On the quantitative analysis of craniofacial asymmetry in 3D

We address a systematic evaluation of facial asymmetry from a population of 100 high-quality laser scans, which are first symmetrized and then manipulated to introduce 25 synthetic patterns with a variety of asymmetries. A quantitative evaluation is performed by comparing these known asymmetries with those estimated by different automatic algorithms. Estimation of the actual asymmetries present in the original surface was also addressed. We find that widely used methods based on least-squares minimization not only fail to produce accurate estimates but, in some cases, recover asymmetry patterns that are radically different from the actual asymmetry of the input surfaces, with low or even negative correlation coefficients. A number of alternative algorithms are tested, including landmark-, midline- and surface-based approaches. Among these, we find that the best performance is obtained by a hybrid approach combining surface and midline points, framed within a least median of squares algorithm with weights that decay exponentially with the distance from the midline and an additional term to ensure that the recovered pattern of asymmetry is itself symmetric.