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Convergence properties of median and weighted median filters

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1 Author(s)
Bing Zeng ; Dept. of Electr. & Electron. Eng., Hong Kong Univ. of Sci. & Technol., Kowloon, Hong Kong

It has been shown that assuming the first and last value carry-on appending strategy, a finite number of passes of the same median filter to an arbitrary signal of finite length results in a root signal that will be invariant to additional filtering passes. This so-called convergence property is reproven using an extremely simple approach. In addition, the well-known idempotent property (i.e., where convergence is achieved with only one filtering pass) of a recursive median filter is reproven similarly, and the convergence behavior of weighted median filters is studied

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Signal Processing, IEEE Transactions on  (Volume:42 ,  Issue: 12 )