NeurEPDiff: Neural Operators to Predict Geodesics in Deformation Spaces

• URL: http://arxiv.org/abs/2303.07115v1
• Date: Mon, 13 Mar 2023 13:47:57 GMT
• Title: NeurEPDiff: Neural Operators to Predict Geodesics in Deformation Spaces
• Authors: Nian Wu and Miaomiao Zhang
• Abstract summary: NeurEPDiff is a novel network to fast predict the geodesics in deformation spaces generated by an Euler-Poincar'e differential equation (EPDiff) We demonstrate the effectiveness of NeurEPDiff in registering two image datasets: 2D synthetic data and 3D brain resonance imaging (MRI)
• Score: 4.721069729610892
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents NeurEPDiff, a novel network to fast predict the geodesics in deformation spaces generated by a well known Euler-Poincar\'e 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 discretiztion/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.

Related papers

• 3D Equivariant Pose Regression via Direct Wigner-D Harmonics Prediction [50.07071392673984]
  Existing methods learn 3D rotations parametrized in the spatial domain using angles or quaternions. We propose a frequency-domain approach that directly predicts Wigner-D coefficients for 3D rotation regression. Our method achieves state-of-the-art results on benchmarks such as ModelNet10-SO(3) and PASCAL3D+.
  arXiv  Detail & Related papers  (2024-11-01T12:50:38Z)
• Learning Geodesics of Geometric Shape Deformations From Images [4.802048897896533]
  This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being able to predict geodesics is important for quantifying and comparing deformable shape presented in images.
  arXiv  Detail & Related papers  (2024-10-24T14:49:59Z)
• WiNet: Wavelet-based Incremental Learning for Efficient Medical Image Registration [68.25711405944239]
  Deep image registration has demonstrated exceptional accuracy and fast inference. Recent advances have adopted either multiple cascades or pyramid architectures to estimate dense deformation fields in a coarse-to-fine manner. We introduce a model-driven WiNet that incrementally estimates scale-wise wavelet coefficients for the displacement/velocity field across various scales.
  arXiv  Detail & Related papers  (2024-07-18T11:51:01Z)
• LeRF: Learning Resampling Function for Adaptive and Efficient Image Interpolation [64.34935748707673]
  Recent deep neural networks (DNNs) have made impressive progress in performance by introducing learned data priors. We propose a novel method of Learning Resampling (termed LeRF) which takes advantage of both the structural priors learned by DNNs and the locally continuous assumption. LeRF assigns spatially varying resampling functions to input image pixels and learns to predict the shapes of these resampling functions with a neural network.
  arXiv  Detail & Related papers  (2024-07-13T16:09:45Z)
• Variational Bayes image restoration with compressive autoencoders [4.879530644978008]
  Regularization of inverse problems is of paramount importance in computational imaging. In this work, we first propose to use compressive autoencoders instead of state-of-the-art generative models. As a second contribution, we introduce the Variational Bayes Latent Estimation (VBLE) algorithm.
  arXiv  Detail & Related papers  (2023-11-29T15:49:31Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• Fast-SNARF: A Fast Deformer for Articulated Neural Fields [92.68788512596254]
  We propose a new articulation module for neural fields, Fast-SNARF, which finds accurate correspondences between canonical space and posed space. Fast-SNARF is a drop-in replacement in to our previous work, SNARF, while significantly improving its computational efficiency. Because learning of deformation maps is a crucial component in many 3D human avatar methods, we believe that this work represents a significant step towards the practical creation of 3D virtual humans.
  arXiv  Detail & Related papers  (2022-11-28T17:55:34Z)
• Medical Image Registration via Neural Fields [35.80302878742334]
  We present a new neural net based image registration framework, called NIR (Neural Image Registration), which is based on optimization but utilizes deep neural nets to model deformations between image pairs. Experiments on two 3D MR brain scan datasets demonstrate that NIR yields state-of-the-art performance in terms of both registration accuracy and regularity, while running significantly faster than traditional optimization-based methods.
  arXiv  Detail & Related papers  (2022-06-07T08:43:31Z)
• Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration [63.15453821022452]
  Recent developments in approaches based on deep learning have achieved sub-second runtimes for DiffIR. We propose a simple iterative scheme that functionally composes intermediate non-stationary velocity fields. We then propose a convex optimisation model that uses a regularisation term of arbitrary order to impose smoothness on these velocity fields.
  arXiv  Detail & Related papers  (2021-09-26T19:56:45Z)
• Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks [11.4219428942199]
  We present a novel, efficient unsupervised symmetric image registration method. We evaluate our method on 3D image registration with a large scale brain image dataset.
  arXiv  Detail & Related papers  (2020-03-20T22:07:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.