Vector median-rational hybrid filters

Abstract

New class of nonlinear filters called Vector Median Rational Hybrid Filters (VMRHF) for multispectral image processing was introduced and applied to color image filtering problem. These filters are based on Rational Functions (RF). There are several advantages to the use of this function. First, it is a universal approximator and a good extrapolator. Second, it can be trained by a linear adaptive algorithm. Third, it has a best approximation for a specified function. The output is the result of vector rational operation taking into account three sub-functions, such as two vector median (VM) sub- filters and one center weighted vector median filter (CWVMF). It was shown that every sub-function will preserve details within its sub-window. These filters exhibit desirable properties, such as, edge and details preservation and accurate chromaticity estimation. The performance of the proposed filter is compared against widely known nonlinear filters for multispectral image processing such as: Vector median filters (VMF) introduced by Astola et al, which are derived as maximum likelihood (ML) estimates from exponential distributions, the class of directional-distance filters (DDF) introduced to study the processing of color image data using directional information. Experimental and comparative results in color image filtering show very good performance measures when the error is measured in the L*a*b* space. L*a*b* is know as a space where equal color differences result in equal distances, and therefore, it is close to the human perception of colors.