Unsupervised Diffeomorphic Surface Registration and Non-Linear Modelling

• URL: http://arxiv.org/abs/2109.13630v1
• Date: Tue, 28 Sep 2021 11:47:12 GMT
• Title: Unsupervised Diffeomorphic Surface Registration and Non-Linear Modelling
• Authors: Balder Croquet, Daan Christiaens, Seth M. Weinberg, Michael Bronstein, Dirk Vandermeulen, Peter Claes
• Abstract summary: We propose a one-step registration model for 3D surfaces that internalises a lower dimensional probabilistic deformation model (PDM) 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.
• Score: 4.761477900658674
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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