Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Constraints on deformable models: recovering 3D shape and nongrid motion
Artificial Intelligence
Recognizing 3-D Objects Using Surface Descriptions
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D visualization of tomographic volume data using the generalized voxel model
The Visual Computer: International Journal of Computer Graphics
CVGIP: Graphical Models and Image Processing
Discrete Combinatorial Surfaces
Graphical Models and Image Processing
A definition of surfaces of Z3 . A new 3D discrete Jordan theorem
Theoretical Computer Science
Euclidean paths: a new representation of boundary of discrete regions
Graphical Models and Image Processing
Euclidean Paths for Representing and Transforming Scanned Characters
GREC '97 Selected Papers from the Second International Workshop on Graphics Recognition, Algorithms and Systems
Geometrical parameters extraction from discrete paths
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Inter-pixel eudlidean pahts for image analysis
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
Coexistence of Tricubes in Digital Naive Plane
DGCI '97 Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery
(n, m)-Cubes and Farey Nets for Naive Planes Understanding
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Continuous Shading of Curved Surfaces
IEEE Transactions on Computers
A statistical approach for geometric smoothing of discrete surfaces
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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In this work we describe a geometric method to smooth the boundary of a discrete 3D object. The method is reversible in the sense that the discrete boundary can be retrieved by digitizing the smoothed one. To this end, we propose a representation of the boundary of a discrete volume that we call Euclidean net and which is a generalization to the three-dimensional space of Euclidean Path introduced by Braquelaire and Vialard. Euclidean nets can be associated either to voxel based boundaries or to inter-voxel based boundaries. In this paper we focus on the first approach.