Another generalisation of vector filters

A new generalisation of vector filters utilising the ordering of vector samples is provided. According to a distance function based on vector distances and vector angles, it is possible to differentiate vector median filters (VMFs), vector directional filters (VDFs) and finally directional distance filters (DDFs) that combine both distance and angles of vector samples in the vector space. For that reason, a class of DDFs represents a generalised class of vector filters. However, it will be shown that by introducing the weight vector to a DDF structure, all the above-mentioned filters, including their weighted structures, can be expressed as special cases of the proposed new class of weighted directional distance filters (WDDFs). Besides the theoretical acquisition, the proposed WDDFs provide a high design flexibility and these filters can be designed to achieve a significant improvement of the filter performance in comparison with standard vector filter classes.