Multimodal Diffeomorphic Registration with Neural ODEs and Structural Descriptors

TL;DR

The paper addresses multimodal brain image registration under modality shifts by modeling large-deformation diffeomorphisms with Neural ODEs. It introduces an instance-specific framework that uses a modality-agnostic similarity $\mathcal{S}$ and a velocity field $v_\theta$ to produce $\varphi = \mathrm{Exp}(v_\theta)$, with a penalty-barrier regularizer $\mathcal{L}_J$ to promote diffeomorphism. It evaluates three descriptor variants: a SSD-based structural descriptor, a contrastively learned dense descriptor, and Local Mutual Information, on OASIS-3 and IXI datasets, demonstrating robust performance across healthy and atrophic brains. The results show competitive Dice scores and controlled Jacobian negativity, supporting applicability to large or small deformations and efficiency comparable to other large-deformation methods.

Abstract

This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their deformation model, and its proper regularization. In addition, they also assume intensity correlation in anatomically homologous regions of interest among image pairs, limiting their applicability to the monomodal setting. Unlike learning-based models, we propose an instance-specific framework that is not subject to high scan requirements for training and does not suffer performance degradation at inference time on modalities unseen during training. Our method exploits the potential of continuous-depth networks in the Neural ODE paradigm with structural descriptors, widely adopted as modality-agnostic metric models which exploit self-similarities on parameterized neighborhood geometries. We propose three different variants that integrate image-based or feature-based structural descriptors and nonstructural image similarities computed by local mutual information. We conduct extensive evaluations on different experiments formed by scan dataset combinations and show surpassing qualitative and quantitative results compared to state-of-the-art baselines adequate for large or small deformations, and specific of multimodal registration. Lastly, we also demonstrate the underlying robustness of the proposed framework to varying levels of explicit regularization while maintaining low error, its suitability for registration at varying scales, and its efficiency with respect to other methods targeted to large-deformation registration.

Figures (10)

• Figure 1: Overview of the registration framework. We represent our adopted pairwise registration method for our tridimensional multimodal setting. For a given pair of images, the Neural ODE backbone is trained to compute the domain transformation on $\varphi$, optimized by a modality-agnostic similarity $\mathcal{S}$.
• Figure 2: Overview of the Neural ODE backbone. The input is the sampled image domain $\Omega$ and it is forwarded to a downsampling layer, followed by convolutions and two linear layers which result in the velocity field $v_{\theta}$.
• Figure 3: Overview of the descriptor network $F_{\theta}$. The output channels of each of the convolutional blocks are represented for each stride level, and the resulting feature map $F_{\theta}$ is used to compute dense descriptors by Equation \ref{['eq:descriptor-ss-token']}. We use bilinear upsampling on each decoder block.
• Figure 4: Selected fixed images for our experiments. We show the slices on the coronal plane of all the chosen fixed scans of all our evaluation pairs.
• Figure 5: Registration accuracy results. We represent the distributions of the registration accuracy, measured by the Dice score coefficient (DSC). Orange-edges boxes correspond to our method proposals for each of our experiments in Table \ref{['table:test-registration-sets']}.