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Displaying 1-50 out of 56 total
Colon Flattening Using Heat Diffusion Riemannian Metric
Found in: IEEE Transactions on Visualization and Computer Graphics
By Krishna Chaitanya Gurijala,Rui Shi,Wei Zeng,Xianfeng Gu,Arie Kaufman
Issue Date:December 2013
pp. 2848-2857
We propose a new colon flattening algorithm that is efficient, shape-preserving, and robust to topological noise. Unlike previous approaches, which require a mandatory topological denoising to remove fake handles, our algorithm directly flattens the colon ...
 
Authalic Parameterization of General Surfaces Using Lie Advection
Found in: IEEE Transactions on Visualization and Computer Graphics
By Guangyu Zou,Jiaxi Hu,Xianfeng Gu,Jing Hua
Issue Date:December 2011
pp. 2005-2014
Parameterization of complex surfaces constitutes a major means of visualizing highly convoluted geometric structures as well as other properties associated with the surface. It also enables users with the ability to navigate, orient, and focus on regions o...
 
Discrete Surface Ricci Flow
Found in: IEEE Transactions on Visualization and Computer Graphics
By Miao Jin, Junho Kim, Feng Luo, Xianfeng Gu
Issue Date:September 2008
pp. 1030-1043
This work introduces a unified framework for discrete surface Ricci flow algorithms, including spherical, Euclidean, and hyperbolic Ricci flows, which can design Riemannian metrics on surfaces with arbitrary topologies by user-defined Gaussian curvatures. ...
 
Geometric Registration Based on Distortion Estimation
Found in: 2013 IEEE International Conference on Computer Vision (ICCV)
By Wei Zeng,Mayank Goswami,Feng Luo,Xianfeng Gu
Issue Date:December 2013
pp. 2632-2639
Surface registration plays a fundamental role in many applications in computer vision and aims at finding a one-to-one correspondence between surfaces. Conformal mapping based surface registration methods conformally map 2D/3D surfaces onto 2D canonical do...
 
A Generic Deformation Model for Dense Non-rigid Surface Registration: A Higher-Order MRF-Based Approach
Found in: 2013 IEEE International Conference on Computer Vision (ICCV)
By Yun Zeng,Chaohui Wang,Xianfeng Gu,Dimitris Samaras,Nikos Paragios
Issue Date:December 2013
pp. 3360-3367
We propose a novel approach for dense non-rigid 3D surface registration, which brings together Riemannian geometry and graphical models. To this end, we first introduce a generic deformation model, called Canonical Distortion Coefficients (CDCs), by charac...
 
Interactive Visibility Retargeting in VR Using Conformal Visualization
Found in: IEEE Transactions on Visualization and Computer Graphics
By K. Petkov,C. Papadopoulos, Min Zhang,A. E. Kaufman, Xianfeng Gu
Issue Date:July 2012
pp. 1027-1040
In Virtual Reality, immersive systems such as the CAVE provide an important tool for the collaborative exploration of large 3D data. Unlike head-mounted displays, these systems are often only partially immersive due to space, access, or cost constraints. T...
 
Parallelizable inpainting and refinement of diffeomorphisms using Beltrami holomorphic flow
Found in: Computer Vision, IEEE International Conference on
By Tsz Wai Wong,Xianfeng Gu,Tony F. Chan,Lok Ming Lui
Issue Date:November 2011
pp. 2383-2390
In this paper, we propose novel algorithms for inpainting and refinement of diffeomorphisms. We first represent a diffeomorphism by its Beltrami coefficient. Then it is possible to refine and inpaint the diffeomorphism by processing this Beltrami coefficie...
 
Multiscale, curvature-based shape representation for surfaces
Found in: Computer Vision, IEEE International Conference on
By Ruirui Jiang,Xianfeng Gu
Issue Date:November 2011
pp. 1887-1894
This paper presents a multiscale, curvature-based shape representation technique for general genus zero closed surfaces. The method is invariant under rotation, translation, scaling, or general isometric deformations; it is robust to noise and preserves in...
 
Intrinsic dense 3D surface tracking
Found in: Computer Vision and Pattern Recognition, IEEE Computer Society Conference on
By Yun Zeng, Chaohui Wang, Yang Wang, Xianfeng Gu,D. Samaras,N. Paragios
Issue Date:June 2011
pp. 1225-1232
This paper presents a novel intrinsic 3D surface distance and its use in a complete probabilistic tracking framework for dynamic 3D data. Registering two frames of a deforming 3D shape relies on accurate correspondences between all points across the two fr...
 
Isotropic Mesh Simplification by Evolving the Geodesic Delaunay Triangulation
Found in: International Symposium on Voronoi Diagrams in Science and Engineering
By Shi-Qing Xin, Shuang-Min Chen, Ying He, Guo-Jin Wang, Xianfeng Gu, Hong Qin
Issue Date:June 2011
pp. 39-47
In this paper, we present an intrinsic algorithm for isotropic mesh simplification. Starting with a set of unevenly distributed samples on the surface, our method computes the geodesic Delaunay triangulation with regard to the sample set and iteratively ev...
 
Conformal visualization for partially-immersive platforms
Found in: Virtual Reality Conference, IEEE
By K Petkov,C Papadopoulos, Min Zhang,A E Kaufman, Xianfeng Gu
Issue Date:March 2011
pp. 143-150
Current VR systems such as the CAVE provide an effective platform for the immersive exploration of large 3D data. A major limitation is that in most cases at least one display surface, such as a ceiling or a back wall, is missing due to space, access or co...
 
Supine and Prone Colon Registration Using Quasi-Conformal Mapping
Found in: IEEE Transactions on Visualization and Computer Graphics
By Wei Zeng, Joseph Marino, Krishna Chaitanya Gurijala, Xianfeng Gu, Arie Kaufman
Issue Date:November 2010
pp. 1348-1357
In virtual colonoscopy, CT scans are typically acquired with the patient in both supine (facing up) and prone (facing down) positions. The registration of these two scans is desirable so that the user can clarify situations or confirm polyp findings at a l...
 
Dense non-rigid surface registration using high-order graph matching
Found in: Computer Vision and Pattern Recognition, IEEE Computer Society Conference on
By Yun Zeng, Chaohui Wang, Yang Wang, Xianfeng Gu, Dimitris Samaras, Nikos Paragios
Issue Date:June 2010
pp. 382-389
In this paper, we propose a high-order graph matching formulation to address non-rigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the high-order terms model the intrinsic embe...
 
Compression of surface registrations using Beltrami coefficients
Found in: Computer Vision and Pattern Recognition, IEEE Computer Society Conference on
By Lok Ming Lui, Tsz Wai Wong, Paul Thompson, Tony Chan, Xianfeng Gu, Shing-Tung Yau
Issue Date:June 2010
pp. 2839-2846
Surface registration is widely used in machine vision and medical imaging, where 1-1 correspondences between surfaces are computed to study their variations. Surface maps are usually stored as the 3D coordinates each vertex is mapped to, which often requir...
 
Direct-Product Volumetric Parameterization of Handlebodies via Harmonic Fields
Found in: Shape Modeling and Applications, International Conference on
By Jiazhi Xia, Ying He, Xiaotian Yin, Shuchu Han, Xianfeng Gu
Issue Date:June 2010
pp. 3-12
Volumetric parameterization plays an important role for geometric modeling. Due to the complicated topological nature of volumes, it is much more challenging than the surface case. This work focuses on the parameterization of volumes with a boundary surfac...
 
Intrinsic Geometric Scale Space by Shape Diffusion
Found in: IEEE Transactions on Visualization and Computer Graphics
By Guangyu Zou, Jing Hua, Zhaoqiang Lai, Xianfeng Gu, Ming Dong
Issue Date:November 2009
pp. 1193-1200
This paper formalizes a novel, intrinsic geometric scale space (IGSS) of 3D surface shapes. The intrinsic geometry of a surface is diffused by means of the Ricci flow for the generation of a geometric scale space. We rigorously prove that this multiscale s...
 
Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology
Found in: Computer Vision and Pattern Recognition, IEEE Computer Society Conference on
By Yalin Wang, Xianfeng Gu, T.F. Chan, P.M. Thompson
Issue Date:June 2009
pp. 202-209
All surfaces can be classified by the conformal equivalence relation. Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used...
 
Metric-Driven RoSy Field Design and Remeshing
Found in: IEEE Transactions on Visualization and Computer Graphics
By Yu-Kun Lai, Miao Jin, Xuexiang Xie, Ying He, Jonathan Palacios, Eugene Zhang, Shi-Min Hu, Xianfeng Gu
Issue Date:January 2010
pp. 95-108
Designing rotational symmetry fields on surfaces is an important task for a wide range of graphics applications. This work introduces a rigorous and practical approach for automatic N-RoSy field design on arbitrary surfaces with user-defined field topologi...
 
Surface Mapping Using Consistent Pants Decomposition
Found in: IEEE Transactions on Visualization and Computer Graphics
By Xin Li, Xianfeng Gu, Hong Qin
Issue Date:July 2009
pp. 558-571
Surface mapping is fundamental to shape computing and various downstream applications. This paper develops a pants decomposition framework for computing maps between surfaces with arbitrary topologies. The framework first conducts pants decomposition on bo...
 
Geodesic Distance-weighted Shape Vector Image Diffusion
Found in: IEEE Transactions on Visualization and Computer Graphics
By Jing Hua, Zhaoqiang Lai, Ming Dong, Xianfeng Gu, Hong Qin
Issue Date:November 2008
pp. 1643-1650
This paper presents a novel and efficient surface matching and visualization framework through the geodesic distance-weighted shape vector image diffusion. Based on conformal geometry, our approach can uniquely map a 3D surface to a canonical rectangular d...
 
Computing Teichm├╝ller Shape Space
Found in: IEEE Transactions on Visualization and Computer Graphics
By Miao Jin, Wei Zeng, Feng Luo, Xianfeng Gu
Issue Date:May 2009
pp. 504-517
Shape indexing, classification, and retrieval are fundamental problems in computer graphics. This work introduces a novel method for surface indexing and classification based on Teichmuller theory. The Teichmuller space for surfaces with the same topology ...
 
3D face matching and registration based on hyperbolic Ricci flow
Found in: Computer Vision and Pattern Recognition Workshop
By Wei Zeng, Xiaotian Yin, Yun Zeng, Yukun Lai, Xianfeng Gu, Dimitris Samaras
Issue Date:June 2008
pp. 1-8
3D surface matching is fundamental for shape analysis. As a powerful method in geometric analysis, Ricci flow can flexibly design metrics by prescribed target curvature. In this paper we describe a novel approach for matching surfaces with complicated topo...
 
Optimal Surface Parameterization Using Inverse Curvature Map
Found in: IEEE Transactions on Visualization and Computer Graphics
By Yong-Liang Yang, Junho Kim, Feng Luo, Shi-Min Hu, Xianfeng Gu
Issue Date:September 2008
pp. 1054-1066
Mesh parameterization is a fundamental technique in computer graphics. Our paper focuses on solving the problem of finding the best discrete conformal mapping that also minimizes area distortion. Firstly, we deduce an exact analytical differential formula ...
 
Globally Optimal Surface Mapping for Surfaces with Arbitrary Topology
Found in: IEEE Transactions on Visualization and Computer Graphics
By Xin Li, Yunfan Bao, Xiaohu Guo, Miao Jin, Xianfeng Gu, Hong Qin
Issue Date:July 2008
pp. 805-819
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 modeling and data visualization. Its vast variety of applications inc...
 
Ricci Flow for 3D Shape Analysis
Found in: Computer Vision, IEEE International Conference on
By Xianfeng Gu, Sen Wang, Junho Kim, Yun Zeng, Yang Wang, Hong Qin, Dimitris Samaras
Issue Date:October 2007
pp. 1-8
Ricci flow is a powerful curvature flow method in geometric analysis. This work is the first application of surface Ricci flow in computer vision. We show that previous methods based on conformal geometries, such as harmonic maps and least-square conformal...
 
An Effective Illustrative Visualization Framework Based on Photic Extremum Lines (PELs)
Found in: IEEE Transactions on Visualization and Computer Graphics
By Xuexiang Xie, Ying He, Feng Tian, Hock-Soon Seah, Xianfeng Gu, Hong Qin
Issue Date:November 2007
pp. 1328-1335
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 solely determined by local geometry properties (e.g., normals and cur...
 
Curves-on-Surface: A General Shape Comparison Framework
Found in: Shape Modeling and Applications, International Conference on
By Xin Li, Ying He, Xianfeng Gu, Hong Qin
Issue Date:June 2006
pp. 38
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. The signature describes not only the shape of the curve , ...
 
3D Surface Matching and Recognition Using Conformal Geometry
Found in: Computer Vision and Pattern Recognition, IEEE Computer Society Conference on
By Sen Wang, Yang Wang, Miao Jin, Xianfeng Gu, Dimitris Samaras
Issue Date:June 2006
pp. 2453-2460
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, occlusion and clutter is a challenging problem. In this paper, ...
 
Surface Parameterization Using Riemann Surface Structure
Found in: Computer Vision, IEEE International Conference on
By Yalin Wang, Xianfeng Gu, Kiralee M. Hayashi, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
Issue Date:October 2005
pp. 1061-1066
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 sphere, we instead use the fact that all orientable surfaces a...
 
Topology-driven Surface Mappings with Robust Feature Alignment
Found in: Visualization Conference, IEEE
By Christopher Carner, Miao Jin, Xianfeng Gu, Hong Qin
Issue Date:October 2005
pp. 69
Topological concepts and techniques have been broadly applied in computer graphics and geometric modeling. However, the homotopy type of a mapping between two surfaces has not been addressed before. In this paper, we present a novel solution to the problem...
 
High Resolution Tracking of Non-Rigid 3D Motion of Densely Sampled Data Using Harmonic Maps
Found in: Computer Vision, IEEE International Conference on
By Yang Wang, Mohit Gupta, Song Zhang, Sen Wang, Xianfeng Gu, Dimitris Samaras, Peisen Huang
Issue Date:October 2005
pp. 388-395
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 phase-shifting structured light ranging technique. To use su...
 
Rational Spherical Splines for Genus Zero Shape Modeling
Found in: Shape Modeling and Applications, International Conference on
By Ying He, Xianfeng Gu, Hong Qin
Issue Date:June 2005
pp. 82-91
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 data into a group of charts, mapping each chart to a plan...
 
Optimal Global Conformal Surface Parameterization
Found in: Visualization Conference, IEEE
By Miao Jin, Yalin Wang, Shing-Tung Yau, Xianfeng Gu
Issue Date:October 2004
pp. 267-274
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, such as heat diffusion and electro-magnetic fields on the su...
 
Surface Classification Using Conformal Structures
Found in: Computer Vision, IEEE International Conference on
By Xianfeng Gu, Shing-Tung Yau
Issue Date:October 2003
pp. 701
3D surface classification is a fundamental problem in computer vision and computational geometry. Surfaces can be classified by different transformation groups. Traditional classification methods mainly use topological transformation groups and Euclidean t...
 
Shape Analysis of Planar Multiply-Connected Objects Using Conformal Welding
Found in: IEEE Transactions on Pattern Analysis and Machine Intelligence
By Lok Ming Lui,Wei Zeng,Shing-Tung Yau,Xianfeng Gu
Issue Date:July 2014
pp. 1-1
Shape analysis is a central problem in the field of computer vision. In 2D shape analysis, classification and recognition of objects from their observed silhouettes are extremely crucial but difficult. It usually involves an efficient representation of 2D ...
 
Colon Flattening Using Heat Diffusion Riemannian Metric
Found in: IEEE Transactions on Visualization and Computer Graphics
By Krishna Chaitanya Gurijala, Rui Shi, Wei Zeng, Xianfeng Gu,Arie Kaufman
Issue Date:December 2013
pp. 2848-2857
We propose a new colon flattening algorithm that is efficient, shape-preserving, and robust to topological noise. Unlike previous approaches, which require a mandatory topological denoising to remove fake handles, our algorithm directly flattens the colon ...
 
Area Preserving Brain Mapping
Found in: 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
By Zhengyu Su,Wei Zeng,Rui Shi,Yalin Wang,Jian Sun,Xianfeng Gu
Issue Date:June 2013
pp. 2235-2242
Brain mapping transforms the brain cortical surface to canonical planar domains, which plays a fundamental role in morphological study. Most existing brain mapping methods are based on angle preserving maps, which may introduce large area distortions. This...
 
Hyperbolic Harmonic Mapping for Constrained Brain Surface Registration
Found in: 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
By Rui Shi,Wei Zeng,Zhengyu Su,Hanna Damasio,Zhonglin Lu,Yalin Wang,Shing-Tung Yau,Xianfeng Gu
Issue Date:June 2013
pp. 2531-2538
Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applicat...
 
Meshless thin-shell simulation based on global conformal parameterization
Found in: IEEE Transactions on Visualization and Computer Graphics
By Xiaohu Guo, Xin Li, Yunfan Bao, Xianfeng Gu, Hong Qin
Issue Date:May 2006
pp. 375-385
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 dynamics. The point-based global parameterization is founded upon the rigo...
 
Surface- and volume-based techniques for shape modeling and analysis
Found in: SIGGRAPH Asia 2013 Courses (SA '13)
By Giuseppe Patane, Xin Shane Li, David Xianfeng Gu
Issue Date:November 2013
pp. 1-65
Extending a shape-driven map to the interior of the input shape and to the surrounding volume is a difficult problem since it typically relies on the integration of shape-based and volumetric information, together with smoothness conditions, interpolating ...
     
C∞ smooth freeform surfaces over hyperbolic domains
Found in: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling (SPM '09)
By Hong Qin, Jiazhi Xia, Wei Zeng, Xianfeng Gu, Ying He
Issue Date:October 2009
pp. 367-372
Constructing smooth freeform surfaces of arbitrary topology with higher order continuity is one of the most fundamental problems in shape and solid modeling. This paper articulates a novel method to construct C∞ smooth surfaces with negative Euler nu...
     
Generalized Koebe's method for conformal mapping multiply connected domains
Found in: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling (SPM '09)
By Feng Luo, Min Zhang, Wei Zeng, Xianfeng Gu, Xiaotian Yin
Issue Date:October 2009
pp. 89-100
Surface parameterization refers to the process of mapping the surface to canonical planar domains, which plays crucial roles in texture mapping and shape analysis purposes. Most existing techniques focus on simply connected surfaces. It is a challenging pr...
     
User-controllable polycube map for manifold spline construction
Found in: Proceedings of the 2008 ACM symposium on Solid and physical modeling (SPM '08)
By Hong Qin, Hongyu Wang, Miao Jin, Xianfeng Gu, Ying He
Issue Date:June 2008
pp. 13-14
Polycube T-spline has been formulated elegantly that can unify T-splines and manifold splines to define a new class of shape representations for surfaces of arbitrary topology by using polycube map as its parametric domain. In essense, The data fitting qua...
     
Surface matching using consistent pants decomposition
Found in: Proceedings of the 2008 ACM symposium on Solid and physical modeling (SPM '08)
By Hong Qin, Xianfeng Gu, Xin Li
Issue Date:June 2008
pp. 13-14
Surface matching is fundamental to shape computing and various downstream applications. This paper develops a powerful pants decomposition framework for computing maps between surfaces with arbitrary topologies. We first conduct pants decomposition on both...
     
Geometric modeling using focal surfaces
Found in: ACM SIGGRAPH 2007 sketches on XX (SIGGRAPH '07)
By Jingyi Yu, Leonard McMillan, Steve Gortler, Xianfeng Gu, Xiaotian Yin
Issue Date:August 2007
pp. 70-es
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 focal surfaces. These focal surfaces are swept by the lo...
     
Computing geodesic spectra of surfaces
Found in: Proceedings of the 2007 ACM symposium on Solid and physical modeling (SPM '07)
By Feng Luo, Miao Jin, Shing-Tung Yau, Xianfeng Gu
Issue Date:June 2007
pp. 387-393
Surface classification is one of the most fundamental problems in geometric modeling. Surfaces can be classified according to their conformal structures. In general, each topological equivalent class has infinite conformally equivalent classes. This paper ...
     
Polycube splines
Found in: Proceedings of the 2007 ACM symposium on Solid and physical modeling (SPM '07)
By Hong Qin, Hongyu Wang, Xianfeng Gu, Xin Li, Ying He
Issue Date:June 2007
pp. 241-251
This paper proposes a new concept of polycube splines and develops novel modeling techniques for using the polycube splines in solid modeling and shape computing. Polycube splines are essentially a novel variant of manifold splines which are built upon the...
     
Harmonic volumetric mapping for solid modeling applications
Found in: Proceedings of the 2007 ACM symposium on Solid and physical modeling (SPM '07)
By Hong Qin, Hongyu Wang, Xianfeng Gu, Xiaohu Guo, Xin Li, Ying He
Issue Date:June 2007
pp. 109-120
Harmonic volumetric mapping for two solid objects establishes a one-to-one smooth correspondence between them. It finds its applications in shape registration and analysis, shape retrieval, information reuse, and material/texture transplant. In sharp contr...
     
Manifold splines with single extraordinary point
Found in: Proceedings of the 2007 ACM symposium on Solid and physical modeling (SPM '07)
By Feng Luo, Hong Qin, Miao Jin, Shing-Tung Yau, Xianfeng Gu, Ying He
Issue Date:June 2007
pp. 61-72
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 central idea and new computational paradigm of manifold spli...
     
Holoimages
Found in: Proceedings of the 2006 ACM symposium on Solid and physical modeling (SPM '06)
By Liangjun Zhang, Peisen Huang, Ralph Martin, Shing-Tung Yau, Song Zhang, Xianfeng Gu
Issue Date:June 2006
pp. 129-138
We introduce a novel geometric representation called the holoimage, which encodes both shading and geometry information within the same image, based on the principles of wave optics. 'Image' referes to the representation and records the amplitude of the li...
     
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