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111
Dual Contouring of Hermite Data
, 2002
"... This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. We extend this contou ..."
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Cited by 261 (17 self)
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This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. We extend this contouring method to the case of multisigned functions and demonstrate how to model textured contours using multisigned functions. Using a new, numerically stable representation for quadratic error functions, we develop an octreebased method for simplifying these contours and their textured regions. We next extend our contouring method to these simplified octrees. This new method imposes no constraints on the octree (such as being a restricted octree) and requires no "crack patching". We conclude with a simple test for preserving the topology of both the contour and its textured regions during simplification.
S.: Geometric surface smoothing via anisotropic diffusion of normals
 Visualization Conference, IEEE (2002
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 106 (14 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Removing excess topology from isosurfaces
 ACM Trans. Graph
, 2004
"... Many highresolution 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 studie ..."
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Cited by 85 (1 self)
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Many highresolution 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 paper we present an efficient method for removing handles in an isosurface. Our algorithm makes an axisaligned sweep through the volume to locate handles, compute their sizes, and selectively remove them. The algorithm is designed for outofcore execution. It finds the handles by incrementally constructing and analyzing a surface Reeb graph. The size of a handle is measured by a short surface loop that breaks it. 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 benefit for subsequent surface processing.
Topology correction in brain cortex segmentation using a multiscale, graphbased algorithm
 IEEE Trans. Med. Imaging
, 2002
"... Abstract — Reconstructing an accurate and topologically correct representation of the cortical surface of the brain is an important objective in various neuroscience applications. Most cortical surface reconstruction methods either ignore topology or correct it using manual editing or methods that l ..."
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Cited by 70 (7 self)
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Abstract — Reconstructing an accurate and topologically correct representation of the cortical surface of the brain is an important objective in various neuroscience applications. Most cortical surface reconstruction methods either ignore topology or correct it using manual editing or methods that lead to inaccurate reconstructions. Shattuck and Leahy recently reported a fullyautomatic method that yields a topologically correct representation with little distortion of the underlying segmentation. We provide an alternate approach that has several advantages over their approach, including the use of arbitrary digital connectivities, a flexible morphologybased multiscale approach, and the option of foregroundonly or backgroundonly correction. A detailed analysis of the method's performance on 15 magnetic resonance brain images is provided.
Optimally cutting a surface into a disk
 Discrete & Computational Geometry
, 2002
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Geometrically Accurate TopologyCorrection of Cortical Surfaces Using Nonseparating Loops
, 2007
"... In this paper, we focus on the retrospective topology correction of surfaces. We propose a technique to accurately correct the spherical topology of cortical surfaces. Specifically, we construct a mapping from the original surface onto the sphere to detect topological defects as minimal nonhomeomor ..."
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Cited by 48 (3 self)
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In this paper, we focus on the retrospective topology correction of surfaces. We propose a technique to accurately correct the spherical topology of cortical surfaces. Specifically, we construct a mapping from the original surface onto the sphere to detect topological defects as minimal nonhomeomorphic regions. The topology of each defect is then corrected by opening and sealing the surface along a set of nonseparating loops that are selected in a Bayesian framework. The proposed method is a wholly selfcontained topology correction algorithm, which determines geometrically accurate, topologically correct solutions based on the magnetic resonance imaging (MRI) intensity profile and the expected local curvature. Applied to real data, our method provides topological corrections similar to those made by a trained operator.
Robust Reconstruction of Watertight 3D Models from Nonuniformly Sampled Point Clouds Without Normal Information
, 2006
"... We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero levelset of a signed distance function, our method uses an unsigned distance function and hence does not requi ..."
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Cited by 46 (0 self)
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We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero levelset of a signed distance function, our method uses an unsigned distance function and hence does not require any information about the local surface orientation. Our algorithm estimates local surface confidence values within a dilated crust around the input samples. The surface which maximizes the global confidence is then extracted by computing the minimum cut of a weighted spatial graph structure. We present an algorithm, which efficiently converts this cut into a closed, manifold triangle mesh with a minimal number of vertices. The use of an unsigned distance function avoids the topological noise artifacts caused by misalignment of 3D scans, which are common to most volumetric reconstruction techniques. Due to a hierarchical approach our method efficiently produces solid models of low genus even for noisy and highly irregular data containing large holes, without loosing fine details in densely sampled regions. We show several examples for different application settings such as model generation from raw laserscanned data, imagebased 3D reconstruction, and mesh repair.
Topologybased Simplification for Feature Extraction from 3D Scalar Fields
"... This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. The MorseSmale complex provides a segmentation of the domain into monotonic regions having uniform gradient flow behavior. We present a combinatorial algorithm that simplifies the Morse ..."
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Cited by 45 (21 self)
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This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. The MorseSmale complex provides a segmentation of the domain into monotonic regions having uniform gradient flow behavior. We present a combinatorial algorithm that simplifies the MorseSmale complex by repeated application of two atomic operations that removes pairs of critical points. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting features. We present a visualization of the simplified topology.
Isosurface Reconstruction with Topology Control
, 2002
"... Extracting isosurfaces from volumetric datasets is an essential step for indirect volume rendering algorithms. For physically measured data like it is used, e.g. in medical imaging applications one often introduces topological errors such as small handles that stem from measurement inaccuracy and ca ..."
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Cited by 42 (2 self)
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Extracting isosurfaces from volumetric datasets is an essential step for indirect volume rendering algorithms. For physically measured data like it is used, e.g. in medical imaging applications one often introduces topological errors such as small handles that stem from measurement inaccuracy and cavities that are generated by tight folds of an organ. During isosurface extraction these measurement errors result in a surface whose genus is much higher than that of the actual surface. In many cases however, the topological type of the object under consideration is known beforehand, e.g., the cortex of a human brain is always homeomorphic to a sphere. By using topology preserving morphological operators we can exploit this knowledge to gradually dilate an initial set of voxels with correct topology until it fits the target isosurface. This approach avoids the formation of handles and cavities and guarantees a topologically correct reconstruction of the object's surface.