A discrete geometry approach for dominant point detection

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 [2]. Starting from results of discrete geometry [3,4], the notion of maximal blurred segment of width ν [2] has been proposed, well adapted to possibly noisy curves. The first method uses a fixed parameter that is the width of considered maximal blurred segments. The second method is deduced from the first one 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 [5] 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.