Unsupervised Diffeomorphic Surface Registration and Non-linear Modelling

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.

[1]  Omid Ekrami,et al.  MeshMonk: Open-source large-scale intensive 3D phenotyping , 2019, Scientific Reports.

[2]  Hao Sun,et al.  Memory-Friendly Deep Mesh Registration , 2020 .

[3]  Mert R. Sabuncu,et al.  Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces , 2019, Medical Image Anal..

[4]  Mert R. Sabuncu,et al.  Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration , 2018, MICCAI.

[5]  Max Welling,et al.  Semi-supervised Learning with Deep Generative Models , 2014, NIPS.

[6]  Peter Claes,et al.  Association Between Prenatal Alcohol Exposure and Craniofacial Shape of Children at 12 Months of Age , 2017, JAMA pediatrics.

[7]  P. Claes,et al.  Pitfalls and Promise of 3-dimensional Image Comparison for Craniofacial Surgical Assessment , 2020, Plastic and reconstructive surgery. Global open.

[8]  John Ashburner,et al.  A fast diffeomorphic image registration algorithm , 2007, NeuroImage.

[9]  Alain Trouvé,et al.  Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms , 2005, International Journal of Computer Vision.

[10]  Leonidas J. Guibas,et al.  PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space , 2017, NIPS.

[11]  Alain Trouvé,et al.  Interpolating between Optimal Transport and MMD using Sinkhorn Divergences , 2018, AISTATS.

[12]  Leonidas J. Guibas,et al.  FlowNet3D: Learning Scene Flow in 3D Point Clouds , 2018, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[13]  George Biros,et al.  Fast GPU 3D Diffeomorphic Image Registration , 2021, J. Parallel Distributed Comput..

[14]  Yang Lei,et al.  Deformable MR-CBCT Prostate Registration using Biomechanically Constrained Deep Learning Networks. , 2020, Medical physics.

[15]  Yuchao Dai,et al.  Deep learning based point cloud registration: an overview , 2020, Virtual Real. Intell. Hardw..

[16]  Xiao Yang,et al.  Fast Predictive Image Registration , 2016, LABELS/DLMIA@MICCAI.

[17]  Ming-Hsuan Yang,et al.  Incremental Learning for Robust Visual Tracking , 2008, International Journal of Computer Vision.

[18]  Jan Eric Lenssen,et al.  Fast Graph Representation Learning with PyTorch Geometric , 2019, ArXiv.

[19]  Nicholas Ayache,et al.  A Log-Euclidean Framework for Statistics on Diffeomorphisms , 2006, MICCAI.

[20]  Ling Shao,et al.  ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks , 2021, ArXiv.

[21]  Hervé Delingette,et al.  Unsupervised Probabilistic Deformation Modeling for Robust Diffeomorphic Registration , 2018, DLMIA/ML-CDS@MICCAI.

[22]  François-Xavier Vialard,et al.  Optimal Transport for Diffeomorphic Registration , 2017, MICCAI.

[23]  Timothy F. Cootes,et al.  A minimum description length approach to statistical shape modeling , 2002, IEEE Transactions on Medical Imaging.

[24]  Feng Liu,et al.  Shape My Face: Registering 3D Face Scans by Surface-to-Surface Translation , 2020, International Journal of Computer Vision.

[25]  Seth M. Weinberg,et al.  The 3D Facial Norms Database: Part 1. A Web-Based Craniofacial Anthropometric and Image Repository for the Clinical and Research Community , 2016, The Cleft palate-craniofacial journal : official publication of the American Cleft Palate-Craniofacial Association.

[26]  Marco Cuturi,et al.  Sinkhorn Distances: Lightspeed Computation of Optimal Transport , 2013, NIPS.

[27]  Stanley Durrleman,et al.  Deformetrica 4: An Open-Source Software for Statistical Shape Analysis , 2018, ShapeMI@MICCAI.

[28]  Joan Alexis Glaunès,et al.  Surface Matching via Currents , 2005, IPMI.

[29]  Tom Vercauteren,et al.  Diffeomorphic demons: Efficient non-parametric image registration , 2009, NeuroImage.