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Image registration is an essential task in medical image analysis. We propose two novel unsupervised diffeomorphic image registration networks, which use deep Residual Networks (ResNets) as numerical approximations of the underlying continuous diffeomorphic setting governed by ordinary differential equations (ODEs), viewed as a Eulerian discretization scheme. While considering the ODE-based parameterizations of diffeomorphisms, we consider both stationary and non-stationary (time varying) velocity fields as the driving velocities to solve the ODEs, which give rise to our two proposed architectures for diffeomorphic registration. We also employ Lipschitz-continuity on the Residual Networks in both architectures to define the admissible Hilbert space of velocity fields as a Reproducing Kernel Hilbert Spaces (RKHS) and regularize the smoothness of the velocity fields. We apply both registration networks to align and segment the OASIS brain MRI dataset. Experimental results demonstrate that our models are computational efficient and achieve comparable registration results with a smoother deformation field.
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NeurEPDiff: Neural Operators to Predict Geodesics in Deformation Spaces
This paper presents NeurEPDiff, a novel network to fast predict the geodesics in deformation spaces generated by a well known Euler-Poincaré differential equation (EPDiff). To achieve this, we develop a neural operator that for the first time learns the evolving trajectory of geodesic deformations parameterized in the tangent space of diffeomorphisms (a.k.a velocity fields). In contrast to previous methods that purely fit the training images, our proposed NeurEPDiff learns a nonlinear mapping function between the time-dependent velocity fields. A composition of integral operators and smooth activation functions is formulated in each layer of NeurEPDiff to effectively approximate such mappings. The fact that NeurEPDiff is able to rapidly provide the numerical solution of EPDiff (given any initial condition) results in a significantly reduced computational cost of geodesic shooting of diffeomorphisms in a high-dimensional image space. Additionally, the properties of discretization/resolution-invariant of NeurEPDiff make its performance generalizable to multiple image resolutions after being trained offline. We demonstrate the effectiveness of NeurEPDiff in registering two image datasets: 2D synthetic data and 3D brain resonance imaging (MRI). The registration accuracy and computational efficiency are compared with the state-of-the-art diffeomophic registration algorithms with geodesic shooting.
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- Award ID(s):
- 2239977
- PAR ID:
- 10509913
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Information processing in medical imaging
- ISSN:
- 1011-2499
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Proceeding:
- https://doi.org/10.1007/978-3-031-34048-2_45
