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46
The ballpivoting algorithm for surface reconstruction.
 IEEE TRansactions on Visualization and Computer Graphics,
, 1999
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Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation
, 2000
"... We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P #R 3 . Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The spe ..."
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Cited by 81 (5 self)
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We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P #R 3 . Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The speed of our algorithm is derived from a projectionbased approach we use to determine the incident faces on a point. We define our sampling criteria to sample the surface and guarantee a topologically correct mesh after surface reconstruction for such a sampled surface. We also present a new algorithm to find the normal at a vertex, when the surface is sampled according our given criteria. We also present results of our surface reconstruction using our algorithm on unorganized point clouds of various models. 1. Introduction The problem of surface reconstruction from unorganized point clouds has been, and continues to be, an important topic of research. The problem can be loosely stated ...
Improved Laplacian smoothing of noisy surface meshes
 Computer Graphics Forum
, 1999
"... This paper presents a technique for smoothing polygonal surface meshes that avoids the wellknown problem of deformation and shrinkage caused by many smoothing methods, like e.g. the Laplacian algorithm. The basic idea is to push the vertices of the smoothed mesh back towards their previous location ..."
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Cited by 69 (0 self)
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This paper presents a technique for smoothing polygonal surface meshes that avoids the wellknown problem of deformation and shrinkage caused by many smoothing methods, like e.g. the Laplacian algorithm. The basic idea is to push the vertices of the smoothed mesh back towards their previous locations. This technique can be also used in order to smooth unstructured point sets, by reconstructing a surface mesh to which the smoothing technique is applied. The key observation is that a surface mesh which is not necessarily topologically correct, but which can efficiently be reconstructed, is sufficient for that purpose. 1.
A geometric convection approach of 3D reconstruction
 EUROGRAPHICS SYMPOSIUM ON GEOMETRY PROCESSING (2003)
, 2003
"... This paper introduces a fast and efficient algorithm for surface reconstruction. As many algorithms of this kind, it produces a piecewise linear approximation of a surface S from a finite, sufficiently dense, subset of its points. Originally, the starting point of this work does not come from the co ..."
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Cited by 46 (6 self)
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This paper introduces a fast and efficient algorithm for surface reconstruction. As many algorithms of this kind, it produces a piecewise linear approximation of a surface S from a finite, sufficiently dense, subset of its points. Originally, the starting point of this work does not come from the computational geometry field. It is inspired by an existing numerical scheme of surface convection developed by Zhao, Osher and Fedkiw. We have translated this scheme to make it depend on the geometry of the input data set only, and not on the precision of some grid around the surface. Our algorithm deforms a closed oriented pseudosurface embedded in the 3D Delaunay triangulation of the sampled points, and the reconstructed surface consists of a set of oriented facets located in this 3D Delaunay triangulation. This paper provides an appropriate data structure to represent a pseudosurface, together with operations that manage deformations and topological changes. The algorithm can handle surfaces with boundaries, surfaces of high genus and, unlike most of the other existing schemes, it does not involve a global heuristic. Its complexity is that of the 3D Delaunay triangulation of the points. We present some results of the method, which turns out to be efficient even on noisy input data.
Point Cloud Representation
, 2001
"... Reconstructing a surface out of a threedimensional set of points, which is obtained by sampling an object's boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object's surface only by ..."
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Cited by 43 (3 self)
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Reconstructing a surface out of a threedimensional set of points, which is obtained by sampling an object's boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object's surface only by the point cloud. We discuss how such a point cloud representation can be visualized and present processing steps like coarsifying and smoothing, which are important for dealing with the objects. Further we apply a multiresolution method to point cloud representations and use this technique as well as others for modelling purposes. 1
On Fast Surface Reconstruction Methods for Large and Noisy Datasets
 in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA
, 2009
"... Abstract — In this paper we present a method for fast surface reconstruction from large noisy datasets. Given an unorganized 3D point cloud, our algorithm recreates the underlying surface’s geometrical properties using data resampling and a robust triangulation algorithm in near realtime. For result ..."
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Cited by 34 (9 self)
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Abstract — In this paper we present a method for fast surface reconstruction from large noisy datasets. Given an unorganized 3D point cloud, our algorithm recreates the underlying surface’s geometrical properties using data resampling and a robust triangulation algorithm in near realtime. For resulting smooth surfaces, the data is resampled with variable densities according to previously estimated surface curvatures. Incremental scans are easily incorporated into an existing surface mesh, by determining the respective overlapping area and reconstructing only the updated part of the surface mesh. The proposed framework is flexible enough to be integrated with additional point label information, where groups of points sharing the same label are clustered together and can be reconstructed separately, thus allowing fast updates via triangular mesh decoupling. To validate our approach, we present results obtained from laser scans acquired in both indoor and outdoor environments. I.
Curve and Surface Reconstruction
, 2004
"... The problem of reconstructing a shape from its sample appears in many scientific and engineering applications. Because of the variety in shapes and applications, many algorithms have been proposed over the last two decades, some of which exploit applicationspecific information and some of which are ..."
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Cited by 23 (0 self)
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The problem of reconstructing a shape from its sample appears in many scientific and engineering applications. Because of the variety in shapes and applications, many algorithms have been proposed over the last two decades, some of which exploit applicationspecific information and some of which are more general. We will concentrate on techniques that apply to the general setting and have proved to provide some guarantees on the quality of reconstruction.
Fixing Geometric Errors on Polygonal Models: A Survey
 J. COMPUT SCI
"... Polygonal models are popular representations of 3D objects. The use of polygonal models in computational applications often requires a model to properly bound a 3D solid. That is, the polygonal model needs to be closed, manifold, and free of selfintersections. This paper surveys a sizeable literatu ..."
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Cited by 22 (1 self)
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Polygonal models are popular representations of 3D objects. The use of polygonal models in computational applications often requires a model to properly bound a 3D solid. That is, the polygonal model needs to be closed, manifold, and free of selfintersections. This paper surveys a sizeable literature for repairing models that do not satisfy this criteria, focusing on categorizing them by their methodology and capability. We hope to offer pointers to further readings for researchers and practitioners, and suggestions of promising directions for future research endeavors.
Regular and NonRegular Point Sets: Properties and Reconstruction
 IN "COMPUTATIONAL GEOMETRY  THEORY AND APPLICATION"
"... In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion ofsampli ..."
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Cited by 22 (0 self)
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In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion ofsampling to the practical case of discrete shapes, seems much more realistic than previously proposed conditions based on properties of the underlying continuous shapes. Indeed, contrary to previous sampling criteria, our regularity condition can be checked on the basis of the samples alone and can be turned into a provably correct curve and surface reconstruction algorithm. Our reconstruction methods can also be applied to nonregular and unorganized point sets, revealing a larger part of the inner structure of such point sets than past approaches. Several realsize reconstruction examples validate the new method.