Estimation of shape model parameters for 3D surfaces

Statistical shape models are widely used as a compact way of representing shape variation. Fitting a shape model to unseen data enables characterizing the data in terms of the model parameters. In this paper a Gauss-Newton optimization scheme is proposed to estimate shape model parameters of 3D surfaces using distance maps, which enables the estimation of model parameters without the requirement of point correspondence. For applications with acquisition limitations such as speed and cost, this formulation enables the fitting of a statistical shape model to arbitrarily sampled data. The method is applied to a database of 3D surfaces from a section of the porcine pelvic bone extracted from 33 CT scans. A leave-one-out validation shows that the parameters of the first 3 modes of the shape model can be predicted with a mean difference within [-0.01,0.02] from the true mean, with a standard deviation less than 0.34.