Best approximate circles on integer grids
ACM Transactions on Graphics (TOG)
Computing the extreme distances between two convex polygons
Journal of Algorithms
Offsetting operations in solid modelling
Computer Aided Geometric Design
Digital circles with non-lattice point centers
The Visual Computer: International Journal of Computer Graphics
On the recognition of digital circles in linear time
Computational Geometry: Theory and Applications
The linear time recognition of digital arcs
Pattern Recognition Letters
Fundamentals of surface voxelization
Graphical Models and Image Processing
Discrete analytical hyperplanes
Graphical Models and Image Processing
A linear algorithm for incremental digital display of circular arcs
Communications of the ACM
The Discrete Analytical Hyperspheres
IEEE Transactions on Visualization and Computer Graphics
Multigrid Convergence of Geometric Features
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Hausdorff Discretizations of Algebraic Sets and Diophantine Sets
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Digital disks and a digital compactness measure
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Discrete linear objects in dimension n: the standard model
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
An elementary algorithm for digital arc segmentation
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
The supercover of an m-flat is a discrete analytical object
Theoretical Computer Science
Exact offset procedures for simple solids
Computer Aided Geometric Design
Analytical description of digital circles
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Circular arc reconstruction of digital contours with chosen Hausdorff error
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
IEEE Transactions on Pattern Analysis and Machine Intelligence
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Arithmetic discrete hyperspheres and separatingness
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Separating Point Sets by Circles, and the Recognition of Digital Disks
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this paper we provide an analytical description of various classes of digital circles, spheres and in some cases hyperspheres, defined in a morphological framework. The topological properties of these objects, especially the separation of the digital space, are discussed according to the shape of the structuring element. The proposed framework is generic enough so that it encompasses most of the digital circle definitions that appear in the literature and extends them to dimension 3 and sometimes dimension n.