Jordan decomposition filters

In this paper we propose a new class of filters called Jordan decomposition filters. They are upper and lower bounds of the well-known max and min filters. Our approach is based on a decomposition scheme by representing bounded variation signals as a difference of two increasing functions. Jordan filters are computed as the difference between the local extrema values of the increasing functions. They are faster than max/min filters. The number of operations per sample is constant, regardless the size of the window filter. The computational complexity of the proposed filters decreases with the number of filtering steps needed in an application. Examples are provided and the application in contrast enhancement is investigated