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GIULIANA D'ERCOLE
Docente a contratto Dipartimento di Ingegneria "Enzo Ferrari"
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Pubblicazioni
2007
- An algorithm for reconstructing a convex polygon from its covariogram
[Articolo su rivista]
Benassi, Carlo 6/8/1962; D'Ercole, Giuliana
abstract
The covariogram $g_{K}(x)$ of a convex body $K$ gives the volume of the intersections of $K$ with its translates $K+x$. Matheron conjectured in 1986 that the covariogram determines, up to translations and reflections, a convex body. Recently, Averkov and Bianchi proved Matheron's conjecture for arbitrary planar convex bodies. In this work, the authors give a new algorithm for reconstructing a convex polygon given its covariogram. This algorithm simplifies another one given in [M. Schmitt, in Mathematical morphology in image processing, 151--169, Dekker, New York, 1993].