Computational geometry: an introduction
Computational geometry: an introduction
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Coding of digital straight lines by continued fractions
Computers and Artificial Intelligence
A parametrization of digital planes by least-squares fits and generalizations
Graphical Models and Image Processing
Discrete representation of spatial objects in computer vision
Discrete representation of spatial objects in computer vision
Convexity rule for shape decomposition based on discrete contour evolution
Computer Vision and Image Understanding
Geometrische Transformationen in der diskreten Ebene
Mustererkennung 1989, 11. DAGM-Symposium
Perceptrons: An Introduction to Computational Geometry
Perceptrons: An Introduction to Computational Geometry
Digital Straight Line Segments
IEEE Transactions on Computers
What Does Digital Straightness Tell about Digital Convexity?
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Digital Steiner sets and Matheron semi-groups
Image and Vision Computing
Convex functions on discrete sets
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Optimal covering of a straight line applied to discrete convexity
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Fast recursive grayscale morphology operators: from the algorithm to the pipeline architecture
Journal of Real-Time Image Processing
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Euclidean geometry on a computer is concerned with the translation of geometric concepts into a discrete world in order to cope with the requirements of representation of abstract geometry on a computer. The basic constructs of digital geometry are digital lines, digital line segments and digitally convex sets. The aim of this paper is to review some approaches for such digital objects. It is shown that digital objects share much of the properties of their continuous counterparts. Finally, it is demonstrated by means of a theorem due to Tietze (1929) that there are fundamental differences between continuous and discrete concepts.