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278
Geometry images
 IN PROC. 29TH SIGGRAPH
, 2002
"... Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create onl ..."
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Cited by 349 (25 self)
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Surface geometry is often modeled with irregular triangle meshes. The process of remeshing refers to approximating such geometry using a mesh with (semi)regular connectivity, which has advantages for many graphics applications. However, current techniques for remeshing arbitrary surfaces create only semiregular meshes. The original mesh is typically decomposed into a set of disklike charts, onto which the geometry is parametrized and sampled. In this paper, we propose to remesh an arbitrary surface onto a completely regular structure we call a geometry image. It captures geometry as a simple 2D array of quantized points. Surface signals like normals and colors are stored in similar 2D arrays using the same implicit surface parametrization — texture coordinates are absent. To create a geometry image, we cut an arbitrary mesh along a network of edge paths, and parametrize the resulting single chart onto a square. Geometry images can be encoded using traditional image compression algorithms, such as waveletbased coders.
Least Squares Conformal Maps for Automatic Texture Atlas Generation
, 2002
"... A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from ..."
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Cited by 326 (7 self)
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A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from several limitations, requiring them to generate a large number of small charts with simple borders. The discontinuities between the charts cause artifacts, and make it difficult to paint large areas with regular patterns.
The Space of Human Body Shapes: Reconstruction And Parameterization from Range Scans
 ACM TRANS. GRAPH
, 2003
"... We develop a novel method for fitting highresolution template meshes to detailed human body range scans with sparse 3D markers. We formulate an optimization problem in which the degrees of freedom are an affine transformation at each template vertex. The objective function is a weighted combination ..."
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Cited by 291 (4 self)
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We develop a novel method for fitting highresolution template meshes to detailed human body range scans with sparse 3D markers. We formulate an optimization problem in which the degrees of freedom are an affine transformation at each template vertex. The objective function is a weighted combination of three measures: proximity of transformed vertices to the range data, similarity between neighboring transformations, and proximity of sparse markers at corresponding locations on the template and target surface. We solve for the transformations with a nonlinear optimizer, run at two resolutions to speed convergence. We demonstrate reconstruction and consistent parameterization of 250 human body models. With this parameterized set, we explore a variety of applications for human body modeling, including: morphing, texture transfer, statistical analysis of shape, model fitting from sparse markers, feature analysis to modify multiple correlated parameters (such as the weight and height of an individual), and transfer of surface detail and animation controls from a template to fitted models.
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...
Surface Parameterization: a Tutorial and Survey
 In Advances in Multiresolution for Geometric Modelling, Mathematics and Visualization
, 2005
"... Summary. This paper provides a tutorial and survey of methods for parameterizing surfaces with a view to applications in geometric modelling and computer graphics. We gather various concepts from differential geometry which are relevant to surface mapping and use them to understand the strengths and ..."
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Cited by 243 (7 self)
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Summary. This paper provides a tutorial and survey of methods for parameterizing surfaces with a view to applications in geometric modelling and computer graphics. We gather various concepts from differential geometry which are relevant to surface mapping and use them to understand the strengths and weaknesses of the many methods for parameterizing piecewise linear surfaces and their relationship to one another. 1
Anisotropic Polygonal Remeshing
"... In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when cre ..."
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Cited by 211 (18 self)
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In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply pointsampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.
Intrinsic Parameterizations of Surface Meshes
, 2002
"... Parameterization of discrete surfaces is a fundamental and widelyused operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute leastdistorted parame ..."
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Cited by 211 (18 self)
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Parameterization of discrete surfaces is a fundamental and widelyused operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute leastdistorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a twodimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain leastdistorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.
Displaced subdivision surfaces
 Siggraph 2000, Computer Graphics Proceedings, Annual Conference Series, pages 85–94. ACM Press / ACM SIGGRAPH
, 2000
"... In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalarvalued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivisio ..."
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Cited by 158 (2 self)
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In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalarvalued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivision framework, allowing for simple and efficient evaluation of analytic surface properties. We present a simple, automatic scheme for converting detailed geometric models into such a representation. The challenge in this conversion process is to find a simple subdivision surface that still faithfully expresses the detailed model as its offset. We demonstrate that displaced subdivision surfaces offer a number of benefits, including geometry compression, editing, animation, scalability, and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact. Additional Keywords: geometry compression, multiresolution geometry, displacement maps, bump maps, multiresolution editing, animation.
Feature Sensitive Surface Extraction from Volume Data
"... The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) ..."
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Cited by 154 (11 self)
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The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) or freeform modeling often need a topological manifold representation where neighborhood information within the surface is explicitly available. Consequently, it is necessary to find effective conversion algorithms to generate explicit surface descriptions for the geometry which is implicitly defined by a volumetric data set. Since volume data is usually sampled on a regular grid with a given step width, we often observe severe alias artifacts at sharp features on the extracted surfaces. In this paper we present a new technique for surface extraction that performs feature sensitive sampling and thus reduces these alias effects while keeping the simple algorithmic structure of the standard Marching Cubes algorithm. We demonstrate the effectiveness of the new technique with a number of application examples ranging from CSG modeling and simulation to surface reconstruction and remeshing of polygonal models. 1