Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
International Journal of Computer Vision
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Real-time 3D model acquisition
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
Journal of Computational Physics
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
SIAM Journal on Numerical Analysis
Journal of Mathematical Imaging and Vision
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
Journal of Computational Physics
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Adaptive variational curve smoothing based on level set method
Journal of Computational Physics
An edge-weighted centroidal Voronoi tessellation model for image segmentation
IEEE Transactions on Image Processing
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
On Variational Curve Smoothing and Reconstruction
Journal of Mathematical Imaging and Vision
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Journal of Scientific Computing
GPU-Assisted Computation of Centroidal Voronoi Tessellation
IEEE Transactions on Visualization and Computer Graphics
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Least squares quantization in PCM
IEEE Transactions on Information Theory
Image Segmentation Using Local Variation and Edge-Weighted Centroidal Voronoi Tessellations
IEEE Transactions on Image Processing
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In this paper, we propose a generalized edge-weighted centroidal Voronoi tessellation (GEWCVT) model and corresponding solution algorithms, then apply them for geometry processing such as curve/surface smoothing and reconstruction. The main idea of the method is to seek a good way to discretize the similarity and regularity measures of the objective functional in the context of centroidal Voronoi tessellation methodology, so that its minimization can be done by clustering-type algorithms. Through various numerical examples, the proposed GEWCVT-based method is shown to be an effective and robust tool for such applications.