Morphological modeling of images by sequential random functions

Abstract After a brief reminder of the Mathematical Morphology (MM) tools used to characterize Random Closed Sets (RACS) and random functions (RF), the construction of sequential RF models with support in R ″ is developed. For each point x in R ″, the models combine families of independent RF, indexed by a parameter t , in different ways: masking, taking the supremum or the infinum of observed values, adding. By the masking process, the sequential RF with Markovian jumps and the Dead Leaves Functions models simulate random images with objects in the foreground partially masking objects in the background, as seen in perspective views. The other constructions of RF give, among other, the ∨ and the ∧ Boolean RF, and the Dilution RF. The main properties and the main distribution functions of the models (e.g. statistical behavior of the RF under the non-linear operations provided by dilation or erosion) are presented. These models illustrate the MM approach for random structure modeling.