Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A convex polygon is determined by its Hough transform
Pattern Recognition Letters
On the Hough transform of a polygon
Pattern Recognition Letters
Geometric Constructions in the Digital Plane
Journal of Mathematical Imaging and Vision
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Defining Discrete Objects for Polygonalization: The Standard Model
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Discrete Representation of Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Unsupervised polygonal reconstruction of noisy contours by a discrete irregular approach
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Dynamic reconstruction of complex planar objects on irregular isothetic grids
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Topological and geometrical reconstruction of complex objects on irregular isothetic grids
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Reversible polygonalization of a 3d planar discrete curve: application on discrete surfaces
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Linear discrete line recognition and reconstruction based on a generalized preimage
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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Invertible Euclidean reconstruction methods without patches for 2D and 3D discrete curves are proposed. From a discrete 4-connected curve in 2D, or 6-connected curve in 3D, the proposed algorithms compute a polygonal line which digitization with the standard model is equal to all the pixels or voxels of the curve. The framework of this method is the discrete analytical geometry and parameter spaces are used in order to simplify the algorithms. Moreover, the reconstructed polyline is more compact than classical methods such as the Marching Cubes.