Xianfeng Gu, Steven J. Gortler
Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages...
Yalin Wang, Xiaotian Yin, Jie Zhang, Xianfeng Gu, Tony F. Chan, M. Thompson, ...
Abstract. By solving the Yamabe equation with the discrete surface Ricci flow method, we can conformally parameterize a multiple boundary surface by a multi-hole disk. The resulting parameterizations...
Abstract Silhouette Clipping (2009)
Pedro V. Sander, Xianfeng Gu, Steven J. Gortler, John Snyder
Approximating detailed models with coarse, texture-mapped meshes results in polygonal silhouettes. To eliminate this artifact, we introduce silhouette clipping, a framework for efficiently clipping...
Meshless Harmonic Volumetric Mapping using Fundamental Solution Methods (2008)
Xin Li, Xiaohu Guo, Hongyu Wang, Ying He, Xianfeng Gu, Hong Qin
Abstract—Harmonic volumetric mapping establishes a smooth bijective correspondence between two solid shapes with same topology. We develop an automatic meshless method for creating such a mapping...
Global Conformal Surface Parameterization (2008)
L. Kobbelt, P. Schröder, Xianfeng Gu, Shing-tung Yau
We solve the problem of computing global conformal parameterizations for surfaces with nontrivial topologies. The parameterization is global in the sense that it preserves the conformality everywhere...
Global Conformal Surface Parameterization (2008)
L. Kobbelt, P. Schröder, Xianfeng Gu, Shing-tung Yau
We solve the problem of computing global conformal parameterizations for surfaces with nontrivial topologies. The parameterization is global in the sense that it preserves the conformality everywhere...
Constructing splines whose parametric domain is an arbitrary manifold and effectively computing such splines in real-world applications are of fundamental importance in solid and shape modeling,...
An Effective Illustrative Visualization Framework Based on Photic Extremum Lines (PELs) (2008)
Xuexiang Xie, Ying He, Feng Tian, Hock-soon Seah, Xianfeng Gu, Hong Qin
Abstract—Conveying shape using feature lines is an important visualization tool in visual computing. The existing feature lines (e.g., ridges, valleys, silhouettes, suggestive contours, etc.) are...
Uniform Texture Synthesis and Texture Mapping Using Global Parameterization (2008)
Lujin Wang, Xianfeng Gu, Klaus Mueller, Shing-tung Yau
Abstract Texture mapping and texture synthesis are two popular methods for the decoration of surfaces with visual detail. Here, an existing challenge is to preserve, or at least balance, two...
CURVE SPACE: CLASSIFYING CURVES ON SURFACES (2008)
Abstract. We design signatures for curves defined on genus zero surfaces. The signature classifies curves according to the conformal geometry of the given curves and their embedded surface. Based on...
Geometric compression using Riemann surface structure,Comm. in info. sys (2008)
Xianfeng Gu, Yalin Wang, Shing-tung Yau
Abstract. This paper introduces a theoretic result that shows any surface in 3 dimensional Euclidean space can be determined by its conformal factor and mean curvature uniquely up to rigid motions....
COMPUTING CONFORMAL INVARIANTS: PERIOD MATRICES ∗ (2008)
Xianfeng Gu, Yalin Wang, Shing-tung Yau
Abstract. This work introduces a system of algorithms to compute period matrices for general surfaces with arbitrary topologies. The algorithms are intrinsic to the geometry, and independent of...
CURVE SPACE: CLASSIFYING CURVES ON SURFACES (2008)
Abstract. We design signatures for curves defined on genus zero surfaces. The signature classifies curves according to the conformal geometry of the given curves and their embedded surface. Based on...
CONFORMAL SPHERICAL PARAMETRIZATION FOR HIGH GENUS SURFACES (2008)
Wei Zeng, Xin Li, Shing-tung Yau, Xianfeng Gu
Abstract. Surface parameterization establishes bijective maps from a surface onto a topolog-ically equivalent standard domain. It is well known that the spherical parameterization is limited to...
CONFORMAL SPHERICAL PARAMETRIZATION FOR HIGH GENUS SURFACES (2008)
Wei Zeng, Xin Li, Shing-tung Yau, Xianfeng Gu
Abstract. Surface parameterization establishes bijective maps from a surface onto a topolog-ically equivalent standard domain. It is well known that the spherical parameterization is limited to...
Craig Gotsman, Xianfeng Gu, Alla Sheffer
Parameterization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to...
Abstract Manifold Splines (2008)
Xianfeng Gu, Ying He, Hong Qin
Constructing splines whose parametric domain is an arbitrary manifold and effectively computing such splines in real-world applications are of fundamental importance in solid and shape modeling,...
Conformal surface parameterization using euclidean ricci flow (2008)
Miao Jin, Juhno Kim, Feng Luo, Seungyong Lee, Xianfeng Gu
Surface parameterization is a fundamental problem in graphics. Conformal surface parameterization is equivalent to finding a Riemannian metric on the surface, such that the metric is conformal to the...
Chinese Academy of Sciences (2008)
Wei Zeng, Xin Li, Shing-tung Yau, Xianfeng Gu
Surface parameterization establishes bijective maps from a surface onto a topologically equivalent standard domain. It is well known that the spherical parameterization is limited to genus-zero...
ACCEPTED MANUSCRIPT Geometric Accuracy Analysis for Discrete Surface Approximation (2008)
Junfei Dai, Wei Luo, Miao Jin, Wei Zeng, Ying He, Shing-tung Yau, ...
doi: 10.1016/j.cagd.2007.04.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the...
Feng-Luo † Rutgers University (2008)
Figure 1: The hyperbolic structure and real projective structure of a genus two closed surface. From left to right, the original surface with a set of canonical fundamental group basis; the isometric...
Focal Surfaces of Discrete Geometry (2008)
Er Belyaev, Michael Garl, Jingyi Yu, Xiaotian Yin, Xianfeng Gu, Leonard Mcmillan, ...
The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated...
Conformal geometry and its applications on 3d shape matching, recognition, and stitching (2008)
Sen Wang, Yang Wang, Miao Jin, Xianfeng Gu, Dimitris Samaras
3D shape matching is a fundamental issue in computer vision with many applications such as shape registration, 3D object recognition and classification. However, shape matching with noise, occlusion...
Shengying Li, Zhe Fan, Xiaotian Yin, Klaus Mueller, Arie E. Kaufman, Xianfeng Gu
A novel method for accurate reflections in real time is introduced using ray tracing in geometry fields, which combine light fields with geometry images. The geometry field of a surface is defined...
SURFACE SEGMENTATION USING GLOBAL CONFORMAL STRUCTURE ∗ (2008)
Yalin Wang, Xianfeng Gu, Shing-tung Yau
Abstract. Surface segmentation is a fundamental problem in computer graphics. It has various applications such as metamorphosis, surface matching, surface compression, 3D shape retrieval, texture...
Uniform Texture Synthesis and Texture Mapping Using Global Parameterization (2008)
Lujin Wang, Xianfeng Gu, Klaus Mueller, Shing-tung Yau
Abstract Texture mapping and texture synthesis are two popular methods for the decoration of surfaces with visual detail. Here, an existing challenge is to preserve, or at least balance, two...
The Visual Computer manuscript No. (will be inserted by the editor) (2008)
Junfei Dai, Junho Kim, Huayi Zeng, Xianfeng Gu
Abstract Silhouettes play a crucial role in visualization, graph- been applied for surface reconstruction, pattern recognition ics and vision. This work focuses on the global behaviors and aspect...
Constructing splines whose parametric domain is an arbitrary manifold and effectively computing such splines in real-world applications are of fundamental importance in solid and shape modeling,...
Shengying Li, Zhe Fan, Xiaotian Yin, Klaus Mueller, Arie E. Kaufman, Xianfeng Gu
A novel method for accurate reflections in real time is introduced using ray tracing in geometry fields, which combine light fields with geometry images. The geometry field of a surface is defined...
Abstract Geometry Images (2008)
Xianfeng Gu, Steven J. Gortler
Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages...
Focal Surfaces of Discrete Geometry (2008)
Er Belyaev, Michael Garl, Jingyi Yu, Xiaotian Yin, Xianfeng Gu, Leonard Mcmillan, ...
The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated...
Abstract Polyhedral Geometry and the Two-Plane Parameterization (2008)
Xianfeng Gu, Steven J. Gortler, Michael F. Cohen
Recently the light-field and lumigraph systems have been proposed as general methods of representing the visual information present in a scene. These methods represent this information as a 4D...
Globally optimal surface mapping for surfaces with arbitrary topology (2008)
Xin Li, Yunfan Bao, Xiaohu Guo, Miao Jin, Xianfeng Gu, Hong Qin
Abstract — Computing smooth and optimal one-to-one maps between surfaces of same topology is a fundamental problem in graphics and such a method provides us a ubiquitous tool for geometric modeling...
Globally optimal surface mapping for surfaces with arbitrary topology (2008)
Xin Li, Yunfan Bao, Xiaohu Guo, Miao Jin, Xianfeng Gu, Hong Qin
Abstract — Computing smooth and optimal one-to-one maps between surfaces of same topology is a fundamental problem in computer graphics and such a method provides us a ubiquitous tool for geometric...
For D Meshes, Craig Gotsman, Xianfeng Gu, Alla Sheffer
Parametrization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to...
Abstract Geometry Images (2007)
Xianfeng Gu, Steven J. Gortler
Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)-regular connectivity, which has advantages...
Brain surface conformal parameterization using riemann surface structure (2007)
Yalin Wang, Lok Ming Lui, Xianfeng Gu, Kiralee M. Hayashi, Tony F. Chan, Arthur W. Toga, ...
Abstract—In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal...
High Resolution Tracking of Non-Rigid Motion of Densely Sampled 3D Data Using Harmonic Maps (2007)
Yang Wang, Mohit Gupta, Song Zhang, Sen Wang, Xianfeng Gu, Dimitris Samaras, ...
We present a novel automatic method for high resolution, non-rigid dense 3D point tracking. High quality dense point clouds of non-rigid geometry moving at video speeds are acquired using a...
Harmonic volumetric mapping for solid modeling applications (2007)
Xin Li, Xiaohu Guo, Hongyu Wang, Ying He, Xianfeng Gu, Hong Qin
Figure 1: Harmonic volumetric mapping from a solid polycube model(a) to the solid Buddha model(b). (c) is the color-coded distance field of the Buddha interior. This color-coded distance field is...
Hongyu Wang, Ying He, Xin Li, Xianfeng Gu, Hong Qin
(a) Conformal polycube map (b) Polycube T-spline (c) T-junctions on polycube spline(d) Close-up of control points Figure 1: Polycube spline for the Isidore Horse model. (a) The conformal polycube map...
Manifold splines with single extraordinary point (2007)
Xianfeng Gu, Ying He, Miao Jin
This paper develops a novel computational technique to define and construct powerful manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The...
Gu, Xianfeng, Zhang, Song, Huang, Peisen, Zhang, Liangjun, Yauk, Shing-Tung, Martin, Ralph R.
We introduce a novel geometric representation called a holoimage, which encodes both shading and geometry information within the same image, based on the principles of wave optics. ‘Image’...
Curves-on-surfaces: A general shape comparison framework (2006)
Xin Li, Ying He, Xianfeng Gu, Hong Qin
We develop a new surface matching framework to handle surface comparisons based on a novel mathematical analysis of curves on surfaces, and propose a unique signature for any closed curve on a...
3d surface matching and recognition using conformal geometry (2006)
Sen Wang, Yang Wang, Miao Jin, Xianfeng Gu, Dimitris Samaras
3D surface matching is a fundamental issue in computer vision with many applications such as shape registration, 3D object recognition and classification. However, surface matching with noise,...
Kexiang Wang, Ying He, Xiaohu Guo, Xianfeng Gu, Hong Qin
Abstract. It has been technically challenging to effectively model and simulate elastic deformation of spline-based, thin-shell objects of complicated topology. This is primarily because traditional...
Meshless thin-shell simulation based on global conformal parameterization (2006)
Xiaohu Guo, Student Member, Student Member, Yunfan Bao, Student Member, Xianfeng Gu, ...
Abstract—This paper presents a new approach to the physically-based thin-shell simulation of point-sampled geometry via explicit, global conformal point-surface parameterization and meshless...
Curves-on-surfaces: A general shape comparison framework (2006)
Xin Li, Ying He, Xianfeng Gu, Hong Qin
We develop a new surface matching framework to handle surface comparisons based on the mathematical analysis of curves on surfaces, and propose a unique signature for any closed curve on a surface....
Conformal virtual colon flattening (2006)
Wei Hong, Xianfeng Gu, Feng Qiu, Miao Jin, Arie Kaufman
Figure 1: Conformal Virtual Colon Flattening: (a) illustrates the holomorphic one-form on the colon surface by texture-mapping a checker board image. (b) exhibits the conformal flattening induced by...
Brain surface conformal parameterization with algebraic functions (2006)
Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal...
Ying He, Kexiang Wang, Hongyu Wang, Xianfeng Gu, Hong Qin
Abstract. This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to...
Brain surface conformal parameterization with algebraic functions (2006)
Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
Abstract. In medical imaging, parameterized 3D surface models are of great interest for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and...
3d surface matching and recognition using conformal geometry (2006)
Sen Wang, Yang Wang, Miao Jin, Xianfeng Gu, Dimitris Samaras
3D surface matching is a fundamental issue in computer vision with many applications such as shape registration, 3D object recognition and classification. However, surface matching with noise,...
Meshless thin-shell simulation based on global conformal parameterization (2006)
Xiaohu Guo, Xin Li, Student Member, Student Member, Yunfan Bao, Xianfeng Gu, ...
Abstract — This paper presents a new approach to the physically-based thin-shell simulation of point-sampled geometry via explicit, global conformal point-surface parameterization and meshless...
Ying He, Kexiang Wang, Hongyu Wang, Xianfeng Gu, Hong Qin
Abstract. This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to...
Gu, Xianfeng, Zhang, Song, Huang, Peisen, Zhang, Liangjun, Yauk, Shing-Tung, Martin, Ralph R.
We introduce a novel geometric representation called a holoimage, which encodes both shading and geometry information within the same image, based on the principles of wave optics. ‘Image’...
Gu, Xianfeng, Zhang, Song, Huang, Peisen, Zhang, Liangjun, Yau, Shing-Tung, Martin, Ralph Robert
We introduce a novel geometric representation called a holoimage, which encodes both shading and geometry information within the same image, based on the principles of wave optics. ‘Image’...
Fairing triangular B-splines of arbitrary topology (2005)
Ying He, Xianfeng Gu, Hong Qin
spherical spline and its mean curvature plot (red, H < 0, cyan, H> 0, green, H ≈ 0). Note that the spline surface has high curvature concentration along the image of edges of the spherical...
Topology-driven surface mappings with robust feature alignment (2005)
Christopher Carner, Miao Jin, Xianfeng Gu, Hong Qin
Figure 1: Surface mapping between horse and lizard. The color-coding shows the mapping of each region, guided by eight user-specified feature curves. Our topology-driven method provides mappings of...
Fairing triangular B-splines of arbitrary topology (2005)
Ying He, Xianfeng Gu, Hong Qin
show a degree 5 ( C continuous) spherical spline and its mean curvature plot. Note that the spline surface has high curvature concentration along the image of edges of the spherical triangles. (e),...
High resolution tracking of non-rigid 3D motion of densely sampled data using harmonic maps (2005)
Yang Wang, Mohit Gupta, Song Zhang, Sen Wang, Xianfeng Gu, Dimitris Samaras, ...
We present a novel fully automatic method for high resolution, non-rigid dense 3D point tracking. High quality dense point clouds of non-rigid geometry moving at video speeds are acquired using a...
Rational spherical splines for genus zero shape modeling (2005)
Ying He, Xianfeng Gu, Hong Qin
Traditional approaches for modeling a closed manifold surface with either regular tensor-product or triangular splines (defined over an open planar domain) require decomposing the acquired geometric...
Brain image analysis using spherical splines (2005)
Ying He, Xin Li, Xianfeng Gu, Hong Qin
Abstract. We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both...
Surface parameterization using riemann surface structure (2005)
Yalin Wang, Tony F. Chan, Xianfeng Gu, Paul M. Thompson, Kiralee M. Hayashi, Shing-tung Yau
We propose a general method that parameterizes general surfaces with complex (possible branching) topology using Riemann surface structure. Rather than evolve the surface geometry to a plane or...
Topology-driven surface mappings with robust feature alignment (2005)
Christopher Carner, Miao Jin, Xianfeng Gu, Hong Qin
Figure 1: Surface mapping between horse and lizard. The color-coding shows the mapping of each region, guided by eight user-specified feature curves. Our topology-driven method provides mappings of...
Surface parameterization using riemann surface structure (2005)
Yalin Wang, Tony F. Chan, Xianfeng Gu, Paul M. Thompson, Kiralee M. Hayashi, Shing-tung Yau
We propose a general method that parameterizes general surfaces with complex (possible branching) topology using Riemann surface structure. Rather than evolve the surface geometry to a plane or...
Topology-driven surface mappings with robust feature alignment (2005)
Christopher Carner, Miao Jin, Xianfeng Gu, Hong Qin
Figure 1: Surface mapping between horse and lizard. The color-coding shows the mapping of each region, guided by eight user-specified feature curves. Our topology-driven method provides mappings of...
Partitioning, Surface/Volume Parameterization/Remeshing Education (2005)
Xin Li, Advisors Hong Qin, Xianfeng Gu, Advisors Hong Qin, Xianfeng Gu
A C 1 globally interpolatory spline of arbitrary topology (2005)
Ying He, Miao Jin, Xianfeng Gu, Hong Qin
Abstract. Converting point samples and/or triangular meshes to a more compact spline representation for arbitrarily topology is both desirable and necessary for computer vision and computer graphics....
Optimal Global Conformal Surface Parameterization for Visualization (2004)
Gu, Xianfeng, Jin, Miao, Wang, Yalin, Yau, Shin-Tung
All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena,...
Surface Segmentation Using Global Conformal Structure (2004)
Gu, Xianfeng, Wang, Yalin, Yau, Shing-Tung
Surface segmentation is a fundamental problem in computer graphics. It has various applications such as metamorphosis, surface matching, surface compression, 3D shape retrieval, texture mapping, etc....
Genus zero surface conformal mapping and its application to brain surface mapping (2004)
Xianfeng Gu, Yalin Wang, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
Abstract—We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and...
Genus zero surface conformal mapping and its application to brain surface mapping (2004)
Xianfeng Gu, Yalin Wang, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
Abstract. It is well known that any genus zero surface can be mapped conformally onto the sphere and any local portion thereof onto a disk. However, it is not trivial to find a general method which...
Genus zero surface conformal mapping and its application to brain surface mapping (2004)
Xianfeng Gu, Yalin Wang, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
Abstract. It is well known that any genus zero surface can be mapped conformally onto the sphere and any local portion thereof onto a disk. However, it is not trivial to find a general method which...
Intrinsic brain surface conformal mapping using a variational method (2004)
Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
Abstract. We propose a new variational method which can find a unique conformal mapping between any two genus zero manifolds by minimizing the harmonic energy of the map and apply it to the cortical...
Genus zero surface conformal mapping and its application to brain surface mapping (2004)
Xianfeng Gu, Yalin Wang, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
It is well known that any genus zero surface can be mapped conformally onto the sphere and any local portion thereof onto a disk. However, it is not trivial to find a general method which finds a...
Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping (2004)
Xianfeng Gu, Yalin Wang, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
It is well known that any genus zero surface can be mapped conformally onto the sphere and any local portion thereof onto a disk. However, it is not trivial to find a general method which computes a...
Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping (2004)
Xianfeng Gu, Yalin Wang, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms with or without boundaries [1], [2]. For genus zero...
Volumetric Harmonic Brain Mapping (2004)
Yalin Wang Xianfeng, Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
In [1], we developed two different techniques to study volume mapping problem in Computer Graphics. The first one is to find a harmonic map from a 3 manifold to a 3D solid sphere and the second is a...
Yalin Wang, Xianfeng Gu, Paul M. Thompson, Shing-tung Yau
Abstract. We developed two techniques to address 3D volume parameterization and deformation mapping problems that arise in medical imaging [1]. The first algorithm finds a harmonic map from a...
Optimal global conformal surface parameterization (2004)
Miao Jin, Yalin Wang, Shing-tung Yau, Xianfeng Gu
Figure 1: Uniform global conformal parameterization ((a) and (b)) and region emphasized conformal parameterization ((c) and (d)). (a). Least uniform conformal parameterization with energy: 21.208e...
Optimal global conformal surface parameterization (2004)
Miao Jin, Yalin Wang, Shing-tung Yau, Xianfeng Gu
Figure 1: Uniform global conformal parameterization ((a) and (b)) and region emphasized conformal parameterization ((c) and (d)). (a). Least uniform conformal parameterization with energy: 21.208e...
Matching 3d shapes using 2d conformal representations (2004)
Matching 3D shapes is a fundamental problem in Medical Imaging with many applications including, but not limited to, shape deformation analysis, tracking etc. Matching 3D shapes poses a...
Optimal global conformal surface parameterization (2004)
Visualization Miao Jin, Yalin Wang, Xianfeng Gu, Shing-tung Yau
Abstract. All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical...
Computing Conformal Invariants: Period Matrices (2003)
Gu , Xianfeng, Wang , Yalin, Yau , Shing-Tung
This work introduces a system of algorithms to compute period matrices for general surfaces with arbitrary topologies. The algorithms are intrinsic to the geometry, and independent of surface...
Geometric Compression Using Riemann Surface Structure (2003)
Gu , Xianfeng, Wang , Yalin, Yau , Shing-Tung
This paper introduces a theoretic result that shows any surface in 3 dimensional Euclidean space can be determined by its conformal factor and mean curvature uniquely up to rigid motions. This...
Volumetric Harmonic Map (2003)
Gu , Xianfeng, Wang , Yalin, Yau , Shing-Tung
We develop two different techniques to study volume mapping problem in Computer Graphics and Medical Imaging fields. The first one is to find a harmonic map from a 3 manifold to a 3D solid sphere and...
Brain surface conformal mapping (2003)
Xianfeng Gu, Yalin Wang Wang, Shing Tung Yau
We propose a new variational method which can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. We demonstrate the feasibility of our algorithm...
Computing Conformal Invariants: Period Matrices (2003)
Xianfeng Gu, Yalin Wang, Shing-tung Yau
This work introduces a system of algorithms to compute period matrices for general surfaces with arbitrary topologies. The algorithms are intrinsic to the geometry, independent of surface...
Surface Classification Using Conformal Structures (2003)
D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods...
Surface classification using conformal structures (2003)
3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods...
Intrinsic Brain Surface Conformal Mapping (2003)
Using Variational Method, Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-tung Yau
We propose a new variational method which can find a unique conformal mapping between any two genus zero manifolds by minimizing the harmonic energy of the map and apply it to the cortical surface...
Fundamentals of spherical parameterization for 3d meshes (2003)
Craig Gotsman, Xianfeng Gu, Alla Sheffer
Parameterization of 3D mesh data is important for many graphics applications, in particular for texture mapping, remeshing and morphing. Closed manifold genus-0 meshes are topologically equivalent to...
Computing Conformal Structure of Surfaces (2002)
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology...
Parametrization of surfaces with arbitrary topologies / (2002)
Thesis (Ph. D., Division of Engineering and Applied Sciences)--Harvard University, 2003.
Computing conformal structures of surfaces (2002)
Abstract. This paper solves the problem of computing conformal structures of general 2manifolds represented as triangular meshes. We approximate the De Rham cohomology by simplicial cohomology and...
Computing Conformal Structures Of Surfaces (2002)
This paper solves the problem of computing conformal structures of general 2manifolds represented as triangular meshes. We approximate the De Rham cohomology by simplicial cohomology and represent...
Parametrization for Surfaces with Arbitrary Topologies (2002)
Surface parametrization is a fundamental problem in computer graphics. It is essential for operations such as texture mapping, texture synthesis, interactive 3D painting, remeshing, multi-resolution...
Pedro Sander, Xianfeng Gu, Steven J. Gortler, Hugues Hoppe, John Snyder
Approximating detailed models with coarse, texture-mapped meshes results in polygonal silhouettes. To eliminate this artifact, we introduce silhouette clipping, a framework for efficiently clipping...
Pedro Sander Xianfeng, Pedro V. Sander, Xianfeng Gu, Steven J. Gortler, John Snyder
Approximating detailed models with coarse, texture-mapped meshes results in polygonal silhouettes. To eliminate this artifact, we introduce silhouette clipping, a framework for efficiently clipping...
Xianfeng Gu, Steven J. Gortler, Leonard Mcmillan, Benedict J. Brown, Abraham D. Stone
Recent image-based rendering techniques have shown success in approximating detailed models using sampled images over coarser meshes. One limitation of these techniques is that the coarseness of the...
Xianfeng Gu, Steven J. Gortler, Hugues Hoppe, Leonard McMillan, Benedict J. Brown, Abraham D. Stone
Recent image-based rendering techniques have shown success in approximating detailed models using sampled images over coarser meshes. One limitation of these techniques is that the coarseness of the...
Xianfeng Gu, Steven J. Gortler, Leonard Mcmillan, Benedict J. Brown, Abraham D. Stone
Recent image-based rendering techniques have shown success in approximating detailed models using sampled images over coarser meshes. One limitation of these techniques is that the coarseness of the...
Regularity of harmonic maps (1999)
Yalin Wang, Xianfeng Gu, Shing-tung Yau
Abstract. We develop two different techniques to study volume mapping problem in Computer Graphics and Medical Imaging fields. The first one is to find a harmonic map from a 3 manifold to a 3D solid...
Xianfeng Gu, Steven J. Gortler, Leonard Mcmillan, Benedict J. Brown, Abraham D. Stone
Recent image-based rendering techniques have shown success in approximating detailed models using sampled images over coarser meshes. One limitation of these techniques is that the coarseness of the...
Polyhedral Geometry and the Two-Plane Parameterization (1997)
Xianfeng Gu, Steven J. Gortler, Michael F. Cohen
Recently the light-field and lumigraph systems have been proposed as general methods of representing the visual information present in a scene. These methods represent this information as a 4D...
Multiresolution computation of conformal structures of surfaces (1996)
Xianfeng Gu, Yalin Wang, Shing-tung Yau
The conformal structures are only determined by
Multiresolution Computation of Conformal Structures of Surfaces (1996)
Xianfeng Gu Yalin, Xianfeng Gu, Yalin Wang, Shing-tung Yau
An e#cient multiresolution method to compute global conformal structures of nonzero genus triangle meshes is introduced. The homology, cohomology groups of meshes are computed explicitly, then a...