Fréchet filters for color and hyperspectral images filtering

Abstract

Median filtering has been widely used in scalar-valued image processing as an edge preserving operation. The basic idea is that the pixel value is replaced by the median of the pixels contained in a window around it. In this paper, we extend the notion of the Fréchet vector median to the general Fréchet vector median, which minimizes the Fréchet cost function (FCF) in the form of an aggregation function instead of the ordinary sum. Moreover, we propose to use an aggregation distance instead of the classical one. We use the generalized Fréchet median for constructing new nonlinear filters based on an arbitrary pair of aggregation operators that can be changed independently. For each pair of parameters, we get the unique class of new nonlinear filters.