Unsupervised Diffeomorphic Surface Registration and Non-linear Modelling

Abstract

Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric representations, despite increased popularity of 3D surface and shape data in medical image analysis. We propose a one-step registration model for 3D surfaces that internalises a lower dimensional probabilistic deformation model (PDM) using conditional variational autoencoders (CVAE). The deformations are constrained to be diffeomorphic using an exponentiation layer. The one-step registration model is benchmarked against iterative techniques, trading in a slightly lower performance in terms of shape fit for a higher compactness. We experiment with two distance metrics, Chamfer distance (CD) and Sinkhorn divergence (SD), as specific distance functions for surface data in real-world registration scenarios. The internalised deformation model is benchmarked against linear principal component analysis (PCA) achieving competitive results and improved generalisability from lower dimensions.

Static and Motion Facial Analysis for Craniofacial Assessment and Diagnosing Diseases

“…Deep learning-based techniques are in their infancy but have the power to reduce the time complexity considerably. By learning a mapping directly from an input 3D mesh to a standard mesh representation, the expensive, usually iterative, optimization required by more traditional methods is reduced to a single-step inference (28)(29)(30).…”