
AbstractThe threshold logic filter is an important nonlinear filter class, which is defined by a threshold logic function of binary input values. It is proved in this paper that not all positive selfdual logical functions are threshold functions if the number of input variables is 5 or more. The positive selfdual logical filter is a limited class but includes almost all filters for noise removal. Our result means that not all positive selfdual filters can be expressed by one operation of the threshold logic filters. In the sense of the filter expression by neural networks, the twolayer network cannot always optimize even this limited class. Keywordsimage processing filters, logical filters, threshold logic, linear separability, positive selfdual logic, neural network 