Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
International Journal of Computer Vision
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Spectral processing of point-sampled geometry
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Real-time 3D model acquisition
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Efficient high quality rendering of point sampled geometry
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
Proceedings of the conference on Visualization '01
Probabilistic surfaces: point based primitives to show surface uncertainty
Proceedings of the conference on Visualization '02
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Proceedings of the 12th Eurographics Workshop on Rendering Techniques
Estimating surface normals in noisy point cloud data
Proceedings of the nineteenth annual symposium on Computational geometry
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Interactive boolean operations on surfel-bounded solids
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
Graphical Models - Special issue on SMI 2004
Feature-preserving non-local denoising of static and time-varying range data
Proceedings of the 2007 ACM symposium on Solid and physical modeling
ACM SIGGRAPH 2007 papers
Example-based 3D scan completion
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Adaptive feature-preserving non-local denoising of static and time-varying range data
Computer-Aided Design
Robust principal axes determination for point-based shapes using least median of squares
Computer-Aided Design
Technical Section: Variational Bayesian noise estimation of point sets
Computers and Graphics
Robust mesh reconstruction from unoriented noisy points
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Technical Section: Visibility of noisy point cloud data
Computers and Graphics
The HybridTree: a hybrid constructive shape representation for free-form modeling
Heterogeneous objects modelling and applications
Fuzzy transform and least-squares approximation: Analogies, differences, and generalizations
Fuzzy Sets and Systems
Effects of noise on quantized triangle meshes
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
A logistic model for the degradation of triangle mesh normals
Proceedings of the 7th international conference on Curves and Surfaces
SMI 2012: Full Local approximation of scalar functions on 3D shapes and volumetric data
Computers and Graphics
Robust filtering of noisy scattered point data
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
A Global Parity Measure for Incomplete Point Cloud Data
Computer Graphics Forum
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Journal of Scientific Computing
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We present a framework for analyzing shape uncertainty and variability in point-sampled geometry. Our representation is mainly targeted towards discrete surface data stemming from 3D acquisition devices, where a finite number of possibly noisy samples provides only incomplete information about the underlying surface. We capture this uncertainty by introducing a statistical representation that quantifies for each point in space the likelihood that a surface fitting the data passes through that point. This likelihood map is constructed by aggregating local linear extrapolators computed from weighted least squares fits. The quality of fit of these extrapolators is combined into a corresponding confidence map that measures the quality of local tangent estimates. We present an analysis of the effect of noise on these maps, show how to efficiently compute them, and extend the basic definition to a scale-space formulation. Various applications of our framework are discussed, including an adaptive re-sampling method, an algorithm for reconstructing surfaces in the presence of noise, and a technique for robustly merging a set of scans into a single point-based representation.