Stationary Velocity Fields on Matrix Groups for Deformable Image Registration
The stationary velocity field (SVF) approach allows to build parametrizations of invertible deformation fields, which is often a desirable property in image registration. Its expressiveness is particularly attractive when used as a block following a machine learning-inspired network. However, it can struggle with large deformations. We extend the SVF approach to matrix groups, in particular $\SE(3)$. This moves Euclidean transformations into the low-frequency part, towards which network architectures are often naturally biased, so that larger motions can be recovered more easily. This requires an extension of the flow equation, for which we provide sufficient conditions for existence. We further prove a decomposition condition that allows us to apply a scaling-and-squaring approach for efficient numerical integration of the flow equation. We numerically validate the approach on inter-patient registration of 3D MRI images of the human brain.
Code (0)
등록된 구현이 없습니다.
Tasks
Image RegistrationNumerical IntegrationSimilar Papers 제목 키워드 기반
Constrained $H^1$-regularization schemes for diffeomorphic image registration
We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is param…
Image RegistrationEqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator
Simulating collisions of deformable objects is a fundamental yet challenging task due to the complexity of modeling solid mechanics and multi-body interactions. Existing data-driven methods often suffer from lack of equi…
Graph Neural NetworkBandit-Based Model Selection for Deformable Object Manipulation
We present a novel approach to deformable object manipulation that does not rely on highly-accurate modeling. The key contribution of this paper is to formulate the task as a Multi-Armed Bandit problem, with each arm rep…
Deformable Object ManipulationmodelModel SelectionObjectGlobally exponentially convergent observer for systems evolving on matrix Lie groups
We propose a globally exponentially convergent observer for the dynamical system evolving on matrix Lie groups with bounded velocity with unknown bound. We design the observer in the ambient Euclidean space and show expo…
TranslationA deep deformable residual learning network for SAR images segmentation
Reliable automatic target segmentation in Synthetic Aperture Radar (SAR) imagery has played an important role in the SAR fields. Different from the traditional methods, Spectral Residual (SR) and CFAR detector, with the …
Learning TheorySegmentation