Statistical evaluation of sequential morphological operations

In order to properly apply sequential morphological operations to random signals in applications concerned with noise suppression, the authors have examined their statistical properties using different structuring elements. The performance of flat and triangular structuring elements has been evaluated for signals with uniform, Gaussian, and Rayleigh density functions. In particular, the statistical properties of sequential morphological operations (i.e,, dilation, closing, clos-erosion, and clos-opening) are examined as a function of the parameters of the structuring element through Monte Carlo simulation, which overcomes the statistical dependency problem arising in the processed signal at different stages of morphological operations. The simulated results and their statistics (mean, variance, and skewness) present an interpretation of the signal root, biasing effects, and noise suppression capability of morphological filters