Nonlinear total variation based noise removal algorithms
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LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
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Atomic Decomposition by Basis Pursuit
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Geometric surface smoothing via anisotropic diffusion of normals
Proceedings of the conference on Visualization '02
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Images, Numerical Analysis of Singularities and Shock Filters
Images, Numerical Analysis of Singularities and Shock Filters
Shape modeling with point-sampled geometry
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Non-iterative, feature-preserving mesh smoothing
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ACM SIGGRAPH 2003 Papers
Bilateral Filtering for Gray and Color Images
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Geometric surface processing via normal maps
ACM Transactions on Graphics (TOG)
Convex Optimization
ACM SIGGRAPH 2004 Papers
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
Row Modifications of a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Linear rotation-invariant coordinates for meshes
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Robust moving least-squares fitting with sharp features
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Robust Smooth Feature Extraction from Point Clouds
SMI '07 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2007
Parameterization-free projection for geometry reconstruction
ACM SIGGRAPH 2007 papers
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An adaptive MLS surface for reconstruction with guarantees
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Data-dependent MLS for faithful surface approximation
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Space-time surface reconstruction using incompressible flow
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SIAM Journal on Matrix Analysis and Applications
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
Normal and feature approximations from noisy point clouds
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
The domain of a point set surface
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
SMI 2011: Full Paper: Harmonic point cloud orientation
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Quasi-interpolation for surface reconstruction from scattered data with radial basis function
Computer Aided Geometric Design
Feature-Preserving Reconstruction of Singular Surfaces
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O-snap: Optimization-based snapping for modeling architecture
ACM Transactions on Graphics (TOG)
Edge-aware point set resampling
ACM Transactions on Graphics (TOG)
Accurate reconstruction of engineered models with surfaces of revolution
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L1-medial skeleton of point cloud
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Technical Section: Reconstructing shape boundaries with multimodal constraints
Computers and Graphics
SMI 2013: Voronoi-based feature curves extraction for sampled singular surfaces
Computers and Graphics
Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets
Journal of Mathematical Imaging and Vision
Noise-adaptive shape reconstruction from raw point sets
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We introduce an ℓ1-sparse method for the reconstruction of a piecewise smooth point set surface. The technique is motivated by recent advancements in sparse signal reconstruction. The assumption underlying our work is that common objects, even geometrically complex ones, can typically be characterized by a rather small number of features. This, in turn, naturally lends itself to incorporating the powerful notion of sparsity into the model. The sparse reconstruction principle gives rise to a reconstructed point set surface that consists mainly of smooth modes, with the residual of the objective function strongly concentrated near sharp features. Our technique is capable of recovering orientation and positions of highly noisy point sets. The global nature of the optimization yields a sparse solution and avoids local minima. Using an interior-point log-barrier solver with a customized preconditioning scheme, the solver for the corresponding convex optimization problem is competitive and the results are of high quality.