Need more control over your median filter? This paper introduces the Weighted Median Filter, a generalization of the standard median filter that offers users more flexibility in predefining feature types to be removed or retained. This filter is designed to overcome the limitations of the traditional median filter when specific requirements must be met. The paper discusses various filter requirements and derives corresponding filters. It introduces the concept of a minimal weighted median filter within a subclass that acts identically and explores methods for determining the number of distinct ways a class of filters can act. This exploration provides valuable tools and insights for signal processing and image analysis applications, enabling more tailored and effective filtering solutions. It enhances capabilities of working with data.
Published in Communications of the ACM, this paper addresses fundamental aspects of computer science and signal processing. The introduction of the weighted median filter and the analysis of its properties align with the journal’s focus on algorithms and data structures. The work contributes to the broader understanding of filtering techniques used in various computational applications.