The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
The approximation power of moving least-squares
Mathematics of Computation
Curve reconstruction: connecting dots with good reason
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A Characterization of Ten Hidden-Surface Algorithms
ACM Computing Surveys (CSUR)
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Proceedings of the conference on Visualization '01
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
ACM SIGGRAPH 2004 Papers
Point-based multiscale surface representation
ACM Transactions on Graphics (TOG)
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Point-Based Graphics
Direct visibility of point sets
ACM SIGGRAPH 2007 papers
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
The Euclidean degree-4 minimum spanning tree problem is NP-hard
Proceedings of the twenty-fifth annual symposium on Computational geometry
Consolidation of unorganized point clouds for surface reconstruction
ACM SIGGRAPH Asia 2009 papers
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Uncertainty and variability in point cloud surface data
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
SMI 2011: Full Paper: Point set silhouettes via local reconstruction
Computers and Graphics
SMI 2012: Full Consensus meshing
Computers and Graphics
Visible neighborhood graph of point clouds
Graphical Models
Real-time rendering of massive unstructured raw point clouds using screen-space operators
VAST'11 Proceedings of the 12th International conference on Virtual Reality, Archaeology and Cultural Heritage
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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We present a robust algorithm for estimating visibility from a given viewpoint for a point set containing concavities, non-uniformly spaced samples, and possibly corrupted with noise. Instead of performing an explicit surface reconstruction for the points set, visibility is computed based on a construction involving convex hull in a dual space, an idea inspired by the work of Katz et al. [26]. We derive theoretical bounds on the behavior of the method in the presence of noise and concavities, and use the derivations to develop a robust visibility estimation algorithm. In addition, computing visibility from a set of adaptively placed viewpoints allows us to generate locally consistent partial reconstructions. Using a graph based approximation algorithm we couple such reconstructions to extract globally consistent reconstructions. We test our method on a variety of 2D and 3D point sets of varying complexity and noise content.