world project onto a 2D image. This generalization will allow us to determine the relative importance of taper and ribbon symmetries in natural scenes.

#### Start Date

17-5-2018 12:00 PM

#### End Date

17-5-2018 12:25 PM

#### Included in

Cognition and Perception Commons, Other Computer Sciences Commons, Quantitative Psychology Commons

Measuring Symmetry in Real-World Scenes Using Derivatives of the Medial Axis Radius Function

Symmetry has been shown to be an important principle that guides the grouping of scene information. Previously, we have described a method for measuring the local, ribbon symmetry content of line-drawings of real-world scenes (Rezanejad, et al., MODVIS 2017), and we demonstrated that this information has important behavioral consequences (Wilder, et al., MODIVS 2017). Here, we describe a continuous, local version of the symmetry measure, that allows for both ribbon and taper symmetry to be captured. Our original method looked at the difference in the radius between successive maximal discs along a symmetric axis. The number of radii differences in a local region that exceeded a threshold, normalized by the number of total differences, was used as the symmetry score at an axis point. We now use the derivative of the radius function along the symmetric axis between two contours, which allows for a continuous method of estimating the score which does not need a threshold. By replacing the first derivative with a second derivative, we can generalize this method to allow pairs of contours which taper with respect to one another, to express high symmetry. Such situations arise, for example, when parallel lines in the 3D world project onto a 2D image. This generalization will allow us to determine the relative importance of taper and ribbon symmetries in natural scenes.