Linear combinations of morphological operators: the midrange, pseudomedian, and LOCO filters

It is shown how linear combinations of morphological operators can be formed to alleviate the bias introduced by the individual morphological operators. Since every morphological operator has a complementary operator that is equally and oppositely biased, the authors 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, called the LOCO filter. Under most conditions, the LOCO filter is the best of these at reducing impulses and noise., Linear combinations of morphological operators allow the shape control of the morphological filters (exerted by the selection of a structuring element) without introducing bias. For example, the LOCO filter with a square structuring element preserves 90 degrees corners in an image while reducing noise almost as well as the square-shaped medium filter, which rounds off such corners.<>