Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
An implicit surface polygonizer
Graphics gems IV
Implicit reconstruction of solids from cloud point sets
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd 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
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Stereo Matching with Nonlinear Diffusion
International Journal of Computer Vision
Inference of Integrated Surface, Curve, and Junction Descriptions From Sparse 3D Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Physically-based visual simulation on graphics hardware
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
An Evaluation of Implicit Surface Tilers
IEEE Computer Graphics and Applications
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
ACM SIGGRAPH 2003 Papers
Non-iterative, feature-preserving mesh smoothing
ACM SIGGRAPH 2003 Papers
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Surface reconstruction based on compactly supported radial basis functions
Geometric modeling
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
Journal of Computational Physics
CPM: A Deformable Model for Shape Recovery and Segmentation Based on Charged Particles
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean curvature evolution and surface area scaling in image filtering
IEEE Transactions on Image Processing
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Processing textured surfaces via anisotropic geometric diffusion
IEEE Transactions on Image Processing
A graph-spectral approach to shape-from-shading
IEEE Transactions on Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
Three-dimensional surface reconstruction from multistatic SAR images
IEEE Transactions on Image Processing
Recovery of surface orientation from diffuse polarization
IEEE Transactions on Image Processing
Local Hull-Based Surface Construction of Volumetric Data From Silhouettes
IEEE Transactions on Image Processing
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Efficient surface reconstruction from noisy data using regularized membrane potentials
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Outer surface reconstruction for 3D fractured objects
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part II
Pattern Recognition Letters
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A physically motivated method for surface reconstruction is proposed that can recover smooth surfaces from noisy and sparse data sets. No orientation information is required. By a new technique based on regularized-membrane potentials the input sample points are aggregated, leading to improved noise tolerability and outlier removal, without sacrificing much with respect to detail (feature) recovery. After aggregating the sample points on a volumetric grid, a novel, iterative algorithm is used to classify grid points as exterior or interior to the surface. This algorithm relies on intrinsic properties of the smooth scalar field on the grid which emerges after the aggregation step. Second, a mesh-smoothing paradigm based on a mass-spring system is introduced. By enhancing this system with a bending-energy minimizing term we ensure that the final triangulated surface is smoother than piecewise linear. In terms of speed and flexibility, the method compares favorably with respect to previous approaches. Most parts of the method are implemented on modern graphics processing units (GPUs). Results in a wide variety of settings are presented, ranging from surface reconstruction on noise-free point clouds to grayscale image segmentation.