Center weighted median filters: Some properties and their applications in image processing
Abstract: Several deterministic properties of center weighted median (CWM) filters are analyzed in this paper. The root structures of CWM filters are derived. A test is devised to check whether a signal is a root of a given CWM filter. The convergence behaviour of recursive and nonrecursive CWM filters is then analyzed. In particular, based on their root structures, it is proven that repeated filtering on any appended finite length signal by any CWM filter produces roots in a finite number of filter passes. A synthesis method of CWM filters under structural constraints is presented. A separable CWM filter is proposed as an application of one-dimensional CWM filters in image processing. It is expected that by using CWM filters, more details can be preserved along the horizontal and vertical directions. Adaptive separable CWM filters are then proposed. We show that they can be better than two-dimensional adaptive CWM filters with the same window size in some cases. Adaptive CWM filters are then extended to adaptive symmetric weighted median filters.
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