Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th 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
Minimal Surfaces Based Object Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
The approximation power of moving least-squares
Mathematics of Computation
Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Point cloud surfaces using geometric proximity graphs
Computers and Graphics
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
Real-time point cloud refinement
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Post-processing of scanned 3D surface data
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
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Variational techniques are a popular approach for reconstructing the surface of an object. In previous work, the surface is represented either implicitly by the use of level sets or explicitly as a triangle mesh. In this paper we describe new formulations and develop fast algorithms for surface reconstruction based on partial differential equations (PDEs) derived from variational calculus using an explicit, purely point-based surface representation. The method is based on a Moving Least-Squares surface approximation of the sample points. Our new approach automatically copes with complicated topology and deformations, without the need for explicit treatment. In contrast to level sets, it requires no postprocessing, easily adapts to varying spatial resolutions and is invariant under rigid body motion. We demonstrate the versatility of our method using several synthetic data sets and show how our technique can be used to reconstruct object surfaces from real-world multi-view footage.