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99
An evaluation of reconstruction filters for volume rendering
 Proceedings of IEEE Visualization
, 1994
"... To render images from a threedimensional array of sample values, it is necessary to interpolate between the samples. This paper is concerned with interpolation methods that are equivalent to convolving the samples with a reconstruction filter; this covers all commonly used schemes, including tril ..."
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Cited by 169 (1 self)
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To render images from a threedimensional array of sample values, it is necessary to interpolate between the samples. This paper is concerned with interpolation methods that are equivalent to convolving the samples with a reconstruction filter; this covers all commonly used schemes, including trilinear and cubic interpolation. We first outline the formal basis of interpolation in threedimensional signal processing theory. We then propose numerical metrics that can be used to measure filter characteristics that are relevant to the appearance of images generated using that filter. We apply those metrics to several previously used filters and relate the results to isosurface images of the interpolations. We show that the choice of interpolation scheme can have a dramatic effect on image quality, and we discuss the cost/benefit tradeoff inherent in choosing a filter. 1
MorseSmale Complexes for Piecewise Linear 3Manifolds
, 2003
"... We define the MorseSmale complex of a Morse function over a 3manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatori ..."
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Cited by 133 (28 self)
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We define the MorseSmale complex of a Morse function over a 3manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatorial algorithm for constructing such complexes for piecewise linear data.
Approaches to uncertainty visualization
 The Visual Computer
, 1997
"... Visualized data often have dubious origins and quality. Di erent forms of uncertainty and errors are also introduced as the data are derived, transformed, interpolated, and nally rendered. In the absence of integrated presentation of data and uncertainty, the analysis of the visualization is incompl ..."
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Cited by 132 (7 self)
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Visualized data often have dubious origins and quality. Di erent forms of uncertainty and errors are also introduced as the data are derived, transformed, interpolated, and nally rendered. In the absence of integrated presentation of data and uncertainty, the analysis of the visualization is incomplete at best and often leads to inaccurate or incorrect conclusions. This paper surveys techniques for presenting data together with uncertainty. These uncertainty visualization techniques present data in such a manner that users are made aware of the locations and degree of uncertainties in their data so as to make more informed analyses and decisions. The techniques include adding glyphs, adding geometry, modifying geometry, modifying attributes, animation, soni cation, and psychovisual approaches. We present our results in uncertainty visualization for environmental visualization, surface interpolation, global illumination with radiosity, ow visualization, and gure animation. We also present a classi cation of the possibilities in uncertainty visualization, and locate our contributions within this classi cation.
G.: Simplification and repair of polygonal models using volumetric techniques
 IEEE Transactions on Visualization and Computer Graphics
, 2003
"... Abstract—Two important tools for manipulating polygonal models are simplification and repair and we present voxelbased methods for performing both of these tasks. We describe a method for converting polygonal models to a volumetric representation in a way that handles models with holes, double wall ..."
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Cited by 124 (3 self)
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Abstract—Two important tools for manipulating polygonal models are simplification and repair and we present voxelbased methods for performing both of these tasks. We describe a method for converting polygonal models to a volumetric representation in a way that handles models with holes, double walls, and intersecting parts. This allows us to perform polygon model repair simply by converting a model to and from the volumetric domain. We also describe a new topologyaltering simplification method that is based on 3D morphological operators. Visually unimportant features such as tubes and holes may be eliminated from a model by the open and close morphological operators. Our simplification approach accepts polygonal models as input, scan converts these to create a volumetric description, performs topology modification, and then converts the results back to polygons. We then apply a topologypreserving polygon simplification technique to produce a final model. Our simplification method produces results that are everywhere manifold. Index Terms—Mesh simplification, mesh repair, volumetric models, morphological operators. æ 1
Simulating Facial Surgery Using Finite Element Models
, 1996
"... This paper describes a prototype system for surgical planning and prediction of human facial shape after craniofacial and maxillofacial surgery for patients with facial deformities. For this purpose it combines, unifies, and extends various methods from geometric modeling, finite element analysis, a ..."
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Cited by 102 (12 self)
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This paper describes a prototype system for surgical planning and prediction of human facial shape after craniofacial and maxillofacial surgery for patients with facial deformities. For this purpose it combines, unifies, and extends various methods from geometric modeling, finite element analysis, and image processing to render highly realistic 3D images of the post surgical situation. The basic concept of the system is to join advanced geometric modeling and animation systems such as Alias with a special purpose finite element model of the human face developed under AVS . In contrast to existing facial models we acquire facial surface and soft tissue data both from photogrammetric and CT scans of the individual. After initial data preprocessing, reconstruction, and registration, a finite element model of the facial surface and soft tissue is provided which is based on triangular finite elements. Stiffness parameters of the soft tissue are computed using segmentations of the underlying...
Discretized Marching Cubes
 Visualization '94 Proceedings
, 1994
"... Since the introduction of standard techniques for isosurface extraction from volumetric datasets, one of the hardest problems has been to reduce the number of triangles (or polygons) generated. This paper presents an algorithm that considerably reduces the number of polygons generated by a Marching ..."
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Cited by 86 (5 self)
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Since the introduction of standard techniques for isosurface extraction from volumetric datasets, one of the hardest problems has been to reduce the number of triangles (or polygons) generated. This paper presents an algorithm that considerably reduces the number of polygons generated by a Marching Cubeslike scheme without excessively increasing the overall computational complexity. The algorithm assumes discretization of the dataset space and replaces cell edge interpolation by midpoint selection. Under these assumptions, the extracted surfaces are composed of polygons lying within a finite number of incidences, thus allowing simple merging of the output facets into large coplanar polygons. An experimental evaluation of the proposed approach on datasets related to biomedical imaging and chemical modelling is reported. 1 Introduction The use of the Marching Cubes (MC) technique, originally proposed by W. Lorensen and H. Cline [7], is considered to be a standard approach to the proble...
Fast Multiresolution Surface Meshing
 IEEE Visualization
, 1995
"... We present a new method for adaptive surface meshing and triangulation which controls the local level–of–detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data s ..."
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Cited by 76 (3 self)
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We present a new method for adaptive surface meshing and triangulation which controls the local level–of–detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi–orthogonal tensor product wavelet transform (WT) and to analyze the resulting coefficients. In surface regions, where the partial energy of the resulting coefficients is low, the polygonal approximation of the surface can be performed with larger triangles without loosing too much fine grain details. However, since the localization of the WT is bound by the Heisenberg principle the meshing method has to be controlled by the detail signals rather than directly by the coefficients. The dyadic scaling of the WT stimulated us to build an hierarchical meshing algorithm which transforms the initially regular data grid into a quadtree representation by rejection of unimportant mesh vertices. The optimum triangulation of the resulting quadtree cells is carried out by selection from a look–up table. The tree grows recursively as controlled by detail signals which are computed from a modified inverse WT. In order to control the local level–of–detail, we introduce a new class of wavelet space filters acting as ”magnifying glasses ” on the data. 1.
Controlled Topology Simplification
 IEEE Transactions on Visualization and Computer Graphics
, 1996
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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.
Reconstruction of the human cerebral cortex from magnetic resonance images
 IEEE Trans. Med. Imag
, 1999
"... Abstract—Reconstructing the geometry of the human cerebral cortex from MR images is an important step in both brain mapping and surgical path planning applications. Difficulties with imaging noise, partial volume averaging, image intensity inhomogeneities, convoluted cortical structures, and the req ..."
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Cited by 68 (11 self)
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Abstract—Reconstructing the geometry of the human cerebral cortex from MR images is an important step in both brain mapping and surgical path planning applications. Difficulties with imaging noise, partial volume averaging, image intensity inhomogeneities, convoluted cortical structures, and the requirement to preserve anatomical topology make the development of accurate automated algorithms particularly challenging. In this paper we address each of these problems and describe a systematic method for obtaining a surface representation of the geometric central layer of the human cerebral cortex. Using fuzzy segmentation, an isosurface algorithm, and a deformable surface model, the method reconstructs the entire cortex with the correct topology, including deep convoluted sulci and gyri. The method is largely automated and its results are robust to imaging noise, partial volume averaging, and image intensity inhomogeneities. The performance of this method is demonstrated, both qualitatively and quantitatively, and the results of its application to six subjects and one simulated MR brain volume are presented. Index Terms—Cortical surface reconstruction, deformable surface models, fuzzy segmentation, isosurface, magnetic resonance imaging. I.