A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance
Isabelle Sivignon
→ BibTeX
@article{ipol.2014.70,
    title   = {{A Near-Linear Time Guaranteed Algorithm for Digital Curve
Simplification Under the Fréchet Distance}},
    author  = {Sivignon, Isabelle},
    journal = {{Image Processing On Line}},
    volume  = {4},
    pages   = {116--127},
    year    = {2014},
    doi     = {10.5201/ipol.2014.70},
}
% if your bibliography style doesn't support doi fields:
    note    = {\url{https://doi.org/10.5201/ipol.2014.70}}
published
2014-05-22
reference
Isabelle Sivignon, A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification Under the Fréchet Distance, Image Processing On Line, 4 (2014), pp. 116–127. https://doi.org/10.5201/ipol.2014.70

Communicated by Bertrand Kerautret
Demo edited by Bertrand Kerautret

Abstract

In this paper, we propose an algorithm that, from a maximum error and a digital curve (4- or 8-connected), computes a simplification of the curve (a polygonal curve) such that the Fréchet distance between the original and the simplified curve is less than the error. The Fréchet distance is known to nicely measure the similarity between two curves. The algorithm we propose uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in O(n log(n)), experiments show a linear behaviour in practice.

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