Linear Combinations of Morphological Operators: the Midrange, Pseudomedian, and Loco Filters

Morphological image processing filters preserve shapes related to the structuring element shape of the operator. The basic morphological operators are minimum (erosion) and maximum (dilation) operations performed on the pixels within a structuring element. Although these operators (and the compound operators formed from them) are able to smooth noise, they also introduce a statistical and deterministic bias, which is unacceptable in some applications. However, since every morphological operator has a complementary operator that is equally and oppositely biased, we propose averaging the complementary operators to alleviate the bias. Of the three filters formed by averaging the standard morphological operators, two are the previously-defined midrange filter and pseudomedian filter, while one is a new filter, which we call the LOCO filter. Under most conditions, the LOCO filter is the best of these at reducing impulses and noise.