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29
Decimation of triangle meshes
 Computer Graphics (SIGGRAPH '92 Proceedings
, 1992
"... The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software. ..."
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Cited by 640 (2 self)
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The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software.
Survey of Polygonal Surface Simplification Algorithms
, 1997
"... This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons ..."
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Cited by 227 (3 self)
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This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons
A Comparison of Mesh Simplification Algorithms
 Computers & Graphics
, 1997
"... In many applications the need for an accurate simplification of surface meshes is becoming more and more urgent. This need is not only due to rendering speed reasons, but also to allow fast transmission of 3D models in networkbased applications. Many different approaches and algorithms for mesh sim ..."
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Cited by 167 (8 self)
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In many applications the need for an accurate simplification of surface meshes is becoming more and more urgent. This need is not only due to rendering speed reasons, but also to allow fast transmission of 3D models in networkbased applications. Many different approaches and algorithms for mesh simplification have been proposed in the last few years. We present a survey and a characterization of the fundamental methods. Moreover, the results of an empirical comparison of the simplification codes available in the public domain are discussed. Five implementations, chosen to give a wide spectrum of different topologypreserving methods, were run on a set of sample surfaces. We compared empirical computational complexities and the approximation accuracy of the resulting output meshes. 1 Introduction Triangles are the most popular drawing primitive. They are managed by all graphics libraries and hardware subsystems, and triangular meshes are thus very common in computer graphics. Very c...
Multiresolution Decimation based on Global Error
 The Visual Computer
, 1997
"... Due to the surface meshes produced at increasing complexity in many applications, interest in efficient simplification algorithms and multiresolution representation is very high. An enhanced simplification approach together with a general multiresolution data scheme are presented here. JADE, a new s ..."
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Cited by 103 (14 self)
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Due to the surface meshes produced at increasing complexity in many applications, interest in efficient simplification algorithms and multiresolution representation is very high. An enhanced simplification approach together with a general multiresolution data scheme are presented here. JADE, a new simplification solution based on the Mesh Decimation approach has been designed to provide both increased approximation precision, based on global error management, and multiresolution output. Moreover, we show that with a small increase in memory, which is needed to store the multiresolution data representation, we are able to extract any level of detail representation from the simplification results in an extremely efficient way. Results are reported on empirical time complexity, approximation quality, and simplification power. Keywords: surface modeling, mesh simplification, bounded approximation error, multiresolution. Address to which proofs should be sent: R. SCOPIGNO, CNUCE  Consigl...
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 85 (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...
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 69 (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.
Variable Resolution Triangulations
, 1998
"... A comprehensive study of multiresolution decompositions of planar domains into triangles is given. A general model is introduced, called a MultiTriangulation (MT), which is based on a collection of fragments of triangulations arranged into a directed acyclic graph. Different decompositions of a dom ..."
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Cited by 38 (1 self)
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A comprehensive study of multiresolution decompositions of planar domains into triangles is given. A general model is introduced, called a MultiTriangulation (MT), which is based on a collection of fragments of triangulations arranged into a directed acyclic graph. Different decompositions of a domain can be obtained by combining different fragments of the model. Theoretical results on the expressive power of the MT are given. An efficient algorithm is proposed that can extract a triangulation from the MT, whose level of detail is variable over the domain according to a given threshold function. The algorithm works in linear time, and the extracted representation has minimum size among all possible triangulations that can be built from triangles in the MT, and that satisfy the given level of detail. Major applications of these results are in realtime rendering of complex surfaces, such as topographic surfaces in flight simulation. Keywords: multiresolution decomposition, triangulatio...
MagicSphere: an insight tool for 3D data visualization
, 1994
"... How to render very complex datasets, and yet maintain interactive response times, is a hot topic in computer graphics. The MagicSphere idea originated as a solution to this problem, but its potential goes much further than this original scope. In fact, it has been designed as a very generical 3D wid ..."
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Cited by 30 (3 self)
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How to render very complex datasets, and yet maintain interactive response times, is a hot topic in computer graphics. The MagicSphere idea originated as a solution to this problem, but its potential goes much further than this original scope. In fact, it has been designed as a very generical 3D widget: it defines a spherical volume of interest in the dataset modeling space. Then, several filters can be associated with the MagicSphere, which apply different visualization modalities to the data contained in the volume of interest. The visualization of multiresolution datasets is selected here as a case study and an ad hoc filter has been designed, the MultiRes filter. Some results of a prototipal implementation are presented and discussed. 1 Introduction We introduce a new tool for the visual analysis of 3D datasets or geometries, which allows interactive focusing on regions of interest, and the modification of the visualization modalities used to render the data contained in those ...
Simplification, LOD and Multiresolution Principles and Applications
, 1997
"... These tutorial notes provide an introduction, review, and discussion of the stateoftheart on simplification methods, Level Of Detail, and multiresolution models for surface meshes, and of their applications. The problem of approximating a surface with a triangular mesh is formally introduced, and ..."
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Cited by 25 (0 self)
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These tutorial notes provide an introduction, review, and discussion of the stateoftheart on simplification methods, Level Of Detail, and multiresolution models for surface meshes, and of their applications. The problem of approximating a surface with a triangular mesh is formally introduced, and major simplification techniques are classified, reviewed, and compared. A general framework is introduced next, which encompasses all multiresolution surface models based on decomposition, and major multiresolution meshes are classified, reviewed, and compared in the context of such a framework. Applications of simplification methods, LOD, and multiresolution to computer graphics, virtual reality, geographical information systems, flight simulation, and volume visualization are also reviewed.
Deformable models with application to human cerebral cortex reconstruction in magnetic resonance images
, 2000
"... Constructing a mathematical representation of an object boundary (boundary mapping) from images is an important problem that is of importance to several active research areas such as image analysis, computer vision, and medical imaging. The focus of this dissertation is to investigate deformable mo ..."
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Cited by 19 (2 self)
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Constructing a mathematical representation of an object boundary (boundary mapping) from images is an important problem that is of importance to several active research areas such as image analysis, computer vision, and medical imaging. The focus of this dissertation is to investigate deformable models, a boundary mapping technique that incorporates both image information and prior knowledge about the boundary geometry to extract a meaningful boundary description. A key problem with methods reported in the literature is that they have diÆculties in reliably mapping boundaries when the models are not initialized near target boundaries or are applied to reconstruct boundaries with concavities. In this research, we make three main contributions to the area of boundary mapping. First, we developed a method called the gradient vector
ow deformable model that is robust to both model initialization and boundary concavities. Second, we developed a generalization of the rst method that allows for improved performance in converging to narrow boundary indentations and greater accuracy in localizing boundaries. Third, we developed a method for reconstructing the central layer of the human cerebral cortex from magnetic resonance images that uses our proposed deformable model as a core component. Our methods are validated on both simulated images and real magnetic resonance images. This thesis is prepared under the direction of Dr. Jerry L. Prince. ii