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339
A Volumetric Method for Building Complex Models from Range Images
, 1996
"... A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, and robus ..."
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Cited by 796 (17 self)
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A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, and robustness in the presence of outliers. Prior algorithms possess subsets of these properties. In this paper, we present a volumetric method for integrating range images that possesses all of these properties. Our volumetric representation consists of a cumulative weighted signed distance function. Working with one range image at a time, we first scanconvert it to a distance function, then combine this with the data already acquired using a simple additive scheme. To achieve space efficiency, we employ a runlength encoding of the volume. To achieve time efficiency, we resample the range image to align with the voxel grid and traverse the range and voxel scanlines synchronously. We generate the f...
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 ..."
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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.
A New VoronoiBased Surface Reconstruction Algorithm
, 2002
"... We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and converg ..."
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Cited by 356 (9 self)
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We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density increases. The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples. The output mesh interpolates, rather than approximates, the input points. Our algorithm is based on the threedimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 342 (11 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on "local feature size", the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs. 1 Introduction The problem of reconstructing a surface from scattered sample points arises in many applications such as computer graphics, medical imaging, and cartography. In this paper we consider the specific reconstruction problem in which the input is a set of sample points S drawn from a smooth twodimensional manifold F embedded in three dimensions, and the desired output is a triangular mesh with vertex set equal to S that faithfully represen...
The Office of the Future: A Unified Approach to ImageBased Modeling and Spatially Immersive Displays
 In SIGGRAPH 98 Conference Proceedings
, 1998
"... We introduce ideas, proposed technologies, and initial results for an office of the future that is based on a unified application of computer vision and computer graphics in a system that combines and builds upon the notions of the CAVE™, tiled display systems, and imagebased modeling. The basic id ..."
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Cited by 277 (25 self)
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We introduce ideas, proposed technologies, and initial results for an office of the future that is based on a unified application of computer vision and computer graphics in a system that combines and builds upon the notions of the CAVE™, tiled display systems, and imagebased modeling. The basic idea is to use realtime computer vision techniques to dynamically extract perpixel depth and reflectance information for the visible surfaces in the office including walls, furniture, objects, and people, and then to either project images on the surfaces, render images of the surfaces, or interpret changes in the surfaces. In the first case, one could designate everyday (potentially irregular) real surfaces in the office to be used as spatially immersive display surfaces, and then project highresolution graphics and text onto those surfaces. In the second case, one could transmit the dynamic imagebased
Topological Persistence and Simplification
, 2000
"... We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast ..."
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Cited by 235 (44 self)
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We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.
The BallPivoting Algorithm for Surface Reconstruction
 IEEE Transactions on Visualization and Computer Graphics
, 1999
"... The BallPivoting Algorithm (BPA) computes a triangle mesh interpolating a given point cloud. Typically the points are surface samples acquired with multiple range scans of an object. The principle of the BPA is very simple: Three points form a triangle if a ball of a userspecified radius touches ..."
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Cited by 207 (14 self)
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The BallPivoting Algorithm (BPA) computes a triangle mesh interpolating a given point cloud. Typically the points are surface samples acquired with multiple range scans of an object. The principle of the BPA is very simple: Three points form a triangle if a ball of a userspecified radius touches them without containing any other point. Starting with a seed triangle, the ball pivots around an edge (i.e. it revolves around the edge while keeping in contact with the edge's endpoints) until it touches another point, forming another triangle. The process continues until all reachable edges have been tried, and then starts from another seed triangle, until all points have been considered. We applied the BPA to datasets of millions of points representing actual scans of complex 3D objects. The relatively small amount of memory required by the BPA, its time efficiency, and the quality of the results obtained compare favorably with existing techniques.
A Simple Algorithm for Homeomorphic Surface Reconstruction
 International Journal of Computational Geometry and Applications
, 2000
"... The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm [1] using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from ..."
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Cited by 204 (29 self)
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The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm [1] using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming the sample was `suciently dense'. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the rst such topological guarantee for this problem. 1 Introduction A number of applications in CAD, computer graphics, computer vision and mathematical modeling involve the computation of a piecewise lin Dept. of Computer Science, U. of Texas, Austin TX 78712. email: amenta@cs.utexas.edu, supported by NSF grant CCR9731977 y Dept. of Computer Science, U. of Texas, Austin, TX 78712. email: sunghe...
The Power Crust
, 2001
"... The power crust is a construction which takes a sample of points from the surface of a threedimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce ..."
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Cited by 200 (6 self)
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The power crust is a construction which takes a sample of points from the surface of a threedimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce the surface representation from the MAT.