NC-Reg : Neural Cortical Maps for Rigid Registration

TL;DR

This work introduces Neural Cortical maps (NC), a continuous neural representation $S_\varphi: \mathbb{S}^2 \to \mathbb{R}^{n_f}$ for cortical feature maps, enabling resolution-agnostic feature computation on the sphere. Training uses an observed mesh $\mathcal{G}=(\mathcal{V},\mathcal{F})$, random barycentric sampling, and a multiresolution hash encoding to produce features that match interpolated targets $I(p)$ via a gradient-based loss. The NC-Reg algorithm performs global rigid registration by optimizing over rotations $R \in SO(3)$ to minimize $\mathcal{L}(F,M,R)$ with random resets and simulated annealing to escape local minima, achieving sub-degree accuracy and robustness to large initial misalignments. Experiments on the ADRC/fsaverage setup show competitive accuracy, faster runtimes than baselines, and improved robustness when using NC-Reg as a pre-alignment in both rigid and non-rigid pipelines.

Abstract

We introduce neural cortical maps, a continuous and compact neural representation for cortical feature maps, as an alternative to traditional discrete structures such as grids and meshes. It can learn from meshes of arbitrary size and provide learnt features at any resolution. Neural cortical maps enable efficient optimization on the sphere and achieve runtimes up to 30 times faster than classic barycentric interpolation (for the same number of iterations). As a proof of concept, we investigate rigid registration of cortical surfaces and propose NC-Reg, a novel iterative algorithm that involves the use of neural cortical feature maps, gradient descent optimization and a simulated annealing strategy. Through ablation studies and subject-to-template experiments, our method demonstrates sub-degree accuracy ($<1^\circ$ from the global optimum), and serves as a promising robust pre-alignment strategy, which is critical in clinical settings.

Figures (2)

• Figure 1: Learning two cortical feature maps using different numbers of training iterations ($N_\text{iter}$). To evaluate cortical feature reconstruction, we realised a linear regression between the interpolated values and the model outputs for an icosahedron of level 6 (40,962 vertices). $\beta$ is the slope, $\epsilon$ the intercept, and $R^2$ the coefficient of determination. The NN recovers both large-scale geometric features (average convexity, top) and high-frequency features (mean curvature, bottom).
• Figure 2: Rotation distance $\text{dist}_R(R^*, R^*_{perturbed}\cdot R_{\text{rand}})$ in degrees (Equation \ref{['eq:dist_R']}) between the solutions obtained on the same subject for two different initializations. For each subject, $R^*$ is the optimized solution (for the default initialization). $R_{\text{rand}}$ is the random perturbation applied to the subject mesh. $R^*_{perturbed}$ is the optimized solution to register the perturbed subject to the template.