SPHARM-Reg: Learning-based Surface Registration

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.

• Lee, S., Lee, S., Ryu, S., Lyu, I., SPHARM-Reg: Unsupervised Cortical Surface Registration using Spherical Harmonics. IEEE Transactions on Medical Imaging, 44(11), 4732–4742, 2025 [link]

• Lee, S., Pyatkovskiy, S., Yoo, J., Lyu, I., Spherical Diffusion Process for Score-Guided Cortical Correspondence via Spectral Attention. Medical Image Computing and Computer Assisted Intervention (MICCAI) 2025, LNCS15975, 544-554, 2025 [link]

HSD: Hierarchical Spherical Deformation

[Software]

We present hierarchical spherical deformation for group-wise shape correspondence to address template selection bias and minimize registration distortion. In this work, our aim is to develop a continuous and smooth deformation field to guide accurate cortical surface registration. In conventional spherical registration methods, global rigid alignment and local deformation are performed independently. Motivated by the composition of precession and intrinsic rotation, we simultaneously optimize global rigid rotation and non-rigid local deformation by utilizing spherical harmonics interpolation of local composite rotations in a single framework. To achieve this, we indirectly encode local displacements as functions of spherical locations using local composite rotations. Additionally, we introduce an extra regularization term to the spherical deformation that maximizes its rigidity while reducing registration distortion. To improve surface registration performance, we employ the second-order approximation of the energy function, enabling rapid convergence of the optimization process.

• Lyu, I., Kang, H., Woodward, N., Styner, M., Landman, B., Hierarchical Spherical Deformation for Cortical Surface Registration. Medical Image Analysis, 57, 72-88, 2019 [link]

• Lyu, I., Styner, M., Landman, B., Hierarchical Spherical Deformation for Shape Correspondence. Medical Image Computing and Computer Assisted Intervention (MICCAI) 2018, LNCS11070, 853-861, 2018 [link]

Group-wise Shape Correspondence via Entropy Minimization

[Software] [Tutorial]

We present hierarchical spherical deformation for group-wise shape correspondence to address template selection bias and to minimize registration distortion. In this work, we aim at a continuous and smooth deformation field to guide accurate cortical surface registration. In conventional spherical registration methods, global rigid alignment and local deformation are independently preformed. Motivated by the composition of precession and intrinsic rotation, we simultaneously optimize global rigid rotation and non-rigid local deformation by utilizing spherical harmonics interpolation of local composite rotations in a single framework. To this end, we indirectly encode local displacements by such local composite rotations as functions of spherical locations. Furthermore, we introduce an additional regularization term to the spherical deformation, which maximizes its rigidity while reducing registration distortion. To improve surface registration performance, we employ the second order approximation of the energy function that enables fast convergence of the optimization.

• Lyu, I., Kim, S., Seong, J., Yoo, S., Evans, A., Shi, Y., Sanchez, M., Niethammer, M., Styner, M., Robust Estimation of Group-wise Cortical Correspondence with an Application to Macaque and Human Neuroimaging Studies. Frontiers in Neuroscience, 9, 210, 2015 [link]

• Lyu, I., Kim, S., Seong, J., Yoo, S., Evans, A., Shi, Y., Sanchez, M., Niethammer, M., Styner, M., Group-wise Cortical Correspondence via Sulcal Curve-constrained Entropy Minimization. In: Information Processing in Medical Imaging (IPMI) 2013. LNCS7917, 364-375, 2013 [link]

Applications: Shape Correspondence-based (non-brain) 3D Object Analysis

• Tessema, A., Lee, H., Gong, Y., Cho, H., Adem, H., Lyu, I., Lee, J., Cho, H., Automated volumetric determination of high R₂* regions in substantia nigra: a feasibility study of quantifying substantia nigra atrophy in progressive supranuclear palsy. NMR in Biomedicine, 35(11), e4795, 2022 [link]

• Roeske, M., Lyu, I., McHugo, M., Blackford, J., Woodward, N., Heckers, S., Incomplete hippocampal inversion determines hippocampal shape deformations in schizophrenia. Biological Psychiatry, 92(4), 314-322, 2022 [link] [cover]

• Lyu, I., Perdomo, J., Yapuncich, G., Paniagua, B., Boyer, D., Styner, M., Group-wise Shape Correspondence of Variable and Complex Objects. SPIE Medical Imaging 2018, SPIE10574, 105742T-1-105742T-7, Houston, Texas, USA, 2018 [link]