The weighted median filter

ABSTRACT

The median filter is well-known [1, 2]. However, if a user wishes to predefine a set of feature types to remove or retain, the median filter does not necessarily satisfy the requirements. A more general filter, called the Weighted Median Filter, of which the median filter is a special case, is described. It enables filters to be designed with a wide variety of properties. Particular cases of filter requirements are discussed and the corresponding filters are derived. The notion of a minimal weighted median filter, of a subclass that act identically, is introduced and discussed. The question of finding the number of distinct ways a class of filters can act is considered and solved for some classes.

REFERENCES

• 1: Tukey. J.W. Exploratory Data Analysis. Addison-Wesley, Reading, Mass., 1974.
• 2: William K. Pratt, Digital image processing, John Wiley & Sons, Inc., New York, NY, 1978
• 3: Stobie, R.S. Royal Observatory Edinburgh, internal publication, 1981.
• 4: Martin, R., and Lulz, R.K. Background following on Schmidt plates using a digital filtering technique. International Workshop on Image Processing in Astronomy, Proceedings 5th. Coll. on Astrophysics, Trieste, 1979.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.5 PATTERN RECOGNITION
      I.5.4 Applications
          Subjects: Signal processing

Additional Classification:
  C. Computer Systems Organization
  C.3 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS
      Subjects: Signal processing systems

  I. Computing Methodologies
  I.4 IMAGE PROCESSING AND COMPUTER VISION
      I.4.3 Enhancement
          Subjects: Filtering

General Terms:
Design, Performance, Theory

Keywords:
backgrounding, feature removal and retention, median filters, weighted median filters