Assessing asymmetry using reflection and rotoinversion in biomedical engineering applications

Symmetry is a trait that has been extensively reviewed, especially clinically, as an indication of ideal geometry and health. Many geometric symmetry assessment techniques rely on two-dimensional measurements that do not account for the three-dimensional nature of the object. In this article, two methods, reflection and a process termed rotoinversion, a combination of reflection and rotation, are presented as potential methods to assess an object’s deviation from symmetry. With reflection, the geometric models are reflected about a calculated best plane of symmetry. With rotoinversion, the models are reflected about an arbitrary plane and then rigidly translated and rotated to best align the translated and original models. The methods give the same results for bilaterally symmetric objects, but different results for bilaterally and rotationally symmetric objects. The two methods are applied to assess asymmetry in adolescent idiopathic scoliosis torso geometric models, producing similar results. There was an angle of 0.408° between the normal to the plane of reflection from the reflection process and the normal from the rotoinversion process and average rotation of 0.067° from rotoinversion. The most appropriate method depends on the purpose of the symmetry assessment and must be determined on a case-by-case basis.