Predicting expected gray level statistics of opened signals

The opening of a model signal with a convex, zero-height structuring element is studied empirically. Experiments are performed in which the input signal model parameters and the opening length are varied over an acceptable range and the corresponding grey level distributions in the opened signal are fit to Pearson distributions. Regressions are then used to relate the Pearson distribution parameters to the input parameters, resulting in equations that may be used to predict the effect of an opening. Characterization experiments show that the maximum absolute errors between actual and predicted cumulative distributions using these regression equations have a mean of 0.036 and a standard deviation of 0.011 (for a range of zero to one); the worst-case maximum absolute error encountered between the cumulative distributions is 0.066