Abstract: Adaptation of an opening possessing a multiparameter structuring element is studied in the context of Markov chains by treating the multiple parameters as a vector r defining the state of the system and considering the operative filter $Lambda$-r$/ to be opening by reconstruction. Adaptation of $Lambda$-r$/ (transition of r) is in accordance to whether or not $Lambda$-r$/ correctly or incorrectly passes signal and noise grains sampled from the image. Signal and noise are modeled as unions of randomly parameterized and randomly translated primary grains. Transition probabilities are discussed for two adaptation protocols and the state- probability increment equations are deduced from the appropriate Chapman-Kolmogorov equations. Adaptation convergence is characterized by the steady-state distributions of the Markov chains and these are computed numerically. !6
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