SITReg: Multi-resolution architecture for symmetric, inverse consistent, and topology preserving image registration

TL;DR

The paper tackles deformable intra-modality medical image registration by ensuring three critical priors—symmetry, inverse consistency, and topology preservation—through a novel multi-resolution architecture called SITReg. It introduces a symmetric, half-way deformation update across scales, a memory-efficient deformation inversion layer based on a fixed-point formulation, and topology-preserving, invertible cubic-spline deformation networks. Theoretical guarantees (inverse consistency, symmetry, topology preservation) are provided, alongside practical convergence and memory benefits via Anderson acceleration. Empirically, SITReg achieves state-of-the-art Dice and TRE on brain MRI (OASIS, LPBA40) and inspiration-exhale lung CT (Lung250M-4B) in an unsupervised setting, with competitive inference performance. The work delivers a principled, end-to-end trainable framework that produces invertible, symmetric deformations without heavy multi-stage training.

Abstract

Deep learning has emerged as a strong alternative for classical iterative methods for deformable medical image registration, where the goal is to find a mapping between the coordinate systems of two images. Popular classical image registration methods enforce the useful inductive biases of symmetricity, inverse consistency, and topology preservation by construction. However, while many deep learning registration methods encourage these properties via loss functions, no earlier methods enforce all of them by construction. Here, we propose a novel registration architecture based on extracting multi-resolution feature representations which is by construction symmetric, inverse consistent, and topology preserving. We also develop an implicit layer for memory efficient inversion of the deformation fields. Our method achieves state-of-the-art registration accuracy on three datasets. The code is available at https://github.com/honkamj/SITReg.

Figures (11)

• Figure 1: Example deformation from the method.Left: Forward deformation. Middle: Inverse deformation. Right: Composition of the forward and inverse deformations. Only one 2D slice is shown of the 3D deformation. The deformation is from the LPBA40 experiment. For more detailed visualization of a predicted deformation, see Figure \ref{['appendix-fig:detailed_deformation_example']} in Appendix \ref{['appendix:result_visualization']}.
• Figure 2: Overview of the proposed architecture. Multi-resolution features are first extracted from the inputs $x_A$ and $x_B$ using convolutional encoder $h$. Output deformations $f_{1\to2}(x_A, x_B)$ and $f_{2\to1}(x_A, x_B)$ are built recursively from the multi-resolution features using the symmetric deformation updates described in Section \ref{['sec:multi-resolution']} and visualized in Figure \ref{['fig:anti-symmetric_update']}. The architecture is symmetric and inverse consistent with respect to the inputs and the final deformation is obtained in both directions. The brain images are from the OASIS dataset marcus2007open
• Figure 3: Recursive multi-resolution deformation update. The deformation update at resolution $k$, described in Section \ref{['sec:multi-resolution']}, takes as input the half-way deformations $d_{1\to1.5}^{(k+1)}$ and $d_{2\to1.5}^{(k+1)}$ from the previous resolution, and updates them through a composition with an update deformation $\delta^{(k)}$. The update deformation $\delta^{(k)}$ is calculated symmetrically from image features $z_1^{(k)}$ and $z_2^{(k)}$ (deformed mid-way towards each other with the previous half-way deformations) using a neural network $u^{(k)}$ according to Equation \ref{['eq:update_deformation_formula']}. The deformation inversion layer for inverting auxiliary deformations predicted by $u^{(k)}$ is described in Section \ref{['sec:def_inv_layer']}.
• Figure 4: Visual deformation regularity comparison. Local Jacobian determinants are visualized for each model for a single predicted deformation in OASIS experiment. Folding voxels (determinant below zero) are marked with black color. Only one axial slice of the predicted 3D deformation is visible.
• Figure 5: Number of fixed point iterations required for convergence in deformation inversion layers with the model trained on OASIS dataset. The stopping criterion for the fixed point iteration was maximum displacement error within the whole volume reaching below one hundredth of a voxel. All deformation inversions for the whole OASIS test set are included.

Theorems & Definitions (7)

• Theorem 1
• Theorem 2
• Theorem 3
• Lemma 4
• Lemma 5
• Theorem 6
• Theorem 7