Direct least-squares fitting of algebraic surfaces
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
A fast level set method for propagating interfaces
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Computer Vision and Image Understanding
A level-set method for flow visualization
Proceedings of the conference on Visualization '00
Level set segmentation from multiple non-uniform volume datasets
Proceedings of the conference on Visualization '02
Fast Ray-Tracing of Rectilinear Volume Data Using Distance Transforms
IEEE Transactions on Visualization and Computer Graphics
Level Set Evolution without Re-Initialization: A New Variational Formulation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Signed Distance Transform Using Graphics Hardware
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Designing with distance fields
ACM SIGGRAPH 2006 Courses
Simulation of clothing with folds and wrinkles
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
IEEE Transactions on Pattern Analysis and Machine Intelligence
A variational formulation for segmenting desired objects in color images
Image and Vision Computing
ACM SIGGRAPH 2007 papers
Shape-topology optimization for Navier-Stokes problem using variational level set method
Journal of Computational and Applied Mathematics
IEEE Transactions on Visualization and Computer Graphics
Smooth Surface Extraction from Unstructured Point-based Volume Data Using PDEs
IEEE Transactions on Visualization and Computer Graphics
A semi-automatic method for burn scar delineation using a modified Chan-Vese model
Computers & Geosciences
Point-Based geometric deformable models for medical image segmentation
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
IEEE Transactions on Image Processing
Direct isosurface extraction from scattered volume data
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
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Signed distance functions (SDF) to explicit or implicit surface representations are intensively used in various computer graphics and visualization algorithms. Among others, they are applied to optimize collision detection, are used to reconstruct data fields or surfaces, and, in particular, are an obligatory ingredient for most level set methods. Level set methods are common in scientific visualization to extract surfaces from scalar or vector fields. Usual approaches for the construction of an SDF to a surface are either based on iterative solutions of a special partial differential equation or on marching algorithms involving a polygonization of the surface. We propose a novel method for a non-iterative approximation of an SDF and its derivatives in a vicinity of a manifold. We use a second-order algebraic fitting scheme to ensure high accuracy of the approximation. The manifold is defined (explicitly or implicitly) as an isosurface of a given volumetric scalar field. The field may be given at a set of irregular and unstructured samples. Stability and reliability of the SDF generation is achieved by a proper scaling of weights for the Moving Least Squares approximation, accurate choice of neighbors, and appropriate handling of degenerate cases. We obtain the solution in an explicit form, such that no iterative solving is necessary, which makes our approach fast.