Math Geosci (2012) 44:805–822 DOI 10.1007/s11004-012-9405-6 Using Two-Point Set Statistics to Estimate the Diameter Distribution in Boolean Models with Circular Grains Xavier Emery · Willy Kracht · Álvaro Egaña · Felipe Garrido Received: 4 January 2012 / Accepted: 17 April 2012 / Published online: 10 May 2012 © International Association for Mathematical Geosciences 2012 Abstract This paper deals with the counting and measuring of overlapping circular objects in binary images, a problem that arises in the mineral processing industry when estimating the distribution of bubble diameters in flotation cells in order to predict the geometallurgical performance of the flotation process. By viewing the images as realizations of a stationary planar Boolean model with circular grains and by using two-point set statistics, it is possible to jointly estimate the average number of objects per unit area and their diameter distribution. When applied to real and simulated images, this method is shown to give accurate estimates, to be robust to the presence of noise contaminating the images and of moderate drifts in the number of objects per unit area, and to speed up the processing time with respect to currently used methods. Combined, these properties serve to make the method suitable for an on-line monitoring of the flotation process. Keywords Overlapping disc modeling · Geometric covariogram · Circular covariogram · Random closed set X. Emery ( ) · W. Kracht Department of Mining Engineering, University of Chile, Santiago, Chile e-mail: xemery@ing.uchile.cl W. Kracht e-mail: wkracht@ing.uchile.cl X. Emery · W. Kracht · Á. Egaña · F. Garrido Advanced Mining Technology Center, University of Chile, Santiago, Chile Á. Egaña e-mail: aegana@amtc.cl F. Garrido e-mail: fgarrido@amtc.cl