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A discrete geometry approach for dominant point detection

Thanh Phuong Nguyen 1 Isabelle Debled-Rennesson 1
1 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We propose two fast methods for dominant point detection and polygonal representation of noisy and possibly disconnected curves based on a study of the decomposition of the curve into the sequence of maximal blurred segments \cite{ND07}. Starting from results of discrete geometry \cite{FT99,Deb05}, the notion of maximal blurred segment of width $\nu$ \cite{ND07} has been proposed, well adapted to noisy curves. The first method uses a fixed parameter that is the width of considered maximal blurred segments. The second one is proposed based on a multi-width approach to obtain a non-parametric method that uses no threshold for working with noisy curves. Comparisons with other methods in the literature prove the efficiency of our approach. Thanks to a recent result \cite{FF08} concerning the construction of the sequence of maximal blurred segments, the complexity of the proposed methods is $O(n\log n)$. An application of vectorization is also given in this paper.
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Thanh Phuong Nguyen, Isabelle Debled-Rennesson. A discrete geometry approach for dominant point detection. Pattern Recognition, Elsevier, 2011, pp.32-44. ⟨inria-00526714⟩

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