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
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Zippered polygon meshes from range images
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Description of complex objects from multiple range images using an inflating balloon model
Computer Vision and Image Understanding
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Pyramid-based texture analysis/synthesis
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
Multiresolution sampling procedure for analysis and synthesis of texture images
Proceedings of the 24th 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
A Level-Set Approach to 3D Reconstruction from Range Data
International Journal of Computer Vision
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
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
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Computer and Robot Vision
The Ball-Pivoting Algorithm for Surface Reconstruction
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)
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Consensus Surfaces for Modeling 3D Objects from Multiple Range Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Filling the Signed Distance Field by Fitting Local Quadrics
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Simultaneous structure and texture image inpainting
IEEE Transactions on Image Processing
Statistical surface recovery: a study on ear canals
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
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Geometric approaches for filling-in surface holes are introduced and studied in this paper. The basic principle is to choose the completing surface as one which minimizes a power of the mean curvature. We interpret this principle in a level set formulation, that is, we represent the surface of interest in implicit form and we construct an energy functional for the embedding function u. We first explore two different formulations (which can be considered as alternative) inspired by the above principle: in the first one we write the mean curvature as the divergence of the normal vector field @q to the isosurfaces of u; in the second one we used the signed distance function D to the surface as embedding function and we write the mean curvature in terms of it. Then we solve the Euler-Lagrange equations of these functionals which consist of a system of second order partial differential equations (PDEs) for u and @q, in the first case, or a fourth order PDE for D in the second case. Then, simpler methods based on second order elliptic PDEs, like Laplace equation or the absolutely minimizing Lipschitz extension, are also proposed and compared with the above higher order methods. The theoretical and computational framework, as well as examples with synthetic and real data, are presented in this paper.