Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
Journal of Computational Physics
Journal of Mathematical Imaging and Vision
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Robust estimation of curvature along digital contours with global optimization
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
A combined multi-scale/irregular algorithm for the vectorization of noisy digital contours
Computer Vision and Image Understanding
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We propose a novel approach to reconstruct shapes from digital data. Contrarily to most methods, reconstructed shapes are smooth with a well-defined curvature field and have the same digitization as the input data: the range of application we have in mind is especially post-processing to image segmentation where labelled regions are digital objects. For this purpose, we introduce three new algorithms to regularize digital contours based on the minimization of Willmore energy: our first algorithm is based on tools coming from discrete geometry, the second is related to convex geometry while the third approach is a constrained phase field minimization. The three algorithms are described in details and the convergence of the phase field approach is investigated. We present a comparative evaluation of all three methods, in terms of the accuracy of curvature estimators and computation time.