Non-local length estimators and concave functions

Abstract : In a previous work [5], the authors introduced the Non-Local Estimators (NLE), a wide class of polygonal estimators including the sparse estimators and a part of the DSS ones. NLE are studied here under concavity assumption and it is shown that concavity almost doubles the multigrid converge rate w.r.t. the general case. A parabola reaching the obtained error bound is exhibited. Moreover, the notion of biconcavity relative to a NLE is proposed to describe the case where the digital polygone is also concave. An example is given to show that concavity does not imply biconcavity. Then, an improved error bound is computed under the biconcavity assumption.
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Loïc Mazo, Étienne Baudrier. Non-local length estimators and concave functions. Theoretical Computer Science, Elsevier, 2017, Volume 690, pp.73-90. ⟨10.1016/j.tcs.2017.06.005⟩. ⟨hal-01346909v2⟩

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