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Semi-regular mesh extraction from volumes
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Topology matching for fully automatic similarity estimation of 3D shapes
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Texture mapping progressive meshes
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Optimally cutting a surface into a disk
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Constructing a Reeb graph automatically from cross sections
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Computing contour trees in all dimensions
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Reliable Surface Reconstructiuon from Multiple Range Images
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Optimal System of Loops on an Orientable Surface
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Labeling the Brain Surface Using a Deformable Multiresolution Mesh
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Topologically defined iso-surfaces
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Simplification and Repair of Polygonal Models Using Volumetric Techniques
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Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
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Isosurface Reconstruction with Topology Control
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The Algorithm for Automatic Cutting of Three-Dimensional Polyhedrons of h-Genus.
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Re-Meshing Techniques for Topological Analysis
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Computing and comprehending topology: persistence and hierarchical morse complexes
Computing and comprehending topology: persistence and hierarchical morse complexes
Computational topology algorithms for discrete 2-manifolds
Computational topology algorithms for discrete 2-manifolds
Extraction of Topologically Simple Isosurfaces from Volume Datasets
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Variational shape approximation
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Feature-based surface parameterization and texture mapping
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Efficient representation and extraction of 2-manifold isosurfaces using kd-trees
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An integrating approach to meshing scattered point data
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Tightening: curvature-limiting morphological simplification
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Mason: morphological simplification
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A topology-preserving polygonal simplification using vertex clustering
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Efficient algorithms for computing Reeb graphs
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Many high-resolution surfaces are created through isosurface extraction from volumetric representations, obtained by 3D photography, CT, or MRI. Noise inherent in the acquisition process can lead to geometrical and topological errors. Reducing geometrical errors during reconstruction is well studied. However, isosurfaces often contain many topological errors in the form of tiny handles. These nearly invisible artifacts hinder subsequent operations like mesh simplification, remeshing, and parametrization. In this article we present a practical method for removing handles in an isosurface. Our algorithm makes an axis-aligned sweep through the volume to locate handles, compute their sizes, and selectively remove them. The algorithm is designed to facilitate out-of-core execution. It finds the handles by incrementally constructing and analyzing a Reeb graph. The size of a handle is measured by a short nonseparating cycle. Handles are removed robustly by modifying the volume rather than attempting "mesh surgery." Finally, the volumetric modifications are spatially localized to preserve geometrical detail. We demonstrate topology simplification on several complex models, and show its benefits for subsequent surface processing.