ABSTRACT
Stack filters are nonlinear filters that are defined via threshold decomposition and positive Boolean functions. An attractive property of stack filters is that it is possible to derive analytical results for their statistical properties. The concept of a positive Boolean function indexed by a set plays a key role when we study the connection between stack and morphological filters. An advantage of expressing cascaded operations as a single stack filter is that it is then possible to derive analytical results for the statistical properties of the filtering operations. In general, the statistical properties of morphological filters depend on both the shape and the size of the structuring set. Median-type filters have their roots in statistical estimation theory, and their analysis can be satisfactorily carried out using standard methods in statistics. To understand the filtering process, it is desirable to determine the output distribution in terms of the input distributions.
