Asymmetry analysis of bilateral shapes

Many biological objects possess approximate bilateral symmetry about a midplane. This paper uses landmark-based methods to measure departures from bilateral symmetry. The landmarks for each object come in pairs either side of a midplane or as solos on or near the midplane. After registration, a vector of unsigned elementary features is constructed to describe the asymmetry of each object. Two approaches are proposed to compare the level of asymmetry between two groups of objects. In the first approach the elementary features are combined into a scalar composite asymmetry score for each object; then standard univariate tests are used on the composite asymmetry score to assess asymmetry. In the second approach a univariate test statistic is constructed for each elementary feature; then the maximum of these statistics is used for a union-intersection test. The methodology is illustrated on two data sets collected to assess the success of two types of surgery: (1) cleft lip surgery, where the level of asymmetry is compared between a group of cleft lip subjects and a group of normal subjects and (2) orthognathic surgery, where for each patient, the level of asymmetry after surgery is compared to that before surgery.