Research

Our current research interests include:

• Applied and Computational Geometry
• Interdisciplinary Mathematical Modeling
• Quantitative Biology
• Medical Imaging
• Metamaterial Design
• Geometry Processing
• Scientific Computing

1. Computational geometry and visualization

Spherical conformal parameterization

• (For genus-0 triangle meshes) P. T. Choi, K. C. Lam, 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.
• (For genus-0 point clouds) G. P.-T. Choi, K. T. Ho, L. M. Lui, Spherical conformal parameterization of genus-0 point clouds for meshing. SIAM Journal on Imaging Sciences, 9(4), 1582-1618, 2016.
• (For genus-0 triangle meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, 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

• (For simply-connected open triangle 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.
• (For simply-connected open triangle 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.
• (For simply-connected open triangle meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, 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

• (For simply-connected open triangle meshes and point clouds) T. W. Meng, G. P. T. Choi, L. M. Lui, TEMPO: Feature-endowed Teichmüller extremal mappings of point clouds. SIAM Journal on Imaging Sciences, 9(4), 1922-1962, 2016.

Conformal parameterization onto a non-convex domain

• (For simply-connected open triangle meshes) G. P. T. Choi, Y. Chen, L. M. Lui, 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.

Free-boundary conformal parameterization

• (For simply-connected open triangle meshes) G. P. T. Choi, Y. Leung-Liu, X. Gu, L. M. Lui, Parallelizable global conformal parameterization of simply-connected surfaces via partial welding. SIAM Journal on Imaging Sciences, 13(3), 1049-1083, 2020.
• (For simply-connected open point clouds) G. P. T. Choi, Y. Liu, 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

• (For multiply-connected triangle meshes) G. P. T. Choi, Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory. Journal of Scientific Computing, 87(3), 70, 2021.
• (For multiply-connected triangle meshes) Z. Zhu, G. P. T. Choi, 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

• (For genus-0 triangle meshes) G. P. T. Choi, M. H. Y. Man, L. M. Lui, Fast spherical quasiconformal parameterization of genus-0 closed surfaces with application to adaptive remeshing. Geometry, Imaging and Computing, 3(1-2), 1-29, 2016.

Spherical landmark aligned optimized conformal parameterization

• (For genus-0 triangle meshes) P. T. Choi, K. C. Lam, 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.

Disk landmark-based quasi-conformal parameterization

• (For simply-connected open triangle meshes) Y. Guo, Q. Chen, G. P. T. Choi, 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.

Ellipsoidal conformal and quasi-conformal parameterization

• (For genus-0 triangle meshes) G. P. T. Choi, Fast ellipsoidal conformal and quasi-conformal parameterization for genus-0 closed surfaces. Journal of Computational and Applied Mathematics, 447, 115888, 2024.

Teichmüller extremal map

• (For simply-connected open point clouds) T. W. Meng, G. P. T. Choi, L. M. Lui, TEMPO: Feature-endowed Teichmüller extremal mappings of point clouds. SIAM Journal on Imaging Sciences, 9(4), 1922-1962, 2016.
• (For simply-connected open triangle 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

• (For volumetric domains) D. Zhang, G. P. T. Choi, J. Zhang, L. M. Lui, A unifying framework for n-dimensional quasi-conformal mappings. SIAM Journal on Imaging Sciences, 15(2), 960-988, 2022.

Density-equalizing map (area-preserving/with controllable area distortion)

• (For simply-connected open triangle 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.
• (For simply-connected open triangle meshes) G. P. T. Choi, B. Chiu, 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.
• (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.
• (For multiply-connected triangle meshes) Z. Lyu, G. P. T. Choi, L. M. Lui, Bijective density-equalizing quasiconformal map for multiply connected open surfaces. SIAM Journal on Imaging Sciences, 17(1), 706-755, 2024.
• (For genus-0 triangle meshes) Z. Lyu, L. M. Lui, G. P. T. Choi, Spherical density-equalizing map for genus-0 closed surfaces. Preprint, arXiv:2401.11795, 2024.

Optimal mass transport map

• (For genus-0 triangle meshes) A. Pumarola, J. Sanchez-Riera, G. P. T. Choi, A. Sanfeliu, F. Moreno-Noguer, 3DPeople: Modeling the geometry of dressed humans. The IEEE International Conference on Computer Vision (ICCV), 2242-2251, 2019.
• (For simply-connected open/closed triangle meshes) A. Giri*, G. P. T. Choi*, L. Kumar, Open and closed anatomical surface description via hemispherical area-preserving map. Signal Processing, 180, 107867, 2021. (*equal contribution)
• (For simply-connected open/closed triangle meshes) G. P. T. Choi, A. Giri, L. Kumar, Adaptive area-preserving parameterization of open and closed anatomical surfaces. Computers in Biology and Medicine, 148, 105715, 2022.

Image triangulation and registration

• C. P. Yung, G. P. T. Choi, K. Chen, L. M. Lui, Efficient feature-nased image registration by mapping sparsified features. Journal of Visual Communication and Image Representation, 55, 561-571, 2018.
• H. Law, G. P. T. Choi, K. C. Lam, L. M. Lui, Quasiconformal model with CNN features for large deformation image registration. Inverse Problems and Imaging, 16(4), 1019-1046, 2022.
• D, Zhang, G. P. T. Choi, J. Zhang, 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

• A. Pumarola, J. Sanchez-Riera, G. P. T. Choi, A. Sanfeliu, F. Moreno-Noguer, 3DPeople: Modeling the geometry of dressed humans. The IEEE International Conference on Computer Vision (ICCV), 2242-2251, 2019.
• H. Law, G. P. T. Choi, K. C. Lam, L. M. Lui, Quasiconformal model with CNN features for large deformation image registration. Inverse Problems and Imaging, 16(4), 1019-1046, 2022.
• Y. Guo, Q. Chen, G. P. T. Choi, 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

• A. Giri*, G. P. T. Choi*, L. Kumar, Open and closed anatomical surface description via hemispherical area-preserving map. Signal Processing, 180, 107867, 2021. (*equal contribution)
• G. P. T. Choi, A. Giri, L. Kumar, Adaptive area-preserving parameterization of open and closed anatomical surfaces. Computers in Biology and Medicine, 148, 105715, 2022.
• M. Shaqfa, G. P. T. Choi, K. Beyer, Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches. Powder Technology, 393, 837-856, 2021.
• M. Shaqfa, G. P. T. Choi, G. Anciaux, K. Beyer, Disk harmonics for analysing curved and flat self-affine rough surfaces and the topological reconstruction of open surfaces. Preprint, arXiv:2403.07001.

Mappings for astronomy

• B. Jarvis, G. P. T. Choi, B. Hockman, B. Morrell, S. Bandopadhyay, D. Lubey, J. Villa, S. Bhaskaran, D. Bayard, 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

• G. Notomista, G. P. T. Choi, M. Saveriano, Reactive robot navigation using quasi-conformal mappings and control barrier functions. Submitted, 2024.

2. Mathematics of materials

Kirigami metamaterials

• G. P. T. Choi, L. H. Dudte, L. Mahadevan, Programming shape using kirigami tessellations. Nature Materials, 18, 999-1004, 2019.
• S. Chen*, G. P. T. Choi*, L. Mahadevan, Deterministic and stochastic control of kirigami topology. Proceedings of the National Academy of Sciences, 117(9), 4511-4517, 2020. (*equal contribution)
• G. P. T. Choi, L. H. Dudte, L. Mahadevan, Compact reconfigurable kirigami. Physical Review Research, 3(4), 043030, 2021.
• L. Liu*, G. P. T. Choi*, L. Mahadevan, Wallpaper group kirigami. Proceedings of the Royal Society A, 477(2252), 20210161, 2021. (*equal contribution)
• L. Liu*, G. P. T. Choi*, L. Mahadevan, Quasicrystal kirigami. Physical Review Research, 4(3), 033114, 2022. (*equal contribution)
• L. H. Dudte*, G. P. T. Choi*, K. P. Becker, L. Mahadevan, An additive framework for kirigami design. Nature Computational Science, 3(5), 443-454, 2023. (*equal contribution)
• G. P. T. Choi, L. Liu, L. Mahadevan, Explosive rigidity percolation in kirigami. Proceedings of the Royal Society A, 479(2271), 20220798, 2023.

Origami metamaterials

• L. H. Dudte, G. P. T. Choi, L. Mahadevan, An additive algorithm for origami design. Proceedings of the National Academy of Sciences, 118(21), e2019241118, 2021.

Structural assemblies

• G. P. T. Choi, S. Chen, L. Mahadevan, Control of connectivity and rigidity in prismatic assemblies. Proceedings of the Royal Society A, 476(2244), 20200485, 2020.

Floppy networks

• S. Chen, F. Giardina, G. P. T. Choi, L. Mahadevan, Modular representation and control of floppy networks. Proceedings of the Royal Society A, 478(2264), 20220082, 2022.

Droplets

• A. Chakrabarti, G. P. T. Choi, L. Mahadevan, Self-excited motions of volatile drops on swellable sheets. Physical Review Letters, 124(25), 258002, 2020.

3. Quantitative biology

Brain morphometry using landmark-matching quasi-conformal maps

• P. T. Choi, K. C. Lam, 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.
• Y. Guo, Q. Chen, G. P. T. Choi, 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.

Shape analysis of human facial point clouds using Teichmüller maps

• T. W. Meng, G. P. T. Choi, L. M. Lui, TEMPO: Feature-endowed Teichmüller extremal mappings of point clouds. SIAM Journal on Imaging Sciences, 9(4), 1922-1962, 2016.

Shape analysis of carotid artery using conformal/area-preserving maps

• G. P. T. Choi, Y. Chen, L. M. Lui, 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.
• G. P. T. Choi, B. Chiu, 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 using Teichmüller maps

• G. P. T. Choi and L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A, 474(2217), 20170905, 2018.

Tooth morphometry using quasi-conformal theory

• G. P. T. Choi, H. L. Chan, R. Yong, S. Ranjitkar, A. Brook, G. Townsend, K. Chen, L. M. Lui, Tooth morphometry using quasi-conformal theory. Pattern Recognition, 99, 107064, 2020.
• G. P. T. Choi, D. Qiu, L. M. Lui, Shape analysis via inconsistent surface registration. Proceedings of the Royal Society A, 476(2242), 20200147, 2020.

Morphometrics and morphogenesis of bird beaks

• S. Al-Mosleh, G. P. T. Choi, A. Abzhanov, L. Mahadevan, Geometry and dynamics link form, function and evolution of finch beaks. Proceedings of the National Academy of Sciences, 118(46), e2105957118, 2021.
• S. Mosleh*, G. P. T. Choi*, G. M. Musser, H. F. James, A. Abzhanov, L. Mahadevan, Beak morphometry and morphogenesis across avian radiations. Proceedings of the Royal Society B, 290(2007), 20230420, 2023. (*equal contribution)

Egg patterns

• T. Dixit, G. P. T. Choi*, S. Al-Mosleh*, J. Lund, J. Troscianko, C. Moya, L. Mahadevan, 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

• M. B. Edwards, G. P. T. Choi, N. Derieg, Y. Min, A. C. Diana, S. A. Hodges, L. Mahadevan, E. M. Kramer, E. S. Ballerini, Genetic architecture of floral traits in bee- and hummingbird-pollinated sister species of Aquilegia (columbine). Evolution, 75(9), 2197-2216, 2021.

Collective dynamics

• R. Supekar, B. Song, A. Hastewell, G. P. T. Choi, A. Mietke, J. Dunkel, Learning hydrodynamic equations for active matter from particle simulations and experiments. Proceedings of the National Academy of Sciences, 120(7), e2206994120, 2023.

Bacterial biofilms

• T. Ohmura, D. J. Skinner, K. Neuhaus, G. P. T. Choi, J. Dunkel, K. Drescher, In vivo microrheology reveals local elastic and plastic responses inside three-dimensional bacterial biofilms. Advanced Materials, 2024.

Quasiconformal flows for morphodynamics

• S. Mosleh*, G. P. T. Choi*, L. Mahadevan, Data-driven quasiconformal morphodynamic flows. Preprint, arXiv:2404.07073, 2024. (*equal contribution)

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