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On the problem of granulometry for a degraded Boolean image model

We consider a geometric coverage process consisting of a random number of disks, or grains, having random radii and positions in the plane. Our objective is granulometry: estimation of a parameter of the disk radius distribution, which is important in diverse applications such bio-assay, ballistics, and numerical taxonomy. These disks are only incompletely observed due to mutual occlusion, spatial blurring and additive noise. We use a measurement channel paradigm to derive an expectation-maximization (EM) type estimation algorithm and a distortion-rate lower bound on estimation error.