Order Statistic-Based Nonlinear Filters: Stack Filters and Weighted Median Filters

Since the introduction of the median filter by John Tukey in 1971, many important classes of order statistic-based nonlinear filters have been developed. In this paper we review some recent results obtained for the two filter classes known as stack filters and weighted median filters. The highlights include new results on optimal filter design and fast training algorithms.

[1]  Sung-Jea Ko,et al.  Center weighted median filters and their applications to image enhancement , 1991 .

[2]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  M. K. Prasad,et al.  Weighted median filters: generation and properties , 1989, IEEE International Symposium on Circuits and Systems,.

[4]  Robert M. Haralick,et al.  Morphologic edge detection , 1987, IEEE J. Robotics Autom..

[5]  Jaakko Astola,et al.  Analysis of the properties of median and weighted median filters using threshold logic and stack filter representation , 1991, IEEE Trans. Signal Process..

[6]  Moncef Gabbouj,et al.  Deterministic Properties of Center Weighted Median Filters , 1992 .

[7]  Moncef Gabbouj,et al.  Optimal stack filtering and the estimation and structural approaches to image processing , 1989, Sixth Multidimensional Signal Processing Workshop,.

[8]  Moncef Gabbouj,et al.  2-D Optimal Weighted Median Filters , 1992 .

[9]  Edward J. Coyle,et al.  Threshold decomposition of multidimensional ranked order operations , 1985 .

[10]  M. Braga,et al.  Exploratory Data Analysis , 2018, Encyclopedia of Social Network Analysis and Mining. 2nd Ed..

[11]  Ioannis Pitas,et al.  Edge Detectors Based on Nonlinear Filters , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Moncef Gabbouj,et al.  Optimal weighted order statistic filters under structural constraints , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[13]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[14]  Charles A. Bouman,et al.  The Nonlinear Prefiltering and Difference of Estimates Approaches to Edge Detection: Applications of Stack Filters , 1993, CVGIP Graph. Model. Image Process..

[15]  Moncef Gabbouj,et al.  Median Based Idempotent filters , 1991, J. Circuits Syst. Comput..

[16]  Edward J. Coyle,et al.  Stack filters and the mean absolute error criterion , 1988, IEEE Trans. Acoust. Speech Signal Process..

[17]  M. Gabbouj,et al.  Optimal weighted median filters under structural constraints , 1993, 1993 IEEE International Symposium on Circuits and Systems.

[18]  Moncef Gabbouj,et al.  Center weighted median filters: Some properties and their applications in image processing , 1994, Signal Process..

[19]  Petros Maragos,et al.  Morphological filters-Part I: Their set-theoretic analysis and relations to linear shift-invariant filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[20]  Ioannis Pitas,et al.  Nonlinear Digital Filters - Principles and Applications , 1990, The Springer International Series in Engineering and Computer Science.

[21]  Moncef Gabbouj,et al.  Image Restoration by One-Dimensional Adaptive Center Weighted Median Filters , 1993 .

[22]  J. Fitch,et al.  Median filtering by threshold decomposition , 1984 .

[23]  Edward J. Coyle,et al.  Adaptive stack filtering under the mean absolute error criterion , 1990, Other Conferences.

[24]  M. K. Prasad,et al.  Analysis of weighted median filters based on inequalities relating the weights , 1992 .

[25]  Jaakko Astola,et al.  Optimal weighted order statistic filters under the mean absolute error criterion , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[26]  Azriel Rosenfeld,et al.  A Note on the Use of Local MIN and MAX Operations in Digital Picture Processing , 1977 .

[27]  N. Gallagher,et al.  An overview of median and stack filtering , 1992 .