11 citations · 17 across the 16 of their papers we have counts for
17 papers
An integrated geometric quantification and shape analysis framework for axillary lymph node metastasis in breast cancer patients
Zixi Yi, Limeng Qu, Gary P. T. Choi
Quantitative characterization of lymph node morphology is important for assessing axillary lymph node metastasis in breast cancer. However, surfaces reconstructed from computed tom…
Adaptive Volumetric Parameterization of Simply Connected 3-Manifolds with Applications
Zhiyuan Lyu, Qiguang Chen, Lok Ming Lui +1
Volumetric parameterization, the process of mapping a 3-manifold onto a simplified volumetric domain, is important for many tasks in computer graphics and imaging science. However,…
Exact Schur-Sylvester Dimensionality Reductions for Non-Smooth Stochastic Complexity and Manifold Sampling
Trenton Lau, Gary P. T. Choi
The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.g., Lasso) has been historically limited by the cubic scaling walls…
Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis
Gary P. T. Choi, Khanh Dao Duc, Shira Faigenbaum-Golovin +6
A central objective of machine learning is to identify structure and patterns in data. Advances in data acquisition have increasingly produced datasets whose observations possess r…
How geometry of subduction zones correlates with earthquake dynamics
Oscar Y. L. Chau, Rebecca Bendick, Gary P. T. Choi +1
Subduction zones on the surface of the Earth, where abrupt sliding leads to earthquakes, are generally curved and localized. How does the geometry of these zones influence the occu…
Resolution-free neural surrogates for geometric parameterization and mapping with spatially varying fields
Yanwen Huang, Lok Ming Lui, Gary P. T. Choi
Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction…
The Normalized Maximum Likelihood for Regular Non-Smooth Models: Measure-Theoretic Foundations and Geometric Sampling
Trenton Lau, Gary P. T. Choi
The Normalized Maximum Likelihood (NML) codelength, or stochastic complexity, represents a principled criterion for universal coding. While recent coarea-based formulations provide…
Planar morphometry via functional shape data analysis and quasi-conformal mappings
Hangyu Li, Gary P. T. Choi
The study of shapes is one of the most fundamental problems in life sciences. Although numerous methods have been developed for the morphometry of planar biological shapes over the…
Conformal tubular parameterization and toroidal bending of tube-like surfaces
Shunyu Yao, Gary P. T. Choi
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not…
Optimization of Constrained Quasiconformal Mapping for Origami Design
Ka Ho Lai, Hei Tung Tsang, Gary P. T. Choi +1
Origami structures, particularly Miura-ori patterns, offer unique capabilities for surface approximation and deployable designs. In this study, a constrained mapping optimization a…
Geometric quantification for nonlinear deformation in knitted fabrics
Jiani Fang, Xiaoxiao Ding, Gary P. T. Choi
Knitted fabrics exemplify a broad class of architected materials capable of large deformations, enabling shape morphing, mechanical biocompatibility, and embedded multifunctionalit…
Volumetric Parameterization for 3-Dimensional Simply-Connected Manifolds
Zhiyuan Lyu, Qiguang Chen, Gary P. T. Choi +1
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D s…
Learning-based density-equalizing map
Yanwen Huang, Lok Ming Lui, Gary P. T. Choi
Density-equalizing map (DEM) serves as a powerful technique for creating shape deformations with the area changes reflecting an underlying density function. In recent decades, DEM…
Toroidal density-equalizing map for genus-one surfaces
Shunyu Yao, Gary P. T. Choi
Density-equalizing map is a shape deformation technique originally developed for cartogram creation and sociological data visualization on planar geographical maps. In recent years…
Ellipsoidal Density-Equalizing Map for Genus-0 Closed Surfaces
Zhiyuan Lyu, Lok Ming Lui, Gary P. T. Choi
Surface parameterization is a fundamental task in geometry processing and plays an important role in many science and engineering applications. In recent years, the density-equaliz…
Spherical Density-Equalizing Map for Genus-0 Closed Surfaces
Zhiyuan Lyu, Lok Ming Lui, Gary P. T. Choi
Density-equalizing maps are a class of mapping methods in which the shape deformation is driven by prescribed density information. In recent years, they have been widely used for d…
Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces
Gary P. T. Choi
Surface parameterization plays a fundamental role in many science and engineering problems. In particular, as genus-0 closed surfaces are topologically equivalent to a sphere, many…