Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Hyperquadrics: smoothly deformable shapes with convex polyhedral bounds
Computer Vision, Graphics, and Image Processing
Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automatic extraction of deformable part models
International Journal of Computer Vision
Generalized B-spline surfaces of arbitrary topology
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Design and recovery of 2-D and 3-D shapes using rational Gaussian curves and surfaces
International Journal of Computer Vision
Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A hybrid hyperquadric model for 2-D and 3-D data fitting
Computer Vision and Image Understanding
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Volumetric segmentation of medical images by three-dimensional bubbles
Computer Vision and Image Understanding - Special issue on physics-based modeling and reasoning in computer vision
Triangular NURBS and their dynamic generalizations
Computer Aided Geometric Design
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A parametric deformable model to fit unstructured 3D data
Computer Vision and Image Understanding
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Progressive compression of arbitrary triangular meshes
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Directional 3D edge detection in anisotropic data: detector design and performance assessment
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
Multilocal creaseness based on the level-set extrinsic curvature
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
Scale-based fuzzy connected image segmentation: theory, algorithms, and validation
Computer Vision and Image Understanding - Special issue on analysis of volumetric image
Displaced subdivision surfaces
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Implicit surface visualization of reconstructed biological molecules
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
A computer-aided design system for revision of segmentation errors
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
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A method for approximating spherical topology digital shapes by rational Gaussian (RaG) surfaces is presented. Points in a shape are parametrized by approximating the shape with a triangular mesh, determining parameter coordinates at mesh vertices, and finding parameter coordinates at shape points from interpolation of parameter coordinates at mesh vertices. Knowing the locations and parameter coordinates of the shape points, the control points of a RaG surface are determined to approximate the shape with a required accuracy. The process starts from a small set of control points and gradually increases the control points until the error between the surface and the digital shape reduces to a required tolerance. Both triangulation and surface approximation proceed from coarse to fine. Therefore, the method is particularly suitable for multiresolution creation and transmission of digital shapes over the Internet. Application of the proposed method in editing of 3D shapes is demonstrated.