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64
Progressive Geometry Compression
, 2000
"... We propose a new progressive compression scheme for arbitrary topology, highly detailed and densely sampled meshes arising from geometry scanning. We observe that meshes consist of three distinct components: geometry, parameter, and connectivity information. The latter two do not contribute to the r ..."
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Cited by 244 (16 self)
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We propose a new progressive compression scheme for arbitrary topology, highly detailed and densely sampled meshes arising from geometry scanning. We observe that meshes consist of three distinct components: geometry, parameter, and connectivity information. The latter two do not contribute to the reduction of error in a compression setting. Using semiregular meshes, parameter and connectivity information can be virtually eliminated. Coupled with semiregular wavelet transforms, zerotree coding, and subdivision based reconstruction we see improvements in error by a factor four (12dB) compared to other progressive coding schemes. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  hierarchy and geometric transformations; G.1.2 [Numerical Analysis]: Approximation  approximation of surfaces and contours, wavelets and fractals; I.4.2 [Image Processing and Computer Vision]: Compression (Coding)  Approximate methods Additional K...
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 166 (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...
Representation and Visualization of Terrain Surfaces at Variable Resolution
, 1997
"... We present a new approach for managing the multiresolution representation of discrete topographic surfaces. A Triangulated Irregular Network (TIN) representing the surface is built from sampled data by iteratively refining an initial triangulation that covers the whole domain. The refinement process ..."
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Cited by 76 (11 self)
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We present a new approach for managing the multiresolution representation of discrete topographic surfaces. A Triangulated Irregular Network (TIN) representing the surface is built from sampled data by iteratively refining an initial triangulation that covers the whole domain. The refinement process generates triangulations of the domain corresponding to increasingly finer approximations of the surface. Such triangulations are embedded into a structure in a three dimensional space. The resulting representation scheme encodes all intermediate representations that were generated during refinement. We propose a data structure and traversal algorithms that are oriented to the efficient extraction of approximated terrain models with an arbitrary precision, either constant or variable over the domain. 1. Introduction The search for multiresolution representation schemes has recently become very popular. Major applications involve generic surfaces embedded in 3D space 16;8;27 , terrains i...
A Wavelet Approach to Foveating Images
 13th ACM Symposium on Computational Geometry
, 1997
"... Motivated by applications of foveated images in visualization, we introduce the foveation transform of an image. We study the basic properties of these transforms using the multiresolution framework of Mallat. We also consider practical methods of realizing such transforms. In particular, we introd ..."
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Cited by 39 (8 self)
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Motivated by applications of foveated images in visualization, we introduce the foveation transform of an image. We study the basic properties of these transforms using the multiresolution framework of Mallat. We also consider practical methods of realizing such transforms. In particular, we introduce a new method for foveating images based on wavelets. Preliminary experimental results are shown. 1 Introduction Conventional images have uniform resolution. Foveated images which have nonuniform resolution arise in biological vision. In figure 1(a) and (b) we show a uniform image and a foveated version of the same image. The process of going from (a) to (b) is called "foveating" the image (a). One of the most interesting forms of foveated images is based on the complex logarithm function. Such logmap images were studied by Rojer and Schwartz [19] and others. The complex logmap is a model consistent with empirical data on the mapping from primate retina to the visual cortex [21, 22]. T...
Extraction of Crackfree Isosurfaces from Adaptive Mesh Refinement Data
, 2000
"... Introduction Physical phenomena often vary substantially in scale. There can be large regions where a given physical quantity only varies slightly. At the same time, there can be small regions where the same quantity changes rapidly. Adaptive mesh refinement (AMR) ,see [1, 2, 3], is a technique use ..."
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Cited by 29 (12 self)
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Introduction Physical phenomena often vary substantially in scale. There can be large regions where a given physical quantity only varies slightly. At the same time, there can be small regions where the same quantity changes rapidly. Adaptive mesh refinement (AMR) ,see [1, 2, 3], is a technique used in computational fluid dynamics (CFD) to simulate phenomena characterized by drastically varying scales. By using a set of nested grids at different resolutions, AMR combines the topological simplicity of structured rectilinear grids permitting the efficient computation and storage of the result with the adaptivity to changes in spatial resolution of unstructured grids. The data sets we visualize result from the simulation of astrophysical phenomena by Bryan et al. [3] using the Berger and Colella [1] AMR algorithm. They consist of a hierarchy of grids of increasing resolutions. Each level consists of a number of axisaligned rectilinear grids with data samples associated with the cell cen
Multiresolution Mesh Representation: Models and Data Structures
 Tutorials on Multiresolution in Geometric Modelling
, 2002
"... Multiresolution meshes are a common basis for building representations of a geometric shape at dierent levels of detail. The use of the term multiresolution depends on the remark that the accuracy (or, level of detail) of a mesh in approximating a shape is related to the mesh resolution, i.e., to t ..."
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Cited by 28 (17 self)
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Multiresolution meshes are a common basis for building representations of a geometric shape at dierent levels of detail. The use of the term multiresolution depends on the remark that the accuracy (or, level of detail) of a mesh in approximating a shape is related to the mesh resolution, i.e., to the density (size and number) of its cells. A multiresolution mesh provides several alternative meshbased approximations of a spatial object (e.g., a surface describing the boundary of a solid object, or the graph of a scalar eld).
Quadtree for embedded surface visualization: Constraints and efficient data structures
 PROC. INT. CONF. IMAGE PROCESSING (ICIP
, 1999
"... The quadtree data structure is widely used in digital image processing and computer graphics for modeling spatial segmentation of images and surfaces. A quadtree is a tree in which each node has four descendants. Since most algorithms based on quadtrees require complex navigation between nodes, effi ..."
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Cited by 27 (5 self)
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The quadtree data structure is widely used in digital image processing and computer graphics for modeling spatial segmentation of images and surfaces. A quadtree is a tree in which each node has four descendants. Since most algorithms based on quadtrees require complex navigation between nodes, efficient traversal methods as well as efficient storage techniques are of great interest. In this paper, we first propose an efficient indexing scheme for a linear (pointerless) quadtree data structure. Such a quadtree is stored using a unidimensional array of nodes. Our indexing scheme has the property that the navigation between any pair of nodes can be computed in constant time. Moreover, the navigation across multiple quadtrees can be achieved at the same cost. We illustrate our results on applications in computer graphics. We first show how the problem of computing a socalled restricted quadtree can be solved at optimal cost, e.g with a computational complexity having the order of magnitude of the problem size. Then, we explain how this problem can be solved in the case of surfaces modeled using multiple quadtrees. Finally, we show how a tessellated sphere can be implemented and navigated using our data structure.
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.
Applications of computational geometry in Geographic Information Systems
 Handbook of Computational Geometry
, 1997
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Multiresolution Visualization and Compression Of Global . . .
 GEOINFORMATICA
, 1999
"... We present a multiresolution model for surfaces which is able to handle largescale global topographic data. It is based on a hierarchical decomposition of the sphere by a recursive bisection triangulation in geographic coordinates. Error indicators allow the representation of the data at various ..."
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Cited by 22 (2 self)
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We present a multiresolution model for surfaces which is able to handle largescale global topographic data. It is based on a hierarchical decomposition of the sphere by a recursive bisection triangulation in geographic coordinates. Error indicators allow the representation of the data at various levels of detail and enable data compression by local omission of data values. The resulting hierarchical triangulation is stored using a bit code of the underlying binary tree and, additionally, relative pointers which allow an adaptive tree traversal. This way, it is possible to work directly on the compressed data. We show that significant compression rates can be obtained already for small threshold values. In a visualization application, adaptive triangulations which consist of hundreds of thousands of shaded triangles are extracted and drawn at interactive rates.