Selected Publications
Selected papers in shape processing and geometric learning
Top Medical AI Conferences: MICCAI, IPMI (acceptance rate: ~30%; early acceptance: ~10%; oral presentation: ~3%)
Shape Matching · 2025 · IEEE TMI
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
Keywords: Shape Matching, Surface Registration, Spherical Harmonics, Diffeomorphism
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.
Shape Segmentation · 2022 · IEEE TMI
SPHARM-Net: Spherical Harmonics-based Convolution for Cortical Parcellation
Seungbo Ha, Ilwoo Lyu
IEEE Transactions on Medical Imaging, 41(10), 2739–2751, 2022
Keywords: Shape Segmentation, Geometric Deep Learning, Spherical Convolution
We present a new spectral convolutional neural network for cortical parcellation, which we call SPHARM-Net. Recent advances in convolutional neural networks offer cortical parcellation on a fine-grained triangle mesh of the cortex. Yet, most convolutional neural networks designed for cortical parcellation employ spatial convolution that depends on extensive data augmentation and allows only predefined neighborhoods of specific spherical tessellation. On the other hand, a rotation-equivariant convolutional filter avoids data augmentation, and rotational equivariance can be achieved in spectral convolution independent of a neighborhood definition. Nevertheless, the limited resources of a modern machine enable only a finite set of spectral components that might lose geometric details. In this paper, we propose (1) a constrained spherical convolutional filter that supports an infinite set of spectral components and (2) an end-to-end framework without data augmentation. The proposed filter encodes all the spectral components without the full expansion of spherical harmonics. We show that rotational equivariance drastically reduces the training time while achieving accurate cortical parcellation. Furthermore, the proposed convolution is fully composed of matrix transformations, which offers efficient and fast spectral processing. In the experiments, we validate SPHARM-Net on two public datasets with manual labels: Mindboggle-101 (N=101) and NAMIC (N=39). The experimental results show that the proposed method outperforms the state-of-the-art methods on both datasets even with fewer learnable parameters without rigid alignment and data augmentation. Our code is publicly available at https://github.com/Shape-Lab/SPHARM-Net.
Shape Matching · 2019 · Medical Image Analysis
Hierarchical Spherical Deformation for Cortical Surface Registration
Ilwoo Lyu, Hakmook Kang, Neil Woodward, Martin Styner, Bennett Landman
Medical Image Analysis, 57, 72–88, 2019
Keywords: Shape Matching, Surface Registration, Spherical Harmonics, Second-order Optimization
A significant challenge in local cortical shape analysis is to establish a surface 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, a global rigid alignment and local deformation are independently performed. 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. In the experiments, we validate our method on healthy normal subjects with manual cortical surface parcellation in registration accuracy and distortion. We show an improved shape correspondence with high accuracy in cortical surface parcellation and significantly low registration distortion in surface area and edge length. In addition to validation, we discuss parameter tuning, optimization, and implementation design with potential acceleration.
Shape Matching · 2018 · MICCAI · early accept, oral
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
Keywords: Shape Matching, Surface Registration, Spherical Harmonics
We present a novel spherical deformation method for landmark-free shape correspondence in a group-wise manner. In this work, we aim at both addressing template selection bias and minimizing registration distortion in a single framework. The proposed spherical deformation yields a non-rigid deformation field without referring to any particular spherical coordinate system. Specifically, we extend a rigid rotation represented by Euler angles to general non-rigid local deformation via spatially varying Euler angles. The proposed method employs spherical harmonics interpolation of the local displacements to simultaneously solve rigid and non-rigid local deformation during optimization. This consequently leads to a continuous, smooth, and hierarchical representation of the deformation field that minimizes registration distortion. In addition, the proposed method is group-wise registration that requires no specific template to establish a shape correspondence. In the experiments, we show improved shape correspondence with high accuracy in cortical surface parcellation as well as significantly low registration distortion in surface area and edge length compared to existing registration methods while achieving fast registration in three minutes per subject.
Shape Quantification · 2018 · Medical Image Analysis
A Cortical Shape-Adaptive Approach to Local Gyrification Index
Ilwoo Lyu, Sun Hyung Kim, Jessica Girault, John Gilmore, Martin Styner
Medical Image Analysis, 48, 244–258, 2018
Keywords: Shape Quantification, Stationary H-J PDE, Longitudinal Data Analysis
Conventional approaches to local gyrification analysis quantify cortical folding in local cortical regions covered by an equidistant geodesic or nearest neighborhood-ring kernel. However, without careful design, such a kernel can easily cover multiple sulcal and gyral regions that may not be functionally related. Furthermore, this can result in smoothing out details of cortical folding, which consequently blurs local gyrification measurements. In this paper, we propose a novel kernel shape to locally quantify cortical gyrification within sulcal and gyral regions. We adapt wavefront propagation to generate a spatially varying kernel shape that encodes cortical folding patterns: neighboring gyral crowns, sulcal fundi, and sulcal banks. For this purpose, we perform anisotropic wavefront propagation that runs fast along gyral crowns and sulcal fundi by solving a static Hamilton-Jacobi partial differential equation. The resulting kernel adaptively elongates along gyral crowns and sulcal fundi, while keeping a uniform shape over flat regions like sulcal banks. We then measure local gyrification within the proposed spatially varying kernel. The experimental results show that the proposed kernel-based gyrification measure achieves a higher reproducibility than the conventional method in a multi-scan dataset. We further apply the proposed kernel to a brain development study in the early postnatal phase from neonate to 2 years of age. In this study we find that our kernel yields both positive and negative associations of gyrification with age, whereas the conventional method only captures positive associations. In general, our method yields sharper and more detailed statistical maps that associate cortical folding with sex and gestational age.
Shape Feature Extraction · 2018 · IEEE TMI
TRACE: A Topological Graph Representation for Automatic Sulcal Curve Extraction
Ilwoo Lyu, Sun Hyung Kim, Neil Woodward, Martin Styner, Bennett Landman
IEEE Transactions on Medical Imaging, 37(7), 1653–1663, 2018
Keywords: Shape Feature Extraction, Ridge/Valley Detection, Geodesics, Graph Representation
Sulcal curves have been recognized as one of the important geometric features for cortical shape analysis and landmark extraction. However, a significant challenge has arisen due to the highly variable, convoluted cortical folding patterns. In this paper, we propose a novel topological graph representation for automatic sulcal curve extraction, called TRACE. In practice, the reconstructed surface suffers from noise influences introduced during image acquisition and surface reconstruction. In the presence of noise on the surface, TRACE determines stable sulcal fundic regions by employing a line simplification method that prevents the sulcal folding pattern from being significantly smoothed out. The sulcal curves are then traced over the connected graph in the determined regions by Dijkstra's shortest path algorithm. For validation, we used state-of-the-art surface reconstruction pipelines on a reproducibility dataset. The experimental results showed higher reproducibility and robustness to noise in TRACE than the existing method with over 20 percent relative improvement in error for both surface reconstruction pipelines. In addition, the extracted sulcal curves by TRACE were well aligned with manually delineated primary sulcal curves. We also provide a choice of parameters to control the quality of the extracted sulcal curves and show the influences of parameter selection on the resulting curves.
Shape Matching · 2013 · IPMI · oral with open-ended discussion
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
Keywords: Shape Matching, Landmark-based Surface Registration, Spherical Harmonics, Group-wise Optimization
We present a novel cortical correspondence method employing group-wise registration in a spherical parametrization space for use in local cortical thickness analysis in human and non-human primate neuroimaging studies. The proposed method is an unbiased registration approach that estimates a continuous smooth deformation field into an unbiased average space via sulcal curve-constrained entropy minimization using spherical harmonic decomposition of the spherical deformation field. We initialize a correspondence by our pair-wise method that establishes a surface correspondence with a prior template. Since this pair-wise correspondence is biased to the choice of a template, we further improve the correspondence by employing unbiased ensemble entropy minimization across all surfaces, which yields a deformation field onto the iteratively updated unbiased average. The specific entropy metric incorporates two terms: the first focused on optimizing the correspondence of automatically extracted sulcal landmarks and the second on that of sulcal depth maps. We also propose an encoding scheme for spherical deformation via spherical harmonics as well as a novel method to choose an optimal spherical polar coordinate system for the most efficient deformation field estimation. The experimental results show evidence that the proposed method improves correspondence quality in non-human primate and human subjects as compared to the pair-wise method.