Categorizing Three-Dimensional Symmetry Using Reflection, Rotoinversion, and Translation Symmetry

Symmetry is a property that has been widely examined clinically as a measurement of health and aesthetic appeal. Many current techniques that assess geometric symmetry rely on interpretation from a trained operator or produce two-dimensional measurements that cannot express the three-dimensional character of an object. In this article, we propose a comprehensive markerless method that describes an object’s symmetry using three types of fundamental symmetry, reflection, rotoinversion a combination of reflection and rotation and translation a process of reflection and rigid movement. This is done by mirroring an object over an arbitrary plane and aligning the mirrored image with the original object in a position that minimizes deviation between both objects. Each object’s symmetry can be displayed in two ways, numerically, with a best plane of symmetry or “Psym”, a fixed point and the mirrored objects rotation and magnitude of translation in relation to the original object, and visually, through a 3D deviation contour map. Three examples were made: Model 1 showed reflection symmetry and resulted in a standard deviation of 0.002 mm, Model 2 expressed rotoinversion symmetry and produced a standard deviation of 0.003 mm and Model 3 expressed translational symmetry which resulted in a translation magnitude difference of 0.015% with respect to model height. This simple procedure accurately recognizes reflection, rotoinversion and translation symmetry, takes minimal time and expertise and has the ability to expand previous case specific methods to a global application of symmetry analysis.