Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data

Master Thesis


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The presence of non-linear shape variation in 3D data is known to influence the reliability of linear statistical shape models (SSM). This problem is regularly acknowledged, but disregarded, as it is assumed that linear models are able to adequately approximate such non-linearities. Model reliability is crucial for medical imaging and computer vision tasks; however, prior to modelling, the non-linearity in the data is not often considered. The study provides a framework to identify the presence of non-linearity in using principal component analysis (PCA) and autoencoders (AE) shape modelling methods. The data identified to have linear and non-linear shape variations is used to compare two sophisticated techniques: linear Gaussian process morphable models (GPMM) and non-linear variational autoencoders (VAE). Their model performance is measured using generalisation, specificity and computational efficiency in training. The research showed that, given limited computational power, GPMMs managed to achieve improved relative generalisation performance compared to VAEs, in the presence of non-linear shape variation by at least a factor of six. However, the non-linear VAEs, despite the simplistic training scheme, presented improved specificity generative performance of at least 18% for both datasets.