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108
Surface reconstruction from unorganized points
 COMPUTER GRAPHICS (SIGGRAPH ’92 PROCEEDINGS)
, 1992
"... We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be know ..."
Abstract

Cited by 651 (8 self)
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We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from twodimensional slices, and interactive surface sketching.
Using Particles to Sample and Control Implicit Surfaces
, 1994
"... We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement c ..."
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Cited by 225 (3 self)
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We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement control points for direct manipulation by specifying particle motions, then solving for surface motion that maintains the constraint. For sampling and rendering, we run the constraint in the other direction, creating floater particles that roam freely over the surface. Local repulsion is used to make floaters spread evenly across the surface. By varying the radius of repulsion adaptively, and fissioning or killing particles based on the local density, we can achieve good sampling distributions very rapidly, and maintain them even in the face of rapid and extreme deformations and changes in surface topology. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling:...
Multilevel Partition of Unity Implicits
 ACM Transactions on Graphics
, 2003
"... We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighti ..."
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Cited by 157 (6 self)
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We present a shape representation, the multilevel partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape.
A levelset approach to 3d reconstruction from range data
 International Journal of Computer Vision
, 1998
"... This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application d ..."
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Cited by 151 (20 self)
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This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application domain. The resulting optimization problem is solved by an incremental process of deformation. We represent a deformable surface as the level set of a discretely sampled scalar function of 3 dimensions, i.e. a volume. Such levelset models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume. The result is a voxelbased modeling technology that offers several advantages over conventional parametric models, including flexible topology, no need for reparameterization, concise descriptions of differential structure, and a natural scale space for hierarchical representations. This paper builds on previous work in both 3D reconstruction and levelset modeling. It presents a fundamental result in surface estimation from range data: an analytical characterization of the surface that maximizes the posterior probability. It also presents a novel computational technique for levelset modeling, called the sparsefield algorithm, which combines the advantages of a levelset approach with the computational efficiency and accuracy of a parametric representation. The sparsefield algorithm is more efficient than other approaches, and because it assigns the level set to a specific set of grid points, it positions the levelset model more accurately than the grid itself. These properties, computational efficiency and subcell accuracy, are essential when trying to reconstruct the shapes of 3D objects. Results are shown for the reconstruction objects from sets of noisy and overlapping range maps.
Function Representation in Geometric Modeling: Concepts, Implementation and Applications
, 1995
"... This paper presents a state of the art report of our project, the main objectives of which are:  Categorization and summary of the geometric concepts required in a functionally based modeling environment;  Elaboration of a rich system of geometric operations closed on functionally represented ob ..."
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Cited by 134 (33 self)
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This paper presents a state of the art report of our project, the main objectives of which are:  Categorization and summary of the geometric concepts required in a functionally based modeling environment;  Elaboration of a rich system of geometric operations closed on functionally represented objects;  Treatment of multidimensional and particularly spacetime objects in a uniform manner; 6
Fast surface reconstruction using the level set method
 In VLSM ’01: Proceedings of the IEEE Workshop on Variational and Level Set Methods
, 2001
"... In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data ..."
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Cited by 118 (11 self)
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In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surfacelike model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
General Object Reconstruction based on Simplex Meshes
, 1999
"... In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconst ..."
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Cited by 101 (16 self)
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In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The di erent tasks performed during the reconstruction include the segmentation of given objects in the scene, the extrapolation of missing data, and the control of smoothness, density, and geometric quality of the reconstructed meshes. The reconstruction takes place in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure. Then, after a few iterations, the mesh topology can be modi ed by creating holes or by increasing its genus. Finally, aniterativere nement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality. Several reconstruction examples are provided with quantitative and qualitative results.
On Reliable Surface Reconstruction from Multiple Range Images
, 1996
"... This paper addresses the problem of integrating multiple registered 2.5D range images into a single 3D surface model which has topology and geometry consistent with the measurements. Reconstruction of a model of the correct surface topology is the primary goal. Extraction of the correct surface topo ..."
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Cited by 97 (11 self)
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This paper addresses the problem of integrating multiple registered 2.5D range images into a single 3D surface model which has topology and geometry consistent with the measurements. Reconstruction of a model of the correct surface topology is the primary goal. Extraction of the correct surface topology is recognised as a fundamental step in building 3D models. Model optimization can then be performed to fit the data to the desired accuracy with an efficient representation. A novel integration algorithm is presented that is based on local reconstruction of surface topology using operations in 3D space. A new continuous implicit surface function is proposed which merges the connectivity information inherent in the individual sampled range images. This enables the construction of a single triangulated model using a standard method. The algorithm is guaranteed to reconstruct the correct topology of surface features larger than the range image sampling resolution. Reconstruction of triangu...
Function Representation of Solids Reconstructed from Scattered Surface Points and Contours
 Computer Graphics Forum
, 1995
"... This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation of sca ..."
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Cited by 83 (11 self)
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This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from crosssections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces. 1. Introduction There are a number of applied problems that require interpolation or smoothing of large arrays of randomly measured points of a surface. The main sources of such data are physical measurements taken by scanning an object from different viewing directions. Scattered points arise also in mathematical simulation, for examp...
Fast Multiresolution Surface Meshing
, 1995
"... We are presenting a new method for adaptive surface meshing and triangulation which controls the local levelofdetail of the surface approximation by local spectral estimates. These estimates are figured out by a wavelet representation of the surface data. The basic idea is to decompose the initial ..."
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Cited by 70 (3 self)
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We are presenting a new method for adaptive surface meshing and triangulation which controls the local levelofdetail of the surface approximation by local spectral estimates. These estimates are figured out by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semiorthogonal 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 polygonial 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 hierachical meshing algorithm which transforms the initially regular data grid into a quadtree representation by...