Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
The homotopy model: a generalized model for smooth surface generation from cross sectional data
The Visual Computer: International Journal of Computer Graphics - Special issue on computer graphics international '89(CGI'89)
Optimal surface reconstruction from planar contours
Communications of the ACM
An interactive computer graphics approach to surface representation
Communications of the ACM
Conversion of complex contour line definitions into polygonal element mosaics
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
A feature-based approach for smooth surfaces
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Contour trees and small seed sets for isosurface traversal
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Construction of contour trees in 3D in O(n log n) steps
Proceedings of the fourteenth annual symposium on Computational geometry
Level set diagrams of polyhedral objects
Proceedings of the fifth ACM symposium on Solid modeling and applications
Computing Morse functions on triangulated manifolds
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computing contour trees in all dimensions
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
Topology recognition of 3D closed freeform objects based on topological graphs
Proceedings of the sixth ACM symposium on Solid modeling and applications
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Shape abstraction using computational topology techniques
From geometric modeling to shape modeling
Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Research Issues in Scientific Visualization
IEEE Computer Graphics and Applications
Surface Reconstruction by Multiaxial Triangulation
IEEE Computer Graphics and Applications
Volume Data Mining Using 3D Field Topology Analysis
IEEE Computer Graphics and Applications
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Extended Reeb Graphs for Surface Understanding and Description
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Topological Quadrangulations of Closed Triangulated Surfaces Using the Reeb Graph
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Loops in reeb graphs of 2-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Graph based topological analysis of tessellated surfaces
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
A Dual Visualizer Method for Interactive Topology
MMM '98 Proceedings of the 1998 Conference on MultiMedia Modeling
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Topological quadrangulations of closed triangulated surfaces using the Reeb graph
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Optimal discrete Morse functions for 2-manifolds
Computational Geometry: Theory and Applications
Applications of Forman's Discrete Morse Theory to Topology Visualization and Mesh Compression
IEEE Transactions on Visualization and Computer Graphics
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
On detecting all saddle points in 2D images
Pattern Recognition Letters
Simple and optimal output-sensitive construction of contour trees using monotone paths
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
A robust technique for surface reconstruction from orthogonal slices
Machine Graphics & Vision International Journal
Simultaneous shape decomposition and skeletonization
Proceedings of the 2006 ACM symposium on Solid and physical modeling
ACM SIGGRAPH 2006 Papers
Topological shape signature for 3D object modelling
MS'06 Proceedings of the 17th IASTED international conference on Modelling and simulation
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Harmonic skeleton for realistic character animation
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Topological Landscapes: A Terrain Metaphor for Scientific Data
IEEE Transactions on Visualization and Computer Graphics
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Volumetric parameterization and trivariate b-spline fitting using harmonic functions
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
An Intrinsic Framework for Analysis of Facial Surfaces
International Journal of Computer Vision
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree
Computational Geometry: Theory and Applications
Simple and optimal output-sensitive construction of contour trees using monotone paths
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Computer Graphics in Italy: Computational methods for understanding 3D shapes
Computers and Graphics
CGIM '07 Proceedings of the Ninth IASTED International Conference on Computer Graphics and Imaging
CW complexes: topological mainframe for numerical representations of objects
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Retrieving articulated 3D objects using normalized distance function
AMDO'10 Proceedings of the 6th international conference on Articulated motion and deformable objects
Matching 2D and 3D articulated shapes using the eccentricity transform
Computer Vision and Image Understanding
Skeleton path based approach for nonrigid 3D shape analysis and retrieval
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Graph-based representations of point clouds
Graphical Models
Video-based descriptors for object recognition
Image and Vision Computing
Adjustment for discrepancies between ALS data strips using a contour tree algorithm
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
Retrieving articulated 3-d models using medial surfaces and their graph spectra
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Fitting a surface to one of its sectional planar curves using adaptive trees in spaces of curves
Proceedings of the 7th international conference on Curves and Surfaces
Stability of Reeb Graphs of Closed Curves
Electronic Notes in Theoretical Computer Science (ENTCS)
Image and Vision Computing
Spaces and manifolds of shapes in computer vision: An overview
Image and Vision Computing
The hitchhiker's guide to the galaxy of mathematical tools for shape analysis
ACM SIGGRAPH 2012 Courses
ConTopo: non-rigid 3D object retrieval using topological information guided by conformal factors
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
Autonomic and trusted computing for ubiquitous intelligence
UIC'07 Proceedings of the 4th international conference on Ubiquitous Intelligence and Computing
Simplified reeb graph as effective shape descriptor for the striatum
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
Extracting skeletal curves from 3D scattered data
The Visual Computer: International Journal of Computer Graphics
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Coding system requirements are briefly discussed. Classical Morse theory, which was primarily motivated by the calculus of variations, is reviewed. The limits of the theory are examined, and an extension that enables 3-D surfaces to be accurately reconstructed from cross sections is presented. The resulting coding works interactively with a range of surface reconstruction systems. The prototype coding system is applied to representing the hierarchical structure of contours.