![Triangulating the Lena image using our TRIM algorithm in [6].](https://scholar.harvard.edu/sites/scholar.harvard.edu/files/styles/os_slideshow_16%3A9_980/public/choi/files/trim_lena.png?m=1714108373&itok=zCZdqSzR)
My current research interests include:
- Applied and Computational Geometry
- Interdisciplinary Mathematical Modeling
- Quantitative Biology
- Medical Imaging
- Metamaterial Design
- Geometry Processing
- Scientific Computing
1. Metamaterial design
(I) Kirigami
- G. P. T. Choi, L. H. Dudte, L. Mahadevan, Programming shape using kirigami tessellations. Nature Materials, 18, pp. 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, S. Chen, L. Mahadevan, Control of connectivity and rigidity in prismatic assemblies. Preprint, arXiv:2005.05845.
(II) Origami
- L. H. Dudte, G. P. T. Choi, L. Mahadevan, Additive origami. Preprint, arXiv:2005.05846.
2. Morphometrics and morphogenesis
(I) Brain morphometry using landmark-matching optimized conformal maps
- 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), pp. 67-94, 2015. [Software]
(II) Shape analysis of human facial point clouds using Teichmüller maps
- 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), pp. 1922-1962, 2016.
(III) Shape analysis of carotid artery using conformal/area-preserving maps
- 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), pp. 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, 1-11, 2020.
(IV) Insect wing morphometry using Teichmüller maps
- G. P. T. Choi and L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 474(2217), 20170905, 2018. [Software]
(V) 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. [Software]
(VI) Physical droplet motion
- A. Chakrabarti, G. P. T. Choi, L. Mahadevan, Self-excited motions of volatile drops on swellable sheets. Physical Review Letters, 124, 258002, 2020.
(VII) Shape analysis via inconsistent surface registration
- G. P. T. Choi, D. Qiu, L. M. Lui, Shape analysis via inconsistent surface registration. Submitted, arXiv:2003.01357.
3. Geometry processing and visualization
One of my research focuses has been on the development of surface parameterization and mapping algorithms. Many of my works have been successfully applied to human brain mapping, cardiac mapping, mechanical engineering, texture mapping, surface registration and so on.
(I) Spherical conformal parameterization
- (For triangle 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), pp. 67-94, 2015. [Software]
- (For 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), pp. 1582-1618, 2016. [Software]
- (For triangle 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. To appear in SIAM Journal on Imaging Sciences.
(II) Disk conformal parameterization
- (For triangle meshes) P. T. Choi and L. M. Lui, Fast Disk Conformal Parameterization of Simply-connected Open Surfaces. Journal of Scientific Computing, 65(3), pp. 1065-1090, 2015. [Software]
- (For 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), pp. 87-114, 2018. [Software]
- (For triangle 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. To appear in SIAM Journal on Imaging Sciences.
(III) Rectangular conformal parameterization
- (For triangle meshes and 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), pp. 1922-1962, 2016. [Software]
(IV) Conformal parameterization onto a non-convex domain
- (For triangle meshes) 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), pp. 2183-2195, 2017.
(V) Free-boundary conformal parameterization
- (For triangle 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. To appear in SIAM Journal on Imaging Sciences.
(VI) Spherical quasi-conformal parameterization
- (For triangle meshes) G. P. T. Choi, M. H. Y. Man, and L. M. Lui, Fast Spherical Quasiconformal Parameterization of Genus-0 Closed Surfaces with Application to Adaptive Remeshing. Geometry, Imaging and Computing, 3(1-2), pp. 1-29, 2016.
(VII) Spherical landmark aligned optimized conformal parameterization
- (For triangle 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), pp. 67-94, 2015. [Software]
(VIII) Teichmüller extremal map
- (For 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), pp. 1922-1962, 2016.
- G. P. T. Choi and L. Mahadevan, Planar morphometrics using Teichmüller maps. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 474(2217), 20170905, 2018.
(IX) Density-equalizing map (area-preserving/with controllable area distortion)
- (For 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), pp. 1134-1178, 2018. [Software]
- (For 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, 1-11, 2020.
- (For volumetric domains) G. P. T. Choi and C. H. Rycroft, Volumetric density-equalizing reference map with applications. Preprint, arXiv:2003.09725.
(X) Image triangulation and registration
- C. P. Yung, G. P. T. Choi, K. Chen, and L. M. Lui, Efficient Feature-Based Image Registration by Mapping Sparsified Features. Journal of Visual Communication and Image Representation, 55, pp. 561-571, 2018. [Software]
(XI) Spherical area-preserving parameterization for deep learning
- 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), pp. 2242-2251, 2019.