Asymmetry Analysis of Bilateral Shapes

TL;DR

This paper develops landmark-based methods to measure and compare bilateral asymmetry in biological shapes, using size-and-shape analysis and statistical tests, demonstrated on a dataset of cleft lip surgery outcomes.

Contribution

It introduces two novel approaches for testing asymmetry differences between groups, including a feature extraction technique for identifying key landmarks.

Findings

Significant asymmetry differences found between cleft lip and normal groups.

Method successfully identifies anatomically relevant landmarks.

Approach applicable to medical shape analysis and symmetry assessment.

Abstract

Many biological objects possess bilateral symmetry about a midline or midplane, up to a ``noise'' term. This paper uses landmark-based methods to measure departures from bilateral symmetry, especially for the two-group problem where one group is more asymmetric than the other. In this paper, we formulate our work in the framework of size-and-shape analysis including registration via rigid body motion. Our starting point is a vector of elementary asymmetry features defined at the individual landmark coordinates for each object. We introduce two approaches for testing. In the first, the elementary features are combined into a scalar composite asymmetry measure for each object. Then standard univariate tests can be used to compare the two groups. In the second approach, a univariate test statistic is constructed for each elementary feature. The maximum of these statistics lead to an overall test statistic to compare the two groups and we then provide a technique to extract the important features from the landmark data. Our methodology is illustrated on a pre-registered smile dataset collected to assess the success of cleft lip surgery on human subjects. The asymmetry in a group of cleft lip subjects is compared to a group of normal subjects, and statistically significant differences have been found by univariate tests in the first approach. Further, our feature extraction method leads to an anatomically plausible set of landmarks for medical applications.