Statistical Characterization of Morphological Operator Sequences

Detection followed by morphological processing is commonly used in machine vision. However, choosing the morphological operators and parameters is often done in a heuristic manner since a statistical characterization of their performance is not easily derivable. If we consider a morphology operator sequence as a classifier distinguishing between two patterns, the automatic choice of the operator sequence and parameters is possible if one derives the misclassification distribution as a function of the input signal distributions, the operator sequence, and parameter choices. The main essence of this paper is the illustration that misclassification statistics, the distribution of bit errors measured by the Hamming distance, can be computed by using an embeddable Markov chain approach. License plate extraction is used as a case study to illustrate the utility of the theory on real data.