## Shape classification based on interpoint distance distributions

- José R. Berrendero, Antonio Cuevas, Beatriz Pateiro-López
- J. Multivariate Analysis
- 2016

@inproceedings{Averkov200730N, title={3 0 N ov 2 00 7 Confirmation of Matheron ’ s Conjecture on the Covariogram of a Planar Convex Body}, author={Gennadiy Averkov and Gabriele Bianchi}, year={2007} }

- Published 2007

The covariogram gK of a convex body K in E d is the function which associates to each x ∈ E d the volume of the intersection of K with K + x. In 1986 G. Matheron conjectured that for d = 2 the covariogram gK determines K within the class of all planar convex bodies, up to translations and reflections in a point. This problem is equivalent to some problems in stochastic geometry and probability as well as to a particular case of the phase retrieval problem in Fourier analysis. It is also… CONTINUE READING