SPHARM-Reg: Unsupervised Cortical Surface Registration using Spherical Harmonics

We present a novel learning-based spherical registration method, called SPHARM-Reg, tailored for establishing cortical shape correspondence. SPHARM-Reg aims to reduce warp distortion that can introduce biases in downstream shape analyses. To achieve this, we tackle two critical challenges: (1) joint rigid and non-rigid alignments and (2) rotation-preserving smoothing. Conventional approaches perform rigid alignment only once before a non-rigid alignment. The resulting rotation is potentially sub-optimal, and the subsequent non-rigid alignment may introduce unnecessary distortion. In addition, common velocity encoding schemes on the unit sphere often fail to preserve the rotation component after spatial smoothing of velocity. To address these issues, we propose a diffeomorphic framework that integrates spherical harmonic decomposition of the velocity field with a novel velocity encoding scheme. SPHARM-Reg optimizes harmonic components of the velocity field, enabling joint adjustments for both rigid and non-rigid alignments. Furthermore, the proposed encoding scheme using spherical functions encourages consistent smoothing that preserves the rotation component. In the experiments, we validate SPHARM-Reg on healthy adult datasets. SPHARM-Reg achieves a substantial reduction in warp distortion while maintaining a high level of registration accuracy compared to existing methods. In the clinical analysis, we show that the extent of warp distortion significantly impacts statistical significance.