On the Number of Digital Straight Line Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fractals everywhere
On the number of factors of Sturmian words
Theoretical Computer Science
Frequencies of Sturmian series factors
Theoretical Computer Science
Discretization in Hausdorff Space
Journal of Mathematical Imaging and Vision
Topological properties of Hausdorff discretization, and comparison to other discretization schemes
Theoretical Computer Science
Discrete Applied Mathematics
Patterns in discretized parabolas and length estimation
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Theoretical Computer Science
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In this paper we investigate some properties of digital segments in floor and Hausdorff discretizations. We characterize the Hausdorff discretization of straight lines and we prove that the frequency of digital segment in a digital straight line is continuous and piecewise affine function relatively to the slope. It allows to prove some combinatorial properties of digital segments. In particular we give a new proof of the results in [3,2,8] corresponding to the frequencies and the numbers of digital segments of size m.