130 citations · 247 across the 19 of their papers we have counts for
19 papers
What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives
Na Lei, Zezeng Li, Zebin Xu +2
Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG ha…
Constant-time Quantum Algorithm for Homology Detection in Closed Curves
Nhat A. Nghiem, Xianfeng David Gu, Tzu-Chieh Wei
Given a loop or more generally 1-cycle of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks…
Global Consistent Point Cloud Registration Based on Lie-algebraic Cohomology
Yuxue Ren, Baowei Jiang, Wei Chen +2
We present a novel, effective method for global point cloud registration problems by geometric topology. Based on many point cloud pairwise registration methods (e.g ICP), we focus…
Quadrilateral Mesh Generation III: Optimizing Singularity Configuration Based on Abel-Jacobi Theory
Xiaopeng Zheng, Yiming Zhu, Na Lei +2
This work proposes a rigorous and practical algorithm for generating meromorphic quartic differentials for the purpose of quad-mesh generation. The work is based on the Abel-Jacobi…
Registration of Volumetric Prostate Scans using Curvature Flow
Saad Nadeem, Rui Shi, Joseph Marino +3
Radiological imaging of the prostate is becoming more popular among researchers and clinicians in searching for diseases, primarily cancer. Scans might be acquired with different e…
Space Filling Curves for 3D Sensor Networks with Complex Topology
Mayank Goswami, Siming Li, Junwei Zhang +3
Several aspects of managing a sensor network (e.g., motion planning for data mules, serial data fusion and inference) benefit once the network is linearized to a path. The lineariz…
Ricci Curvature of the Internet Topology
Chien-Chun Ni, Yu-Yao Lin, Jie Gao +2
Analysis of Internet topologies has shown that the Internet topology has negative curvature, measured by Gromov's "thin triangle condition", which is tightly related to core conges…
Discrete Conformal Deformation: Algorithm and Experiments
Jian Sun, Tianqi Wu, Xianfeng Gu +1
In this paper, we introduce a definition of discrete conformality for triangulated surfaces with flat cone metrics and describe an algorithm for solving the problem of prescribing…
Computing Teichmüller Maps between Polygons
Mayank Goswami, Xianfeng Gu, Vamsi P. Pingali +1
By the Riemann-mapping theorem, one can bijectively map the interior of an -gon to that of another -gon conformally. However, (the boundary extension of) this mapping…
A discrete uniformization theorem for polyhedral surfaces II
Xianfeng Gu, Ren Guo, Feng Luo +2
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic poly…
The Unified Surface Ricci Flow
Min Zhang, Ren Guo, Wei Zeng +3
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant ever…
A discrete uniformization theorem for polyhedral surfaces
Xianfeng Gu, Feng Luo, Jian Sun +1
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a s…
A Variational Principle for Improving 2D Triangle Meshes based on Hyperbolic Volume
Jian Sun, Wei Chen, Junhui Deng +3
In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where th…
A Novel Skew-Hamiltonian Isotropic Lanczos Algorithm for Spectral Conformal Parameterizations
Wei-Qiang Huang, Xianfeng David Gu, Wen-Wei Lin +1
Numerous methods for computing conformal mesh paramterizations has been developed due to the vast applications in the field of geometry processing. Spectral conformal parameterizat…
Convergence of an iterative algorithm for Teichmüller maps via generalized harmonic maps
Lui Lok Ming, Gu Xianfeng, Yau Shing-Tung
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichmüller maps are surface mappings with least conformality distortion.…
Rigidity of Infinite Hexagonal Triangulation of the Plane
Tianqi Wu, Xianfeng Gu, Jian Sun
In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our resul…
A Conformal Approach for Surface Inpainting
Lok Ming Lui, Chengfeng Wen, Xianfeng Gu
We address the problem of surface inpainting, which aims to fill in holes or missing regions on a Riemann surface based on its surface geometry. In practical situation, surfaces ob…
Kernel Estimation from Salient Structure for Robust Motion Deblurring
Jinshan Pan, Risheng Liu, Zhixun Su +1
Blind image deblurring algorithms have been improving steadily in the past years. Most state-of-the-art algorithms, however, still cannot perform perfectly in challenging cases, es…
Optimization of Surface Registrations using Beltrami Holomorphic Flow
L. M. Lui, T. W. Wong, W. Zeng +4
In shape analysis, finding an optimal 1-1 correspondence between surfaces within a large class of admissible bijective mappings is of great importance. Such process is called surfa…