Properties of binary statistical morphology

The properties and applications of a class of statistical morphological operators, i.e. binary statistical morphology (BSM) operators, for binary image processing are described. The proposed operators are based on quantization of the output of a statistical morphological operator, modeled as a binary probabilistic hypothesis-testing step. The operator obtained is shown to be equivalent to a rank-order filter. Relationships are established between the quantization threshold, rank of the equivalent rank-order filter and parameters of the model. It is also shown that basic BSM operators, i.e. binary statistical dilation and binary statistical erosion can be used as the basis for defining more complex filters. In this paper, attention is paid to describe specific properties of BSM operators which are useful for different applications, e.g. shape description