Abstract
We present novel learning-based spherical registration using the spherical harmonics. Our goal is to achieve a continuous and smooth warp field that can effectively facilitate precise cortical surface registration. Conventional spherical registration typically involve sequential procedures for rigid and non-rigid alignments, which can potentially introduce substantial warp distortion. By contrast, the proposed method aims at joint optimization of both types of alignments. Inspired by a recent study that represents a rotation by 6D parameters as a continuous form in the Euclidean domain, we extend the idea to encode and regularize a velocity field. Specifically, a local velocity is represented by a single rotation with 6D parameters that can vary smoothly over the unit sphere via spherical harmonic decomposition, yielding smooth, spatially varying rotations. To this end, our method can lead to a significant reduction in warp distortion. We also incorporate a spherical convolutional neural network to achieve fast registration in an unsupervised manner. In the experiments, we compare our method with popular spherical registration methods on a publicly available human brain dataset. We show that the proposed method can significantly reduce warp distortion without sacrificing registration accuracy.
S. Lee and S. Ryu—Contributed equally to this work.
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Acknowledgments
This work was supported in part by the NRF under Grant RS-2023-00251298 and RS-2023-00266120, in part by the IITP under Grant 2020-0-01336, the Artificial Intelligence Graduate School Program, UNIST.
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Lee, S., Ryu, S., Lee, S., Lyu, I. (2023). Unsupervised Learning of Cortical Surface Registration Using Spherical Harmonics. In: Wachinger, C., Paniagua, B., Elhabian, S., Li, J., Egger, J. (eds) Shape in Medical Imaging. ShapeMI 2023. Lecture Notes in Computer Science, vol 14350. Springer, Cham. https://doi.org/10.1007/978-3-031-46914-5_6
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