Symmetry-Factored Statistical Modelling of Craniofacial Shape

Abstract

We present a new method for symmetry-factored statistical modelling of 3D shape. Our method comprises three novel components. First, a means to symmetrise a 3D mesh, regularised using the Laplace-Beltrami operator. Second, a symmetry-aware variant of Generalized Procrustes Analysis (GPA). Third, a means to compute a linear statistical shape model in which symmetry and asymmetric shape variation are modelled separately. We focus on human head data and build the first 3D morphable model of craniofacial asymmetry. The qualitative and quantitative evaluation demonstrates that the proposed model outperforms a linear model that does not decompose symmetric and asymmetric variation. It also validates that symmetry-aware GPA can improve the data generalisation and reconstruction ability of the standard PCA model. We will make our model and the implementation of our method publicly available1.