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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.
Surface Reconstruction from Noisy Point Clouds
, 2005
"... We show that a simple modification of the power crust algorithm for surface reconstruction produces correct outputs in presence of noise. This is proved using a fairly realistic noise model. Our theoretical results are related to the problem of computing a stable subset of the medial axis. We demost ..."
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Cited by 15 (0 self)
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We show that a simple modification of the power crust algorithm for surface reconstruction produces correct outputs in presence of noise. This is proved using a fairly realistic noise model. Our theoretical results are related to the problem of computing a stable subset of the medial axis. We demostrate the effectiveness of our algorithm with a number of experimental results.
Kuijper A.: A new projection method for point set surfaces
 In Annex Proceedings Eurographics (2009
"... A successful approach in triangulating point set surfaces is to apply operations, like a projection operator for advancing front algorithms, directly to MovingLeast Squares (MLS) surfaces. The MLS method naturally handles noisy input data and is especially useful for point clouds derived from real ..."
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Cited by 2 (2 self)
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A successful approach in triangulating point set surfaces is to apply operations, like a projection operator for advancing front algorithms, directly to MovingLeast Squares (MLS) surfaces. The MLS method naturally handles noisy input data and is especially useful for point clouds derived from realworld solids. Unfortunately, MLS is computationally extensive and complex. We present a novel projection method that does not require solving a nonlinear optimization problem as MLS does. We create a polynomial approximation of the surface similar to MLS but our method adapts the degree of the polynomial with respect to the points to be approximated. The approximated points are iteratively collected compromising connectivity information. We enhance the orientation of the local coordinate system to further improve the method. The results confirm that our method is more robust and also accelerates triangulation due to a preprocessing step that needs to be done only once per data set. Categories and Subject Descriptors (according to ACM CCS): Computer Graphics [I.3.5]: Mesh Generation—. 1.
1 Usage of 2D Region Similarity For Surface Reconstruction From Planar Samples
"... In surface reconstruction from planar slices it is necessary to build surfaces between corresponding 2D regions in consecutive levels. The problem has been traditionally attacked with (i) direct reconstruction based on local geometric proximity between the regions, and (ii) classification of topolog ..."
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In surface reconstruction from planar slices it is necessary to build surfaces between corresponding 2D regions in consecutive levels. The problem has been traditionally attacked with (i) direct reconstruction based on local geometric proximity between the regions, and (ii) classification of topological events between the slices, which control the evolution of the cross cuts. These approaches have been separately applied with mixed success. In the case (i), the results may be surfaces with overstretched or unnatural branches, resulting from a local contour proximity which does not correspond to global similarity between regions. In (ii), the consequences from topological events upon the actual surface realization have not been drawn. In this paper an integration of (i) and (ii) is presented, which uses a criteria of similarity between composed 2D regions in consecutive slices to: (a) decide if a surface should actually relate those regions, (b) identify the topological transitions between levels and (c) construct the local surface for the related regions. The method implemented hinders overstretched and unnatural branches, therefore rendering a surface which adjusts to geometricallysound topological events. This is a good alternative when the surface reconstructed needs to be topologically faithful (for example in flow simulation) in addition to represent the a rough geometrical space (for example in radiation planning). Glossary Πi, Πi+1 Consecutive cross section planes sampling an object surface. Also apply to the (polygonal) cross sections contained in these planes. A, B,... Jordan Curve on plane Πi, parallel to the xyplane. 1, 2,... Jordan Curve on plane Πi+1 parallel to the xyplane. Si, Si+1 Sets of Jordan Curves on planes Πi and Πi+1 respectively. Si= { A, B,...},