Research
Our current research interests include:
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Applied and Computational Geometry
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Interdisciplinary Mathematical Modeling
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Quantitative Biology
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Medical Imaging
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Metamaterial Design
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Geometry Processing
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Scientific Computing
1. Computational geometry and visualization
Spherical conformal parameterization
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(For genus-0 surface meshes) P. T. Choi, K. C. Lam, and L. M. Lui, FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM Journal on Imaging Sciences, 8(1), 67-94, 2015.
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(For genus-0 point clouds) G. P.-T. Choi, K. T. Ho, and L. M. Lui, Spherical conformal parameterization of genus-0 point clouds for meshing. SIAM Journal on Imaging Sciences, 9(4), 1582-1618, 2016.
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(For genus-0 surface meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, and L. M. Lui, Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 13(3), 1049-1083, 2020.
Disk conformal parameterization
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(For simply-connected open surface meshes) P. T. Choi and L. M. Lui, Fast disk conformal parameterization of simply-connected open surfaces. Journal of Scientific Computing, 65(3), 1065-1090, 2015.
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(For simply-connected open surface meshes) G. P. T. Choi and L. M. Lui, A linear formulation for disk conformal parameterization of simply-connected open surfaces. Advances in Computational Mathematics, 44(1), 87-114, 2018.
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(For simply-connected open surface meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, and L. M. Lui, Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 13(3), 1049-1083, 2020.
Rectangular conformal parameterization
Conformal parameterization onto a non-convex domain
Free-boundary conformal parameterization
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(For simply-connected open surface meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, and L. M. Lui, Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 13(3), 1049-1083, 2020.
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(For simply-connected open point clouds) G. P. T. Choi, Y. Liu, and L. M. Lui, Free-boundary conformal parameterization of point clouds. Journal of Scientific Computing, 90(1), 14, 2022.
Conformal and quasi-conformal parameterization of multiply-connected surfaces
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(For multiply-connected surface meshes) G. P. T. Choi, Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory. Journal of Scientific Computing, 87(3), 70, 2021.
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(For multiply-connected surface meshes) Z. Zhu, G. P. T. Choi, and L. M. Lui, Parallelizable global quasi-conformal parameterization of multiply connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 15(4), 1765-1807, 2022.
Spherical quasi-conformal parameterization
Spherical landmark aligned optimized conformal parameterization
Disk landmark-based quasi-conformal parameterization
Ellipsoidal conformal and quasi-conformal parameterization
Teichmüller extremal map
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(For simply-connected open point clouds) T. W. Meng, G. P. T. Choi, and L. M. Lui, TEMPO: Feature-endowed Teichmüller extremal mappings of point clouds. SIAM Journal on Imaging Sciences, 9(4), 1922-1962, 2016.
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(For simply-connected open surface meshes) G. P. T. Choi and L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A, 474(2217), 20170905, 2018.
Higher-dimensional quasi-conformal map
Density-equalizing map (area-preserving/with controllable area distortion)
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(For simply-connected open surface meshes) G. P. T. Choi and C. H. Rycroft, Density-equalizing maps for simply connected open surfaces. SIAM Journal on Imaging Sciences, 11(2), 1134-1178, 2018.
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(For simply-connected open surface meshes) G. P. T. Choi, B. Chiu, and C. H. Rycroft, Area-preserving mapping of 3D ultrasound carotid artery images using density-equalizing reference map. IEEE Transactions on Biomedical Engineering, 67(9), 1507-1517, 2020.
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(For simply-connected open surface meshes) M. Shaqfa, G. P. T. Choi, G. Anciaux, and K. Beyer, Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces. Journal of Computational Physics, 522, 113578, 2025.
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(For simply-connected open surface meshes) G. P. T. Choi and M. Shaqfa, Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces. Journal of Computational and Applied Mathematics, 461, 116455, 2025.
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(For multiply-connected open surface meshes) Z. Lyu, G. P. T. Choi, and L. M. Lui, Bijective density-equalizing quasiconformal map for multiply connected open surfaces. SIAM Journal on Imaging Sciences, 17(1), 706-755, 2024.
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(For genus-0 surface meshes) Z. Lyu, L. M. Lui, and G. P. T. Choi, Spherical density-equalizing map for genus-0 closed surfaces. SIAM Journal on Imaging Sciences, 17(4), 2110-2141, 2024.
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(For genus-0 surface meshes) Z. Lyu, L. M. Lui, and G. P. T. Choi, Ellipsoidal density-equalizing map for genus-0 closed surfaces. Preprint, arXiv:2410.12331, 2024.
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(For genus-1 surface meshes) S. Yao and G. P. T. Choi, Toroidal density-equalizing map for genus-one surfaces. Preprint, arXiv:2410.16833, 2024.
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(For volumetric domains) G. P. T. Choi and C. H. Rycroft, Volumetric density-equalizing reference map with applications. Journal of Scientific Computing, 86(3), 41, 2021.
Optimal mass transport map
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(For genus-0 surface meshes) A. Pumarola, J. Sanchez-Riera, G. P. T. Choi, A. Sanfeliu, and F. Moreno-Noguer, 3DPeople: Modeling the geometry of dressed humans. The IEEE International Conference on Computer Vision (ICCV), 2242-2251, 2019.
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(For simply-connected open/closed surface meshes) A. Giri*, G. P. T. Choi*, and L. Kumar, Open and closed anatomical surface description via hemispherical area-preserving map. Signal Processing, 180, 107867, 2021. (*equal contribution)
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(For simply-connected open/closed surface meshes) G. P. T. Choi, A. Giri, and L. Kumar, Adaptive area-preserving parameterization of open and closed anatomical surfaces. Computers in Biology and Medicine, 148, 105715, 2022.
Image triangulation and registration
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C. P. Yung, G. P. T. Choi, K. Chen, and L. M. Lui, Efficient feature-nased image registration by mapping sparsified features. Journal of Visual Communication and Image Representation, 55, 561-571, 2018.
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H. Law, G. P. T. Choi, K. C. Lam, and L. M. Lui, Quasiconformal model with CNN features for large deformation image registration. Inverse Problems and Imaging, 16(4), 1019-1046, 2022.
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D, Zhang, G. P. T. Choi, J. Zhang, and L. M. Lui, A unifying framework for n-dimensional quasi-conformal mappings. SIAM Journal on Imaging Sciences, 15(2), 960-988, 2022.
Mappings and deep learning
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A. Pumarola, J. Sanchez-Riera, G. P. T. Choi, A. Sanfeliu, and F. Moreno-Noguer, 3DPeople: Modeling the geometry of dressed humans. The IEEE International Conference on Computer Vision (ICCV), 2242-2251, 2019.
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H. Law, G. P. T. Choi, K. C. Lam, and L. M. Lui, Quasiconformal model with CNN features for large deformation image registration. Inverse Problems and Imaging, 16(4), 1019-1046, 2022.
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Y. Guo, Q. Chen, G. P. T. Choi, and L. M. Lui, Automatic landmark detection and registration of brain cortical surfaces via quasi-conformal geometry and convolutional neural networks. Computers in Biology and Medicine, 163, 107185, 2023.
Surface harmonics
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A. Giri*, G. P. T. Choi*, and L. Kumar, Open and closed anatomical surface description via hemispherical area-preserving map. Signal Processing, 180, 107867, 2021. (*equal contribution)
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G. P. T. Choi, A. Giri, and L. Kumar, Adaptive area-preserving parameterization of open and closed anatomical surfaces. Computers in Biology and Medicine, 148, 105715, 2022.
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M. Shaqfa, G. P. T. Choi, and K. Beyer, Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches. Powder Technology, 393, 837-856, 2021.
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M. Shaqfa, G. P. T. Choi, G. Anciaux, and K. Beyer, Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces. Journal of Computational Physics, 522, 113578, 2025.
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G. P. T. Choi and M. Shaqfa, Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces. Journal of Computational and Applied Mathematics, 461, 116455, 2025.
Mappings for astronomy
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B. Jarvis, G. P. T. Choi, B. Hockman, B. Morrell, S. Bandopadhyay, D. Lubey, J. Villa, S. Bhaskaran, D. Bayard, and I. A. Nesnas, 3D shape reconstruction of small bodies from sparse features. IEEE Robotics and Automation Letters, 6(4), 7089-7096, 2021.
Mappings for robotics
2. Mathematics of materials
Kirigami metamaterials
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G. P. T. Choi, L. H. Dudte, and L. Mahadevan, Programming shape using kirigami tessellations. Nature Materials, 18, 999-1004, 2019.
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S. Chen*, G. P. T. Choi*, and L. Mahadevan, Deterministic and stochastic control of kirigami topology. Proceedings of the National Academy of Sciences, 117(9), 4511-4517, 2020. (*equal contribution)
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G. P. T. Choi, L. H. Dudte, and L. Mahadevan, Compact reconfigurable kirigami. Physical Review Research, 3(4), 043030, 2021.
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L. Liu*, G. P. T. Choi*, and L. Mahadevan, Wallpaper group kirigami. Proceedings of the Royal Society A, 477(2252), 20210161, 2021. (*equal contribution)
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L. Liu*, G. P. T. Choi*, and L. Mahadevan, Quasicrystal kirigami. Physical Review Research, 4(3), 033114, 2022. (*equal contribution)
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L. H. Dudte*, G. P. T. Choi*, K. P. Becker, and L. Mahadevan, An additive framework for kirigami design. Nature Computational Science, 3(5), 443-454, 2023. (*equal contribution)
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G. P. T. Choi, L. Liu, and L. Mahadevan, Explosive rigidity percolation in kirigami. Proceedings of the Royal Society A, 479(2271), 20220798, 2023.
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G. P. T. Choi, Computational design of art-inspired metamaterials. Nature Computational Science, 4(8), 549-552, 2024.
Origami metamaterials
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L. H. Dudte, G. P. T. Choi, and L. Mahadevan, An additive algorithm for origami design. Proceedings of the National Academy of Sciences, 118(21), e2019241118, 2021.
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G. P. T. Choi, Computational design of art-inspired metamaterials. Nature Computational Science, 4(8), 549-552, 2024.
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R. Li and G. P. T. Choi, Explosive rigidity percolation in origami. Preprint, arXiv:2410.13945, 2024.
Structural assemblies
Floppy networks
Droplets
3. Quantitative biology
Brain morphometry and morphogenesis
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P. T. Choi, K. C. Lam, and L. M. Lui, FLASH: Fast landmark aligned spherical harmonic parameterization for genus-0 closed brain surfaces. SIAM Journal on Imaging Sciences, 8(1), 67-94, 2015.
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Y. Guo, Q. Chen, G. P. T. Choi, and L. M. Lui, Automatic landmark detection and registration of brain cortical surfaces via quasi-conformal geometry and convolutional neural networks. Computers in Biology and Medicine, 107185, 2023.
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G. P. T. Choi, C. Liu, S. Yin, G. Séjourné, R. S. Smith, C. A. Walsh, and L. Mahadevan, Biophysical basis for brain folding and misfolding patterns in ferrets and humans. Preprint, bioRxiv 2025.03.05.641682.
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S. Yin, C. Liu, G. P. T. Choi, Y. Jung, K. Heuer, R. Toro, and L. Mahadevan, Morphogenesis and morphometry of brain folding patterns across species. Preprint, bioRxiv 2025.03.05.641692.
Face shape analysis
Shape analysis of carotid artery
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G. P. T. Choi, Y. Chen, L. M. Lui, and B. Chiu, Conformal mapping of carotid vessel wall and plaque thickness measured from 3D ultrasound images. Medical & Biological Engineering & Computing, 55(12), 2183-2195, 2017.
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G. P. T. Choi, B. Chiu, and C. H. Rycroft, Area-preserving mapping of 3D carotid ultrasound images using density-equalizing reference map. IEEE Transactions on Biomedical Engineering, 67(9), 1507-1517, 2020.
Insect wing morphometry
Tooth morphometry
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G. P. T. Choi, H. L. Chan, R. Yong, S. Ranjitkar, A. Brook, G. Townsend, K. Chen, and L. M. Lui, Tooth morphometry using quasi-conformal theory. Pattern Recognition, 99, 107064, 2020.
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G. P. T. Choi, D. Qiu, and L. M. Lui, Shape analysis via inconsistent surface registration. Proceedings of the Royal Society A, 476(2242), 20200147, 2020.
Avian beak morphometry and morphogenesis
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S. Al-Mosleh, G. P. T. Choi, A. Abzhanov, and L. Mahadevan, Geometry and dynamics link form, function and evolution of finch beaks. Proceedings of the National Academy of Sciences, 118(46), e2105957118, 2021.
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S. Mosleh*, G. P. T. Choi*, G. M. Musser, H. F. James, A. Abzhanov, and L. Mahadevan, Beak morphometry and morphogenesis across avian radiations. Proceedings of the Royal Society B, 290(2007), 20230420, 2023. (*equal contribution)
Egg patterns
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T. Dixit, G. P. T. Choi*, S. Al-Mosleh*, J. Lund, J. Troscianko, C. Moya, L. Mahadevan, and C. N. Spottiswoode, Combined measures of mimetic fidelity explain imperfect mimicry in a brood parasite-host system. Biology Letters, 19(2), 20220538, 2023. (*equal contribution)
Flower morphology
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M. B. Edwards, G. P. T. Choi, N. Derieg, Y. Min, A. C. Diana, S. A. Hodges, L. Mahadevan, E. M. Kramer, and E. S. Ballerini, Genetic architecture of floral traits in bee- and hummingbird-pollinated sister species of Aquilegia (columbine). Evolution, 75(9), 2197-2216, 2021.
Bacterial biofilms
Collective dynamics
Quasi-conformal flows for morphodynamics
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