Shape Matching

SPHARM-Reg is a learning-based spherical registration method for accurate cortical shape correspondence with reduced warp distortion, a major source of bias in downstream analyses. The method addresses key limitations of existing approaches, including the decoupling of rigid and non-rigid alignment that often leads to suboptimal rotations and unnecessary deformation, as well as the lack of rotation preservation in conventional velocity smoothing on the sphere. To overcome these issues, SPHARM-Reg introduces a diffeomorphic formulation that combines spherical harmonic decomposition of the velocity field with a novel rotation-preserving encoding scheme. This enables joint optimization of rigid and non-rigid transformations, while enforcing consistent smoothing that retains rotational structure.

• SPHARM-Reg: Unsupervised Cortical Surface Registration using Spherical Harmonics

  Seungeun Lee, Seunghwan Lee, Sunghwa Ryu, Ilwoo Lyu

  IEEE Transactions on Medical Imaging, 44(11), 4732–4742, 2025

• Spherical Diffusion Process for Score-Guided Cortical Correspondence via Spectral Attention

  Seungeun Lee, Sergey Pyatkovskiy, Jaejun Yoo, Ilwoo Lyu

  Medical Image Computing and Computer Assisted Intervention (MICCAI) 2025, LNCS15975, 544–554, Daejeon, Korea, 2025

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.

• Hierarchical Spherical Deformation for Cortical Surface Registration

  Ilwoo Lyu, Hakmook Kang, Neil Woodward, Martin Styner, Bennett Landman

  Medical Image Analysis, 57, 72–88, 2019

• Hierarchical Spherical Deformation for Shape Correspondence

  Ilwoo Lyu, Martin Styner, Bennett Landman

  Medical Image Computing and Computer Assisted Intervention (MICCAI) 2018, LNCS11070, 853–861, Granada, Spain, 2018 · early accept, oral presentation

We propose a group-wise shape correspondence framework via entropy minimization to establish consistent correspondences across a population of shapes without relying on a single reference template. Conventional pairwise registration approaches introduce template selection bias, where the choice of reference shape can significantly influence the resulting correspondences. Our entropy minimization approach addresses this by simultaneously optimizing correspondences across all subjects in the group. We incorporate sulcal curve constraints to guide the registration along anatomically meaningful features, ensuring biologically consistent correspondences. This group-wise framework produces unbiased shape correspondences that enable more reliable statistical analysis of cortical surface morphology across populations.

• Robust Estimation of Group-wise Cortical Correspondence with an Application to Macaque and Human Neuroimaging Studies

  Ilwoo Lyu, Sun Hyung Kim, Joon-Kyung Seong, Sang Wook Yoo, Alan Evans, Yundi Shi, Mar Sanchez, Marc Niethammer, Martin Styner

  Frontiers in Neuroscience, 9, 210, 2015

• Group-Wise Cortical Correspondence via Sulcal Curve-Constrained Entropy Minimization

  Ilwoo Lyu, Sun Hyung Kim, Joon-Kyung Seong, Sang Wook Yoo, Alan Evans, Yundi Shi, Mar Sanchez, Marc Niethammer, Martin Styner

  Information Processing in Medical Imaging (IPMI) 2013, LNCS7917, 364–375, Asilomar, CA, 2013 · oral presentation with open-ended discussion