Robustness of granulometric moments

摘要

Granulometric moments are used for classification of random sets and estimation of their parameters. These moments are random variables possessing their own probability distributions. For certain random sets composed of nonoverlapping 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 being known for all grain primitives generating the random set. This paper investigates model robustness by considering the effects of the following violations of the assumptions: (1) assuming an incorrect sizing distribution, (2) using erroneous parameters for the sizing distribution, and (3) prior segmentation when there is modest overlapping. The last situation occurs because the paper proposes segmentation prior to granulometric analysis when there is modest overlapping. Both nonreconstructive and reconstructive granulometries are investigated in the case of prior segmentation.