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283
Poisson Surface Reconstruction
, 2006
"... We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function ..."
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Cited by 369 (5 self)
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We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.
Point Set Surfaces
, 2001
"... We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We pre ..."
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Cited by 299 (41 self)
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We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.
The Power Crust
, 2001
"... The power crust is a construction which takes a sample of points from the surface of a three-dimensional 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 259 (7 self)
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The power crust is a construction which takes a sample of points from the surface of a three-dimensional 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.
Computing and rendering point set surfaces.
- IEEE Transactions on Visualization and Computer Graphics,
, 2003
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The Power Crust, Unions of Balls, and the Medial Axis Transform
- Computational Geometry: Theory and Applications
, 2000
"... The medial axis transform (or MAT) is a representation of an object as an infinite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a finite union of balls. Using this approximate MAT we define a new piecewise-linear approximation to the objec ..."
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Cited by 193 (5 self)
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The medial axis transform (or MAT) is a representation of an object as an infinite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a finite union of balls. Using this approximate MAT we define a new piecewise-linear approximation to the object surface, which we call the power crust. We assume that we are given as input a suficiently dense sample of points from the object surface. We select a subset of the Voronoi balls of the sample, the polar balls, as the union of balls representation. We bound the geometric error of the union, and of the corresponding power crust, and show that both representations are topologically correct as well. Thus, our results provide a new algorithm for surface reconstruction from sample points. By construction, the power crust is always the boundary of a solid, so we avoid the hole-filling or manifold extraction steps used in previous algorithms. The union of balls representation and the power crust have corresponding piecewise-linear dual representations, which in some sense approximate the medial axis. We show a geometric relationship between these duals and the medial axis by proving that, as the sampling density goes to infinity, the set of poles, the centers of the polar balls, converge to the medial axis.
Filling Holes In Complex Surfaces Using Volumetric Diffusion
, 2001
"... We address the problem of building watertight 3D models from surfaces that contain holes---for example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation al ..."
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Cited by 172 (2 self)
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We address the problem of building watertight 3D models from surfaces that contain holes---for example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation algorithms. Our solution begins by constructing a signed distance function, the zero set of which defines the surface. Initially, this function is defined only in the vicinity of observed surfaces. We then apply a diffusion process to extend this function through the volume until its zero set bridges whatever holes may be present. If additional information is available, such as known-empty regions of space inferred from the lines of sight to a 3D scanner, it can be incorporated into the diffusion process. Our algorithm is simple to implement, is guaranteed to produce manifold non-interpenetrating surfaces, and is efficient to run on large datasets because computation is limited to areas near holes. By showing results for complex range scans, we demonstrate that our algorithm produces hole-free surfaces that are plausible, visually acceptable, and usually close to the intended geometry.
Out-of-Core Simplification of Large Polygonal Models
, 2000
"... We present an algorithm for out-of-core simplification of large polygonal datasets that are too complex to fit in main memory. The algorithm extends the vertex clustering scheme of Rossignac and Borrel [13] by using error quadric information for the placement of each cluster's representative ve ..."
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Cited by 159 (10 self)
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We present an algorithm for out-of-core simplification of large polygonal datasets that are too complex to fit in main memory. The algorithm extends the vertex clustering scheme of Rossignac and Borrel [13] by using error quadric information for the placement of each cluster's representative vertex, which better preserves fine details and results in a low mean geometric error. The use of quadrics instead of the vertex grading approach in [13] has the additional benefits of requiring less disk space and only a single pass over the model rather than two. The resulting linear time algorithm allows simplification of datasets of arbitrary complexity. In order
Tight cocone: A water-tight surface reconstructor
- JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING
, 2003
"... Surface reconstruction from unorganized sample points is an important problem in computer graphics, computer aided design, medical imaging and solid modeling. Recently a few algorithms have been developed that have theoretical guarantee of computing a topologically correct and geometrically close su ..."
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Cited by 123 (7 self)
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Surface reconstruction from unorganized sample points is an important problem in computer graphics, computer aided design, medical imaging and solid modeling. Recently a few algorithms have been developed that have theoretical guarantee of computing a topologically correct and geometrically close surface under certain condition on sampling density. Unfortunately, this sampling condition is not always met in practice due to noise, non-smoothness or simply due to inadequate sampling. This leads to undesired holes and other artifacts in the output surface. Certain CAD applications such as creating a prototype from a model boundary require a water-tight surface, i.e., no hole should be allowed in the surface. In this paper we describe a simple algorithm called Tight Cocone that works on an initial mesh generated by a popular surface reconstruction algorithm and fills up all holes to output a water-tight surface. In doing so, it does not introduce any extra points and produces a triangulated surface interpolating the input sample points. In support of our method we present experimental results with a number of difficult data sets.
Building a Digital Model of Michelangelo's Florentine PietÃ
- IEEE Computer Graphics and Applications
, 2002
"... We describe a project to create a three-dimensional digital model of Michelangelo's Florentine Piet a. The model is being used in a comprehensive art-historical study of this sculpture that includes a consideration of historical records and artistic significance as well as scientific data. ..."
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Cited by 103 (7 self)
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We describe a project to create a three-dimensional digital model of Michelangelo's Florentine Piet a. The model is being used in a comprehensive art-historical study of this sculpture that includes a consideration of historical records and artistic significance as well as scientific data.
