On the Number of Digital Straight Line Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric interpretation of Euclid's algorithm and recognition of segments
Theoretical Computer Science
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Approximating a real number by a rational number with a limited denominator: A geometric approach
Discrete Applied Mathematics
On digital plane preimage structure
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Computing the characteristics of a subsegment of a digital straight line in logarithmic time
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Discrete Representation of Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
The number of digital straight lines on an N×N grid
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
Given a Digital Straight Line (DSL) of known characteristics (a,b,μ), we address the problem of computing the characteristics of any of its subsegments. We propose a new algorithm as a smart walk in the so called Farey Fan. We take profit of the fact that the Farey Fan of order n represents in a certain way all the digital segments of length n. The computation of the characteristics of a DSL subsegment is then equivalent to the localization of a point in the Farey Fan. Using fine arithmetical properties of the fan, we design a fast algorithm of theoretical complexity $\mathcal{O}(\log(n))$ where n is the length of the subsegment. Experiments show that our algorithm is faster than the one previously proposed by Said and Lachaud in [15,14] for "short" segments.