Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Steerable Deep Network for Model-Free Diffusion MRI Registration

Gianfranco Cortes, Xiaoda Qu, Baba C. Vemuri

TL;DR

This work tackles nonrigid registration for diffusion MRI by proposing a model-free diff-$\mathbf{pq}$ framework that operates directly on raw dMRI data. It introduces an $\mathsf{SE}(3)$-equivariant UNet that generates velocity fields on the diffusion domain and integrates them into a diffeomorphism, using a Fourier-space MMD loss to align ensemble propagators without reorientation. The method leverages $\mathsf{SO}(5)$-steerable convolutions on the diffusion domain, affine pre-alignment, and specialized input processing to preserve the geometry linking $p$-space and $q$-space. Experimental results on HCP data show competitive Dice scores against state-of-the-art methods while avoiding overhead from derived representations, highlighting the practical impact of geometry-aware, acquisition-space registration for diffusion MRI analysis.

Abstract

Nonrigid registration is vital to medical image analysis but remains challenging for diffusion MRI (dMRI) due to its high-dimensional, orientation-dependent nature. While classical methods are accurate, they are computationally demanding, and deep neural networks, though efficient, have been underexplored for nonrigid dMRI registration compared to structural imaging. We present a novel, deep learning framework for model-free, nonrigid registration of raw diffusion MRI data that does not require explicit reorientation. Unlike previous methods relying on derived representations such as diffusion tensors or fiber orientation distribution functions, in our approach, we formulate the registration as an equivariant diffeomorphism of position-and-orientation space. Central to our method is an $\mathsf{SE}(3)$-equivariant UNet that generates velocity fields while preserving the geometric properties of a raw dMRI's domain. We introduce a new loss function based on the maximum mean discrepancy in Fourier space, implicitly matching ensemble average propagators across images. Experimental results on Human Connectome Project dMRI data demonstrate competitive performance compared to state-of-the-art approaches, with the added advantage of bypassing the overhead for estimating derived representations. This work establishes a foundation for data-driven, geometry-aware dMRI registration directly in the acquisition space.

A Steerable Deep Network for Model-Free Diffusion MRI Registration

TL;DR

This work tackles nonrigid registration for diffusion MRI by proposing a model-free diff- framework that operates directly on raw dMRI data. It introduces an -equivariant UNet that generates velocity fields on the diffusion domain and integrates them into a diffeomorphism, using a Fourier-space MMD loss to align ensemble propagators without reorientation. The method leverages -steerable convolutions on the diffusion domain, affine pre-alignment, and specialized input processing to preserve the geometry linking -space and -space. Experimental results on HCP data show competitive Dice scores against state-of-the-art methods while avoiding overhead from derived representations, highlighting the practical impact of geometry-aware, acquisition-space registration for diffusion MRI analysis.

Abstract

Nonrigid registration is vital to medical image analysis but remains challenging for diffusion MRI (dMRI) due to its high-dimensional, orientation-dependent nature. While classical methods are accurate, they are computationally demanding, and deep neural networks, though efficient, have been underexplored for nonrigid dMRI registration compared to structural imaging. We present a novel, deep learning framework for model-free, nonrigid registration of raw diffusion MRI data that does not require explicit reorientation. Unlike previous methods relying on derived representations such as diffusion tensors or fiber orientation distribution functions, in our approach, we formulate the registration as an equivariant diffeomorphism of position-and-orientation space. Central to our method is an -equivariant UNet that generates velocity fields while preserving the geometric properties of a raw dMRI's domain. We introduce a new loss function based on the maximum mean discrepancy in Fourier space, implicitly matching ensemble average propagators across images. Experimental results on Human Connectome Project dMRI data demonstrate competitive performance compared to state-of-the-art approaches, with the added advantage of bypassing the overhead for estimating derived representations. This work establishes a foundation for data-driven, geometry-aware dMRI registration directly in the acquisition space.
Paper Structure (17 sections, 2 theorems, 18 equations, 3 figures, 1 table)

This paper contains 17 sections, 2 theorems, 18 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Representations and Equivariance
  4. The Geometry of Diffusion-Weighted Images
  5. The diff-pq Registration Problem
  6. Steerable Convolutions
  7. An MMD Loss via Characteristic Functions
  8. Implementation
  9. Constructing $\mathsf{SE}(3)$-Equivariant Convolution Layers
  10. Network Input
  11. Network Architecture
  12. Experiments
  13. dMRI Registration Applied to HCP Data
  14. Dataset
  15. Evaluation
  16. ...and 2 more sections

Key Result

theorem thmcountertheorem

wasserman1969 Let $M$ be a Riemannian manifold with a Lie group $G$ acting on it. Let $X$ be an equivariant vector field on $M$, i.e. $X_{gp} = gX_p$ for all $p \in M$ and $g \in G$. Then, the flow generated by $X$ is an equivariant diffeomorphism.

Figures (3)

  • Figure 1: Comparison of three registration scenarios in which we try to estimate a deformation $\Phi$ that minimizes $\mathcal{L}(S_f, S_m \circ \Phi)$ for some dissimilarity $\mathcal{L}$.
  • Figure 2: Overview of the proposed registration pipeline, parameterized by an $\mathsf{SE}(3)$-equivariant UNet $g_\theta$.
  • Figure 3: Visualization of registration results. Top row: $b=0$ axial slices with overlaid fODF maps. Bottom row: $b=0$ coronal slices with overlaid fODF maps. (a) Moving source image, (b) warped source image, (c) fixed target image, (d) checkerboard view of moving vs. fixed image, (e) checkerboard view of warped vs. fixed image. The highlighted ROI shows a tract discontinuity in (d) that is resolved after warping in (e). Note that $\mathsf{SE}(3)$-equivariance preserves white matter fiber tracts during warping.

Theorems & Definitions (5)

  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • theorem thmcountertheorem
  • lemma thmcounterlemma