Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
New Models and Heuristics for Component Placement in Printed Circuit Board Assembly
ICIIS '99 Proceedings of the 1999 International Conference on Information Intelligence and Systems
Volume Sculpting Using the Level-Set Method
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Row Modifications of a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
3D Distance Fields: A Survey of Techniques and Applications
IEEE Transactions on Visualization and Computer Graphics
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Geometric fairing of irregular meshes for free-form surface design
Computer Aided Geometric Design
Variational volumetric surface reconstruction from unorganized points
VG'07 Proceedings of the Sixth Eurographics / Ieee VGTC conference on Volume Graphics
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Signed 3D distance fields are used a in a variety of domains. From shape modelling to surface registration. They are typically computed based on sampled point sets. If the input point set contains holes, the behaviour of the zero-level surface of the distance field is not well defined. In this paper, a novel regularisation approach is described. It is based on an energy formulation, where both local smoothness and data fidelity are included. The minimisation of the global energy is shown to be the solution of a large set of linear equations. The solution to the linear system is found by sparse Cholesky factorisation. It is demonstrated that the zero-level surface will act as a membrane after the proposed regularisation. This effectively closes holes in a predictable way. Finally, the performance of the method is tested with a set of synthetic point clouds of increasing complexity.