Discrete morphological size distributions and densities: estimation techniques and applications

Abstract

Morphological size distributions and densities are frequently used as descriptors of granularity or texture within an image. They have been successfully employed in a number of image processing and analysis tasks, including shape analysis, multiscale shape representation, texture classification, and noise filtering. In most cases however it is not possible to analytically compute these quantities. In this paper, we study the problem of estimating the (discrete) morphological size distribution and density of random images, by means of empirical as well as Monte Carlo estimators. Theoretical and experimental results demonstrate clear superiority of the Monte Carlo estimation approach. Examples illustrate the usefulness of the proposed estimators in traditional image processing and analysis problems.