Robustness of granulometric moments

Granulometric moments are used for classification of random sets and estima tion of their parameters. These moments are random variables possessing the ir own probability distributions. For certain random sets composed of nonov erlapping grains, there are expressions for the granulometric moments, the moments are asymptotically normal, and their asymptotic means and variances are known. All representations depend on the grain sizing distributions be ing known for all grain primitives generating the random set. This paper in vestigates model robustness by considering the effects of the following vio lations of the assumptions: (1) assuming an incorrect sizing distribution, (2) using erroneous parameters for the sizing distribution, and (3) prior s egmentation when there is modest overlapping. The last situation occurs bec ause the paper proposes segmentation prior to granulometric analysis when t here is modest overlapping. Both nonreconstructive and reconstructive granu lometries are investigated in the case of prior segmentation. (C) 1999 Patt ern Recognition Society. Published by Elsevier Science Ltd. All rights rese rved.