Rank order operators and the mean absolute error criterion

The author shows that among all randomizing stack filters whose output decisions are based on the sum of the bits in the window on each level of the threshold decomposition architecture, rank-order operators are optimal under an error criterion which is the sum of the absolute error incurred on each level of the threshold decomposition architecture. He also shows that if the filtering class being optimized obeys a deterministic stacking property, then the traditional multilevel mean absolute error criterion reduces to the sum of the absolute error incurred to each level. This leads to an efficient algorithm for choosing the rank-order filter which minimizes the multilevel mean absolute error criterion. >

[1]  Gonzalo R. Arce,et al.  BTC Image Coding Using Median Filter Roots , 1983, IEEE Trans. Commun..

[2]  Yong Hoon Lee,et al.  An edge gradient enhancing adaptive order statistic filter , 1986, IEEE Trans. Acoust. Speech Signal Process..

[3]  S. G. Tyan,et al.  Median Filtering: Deterministic Properties , 1981 .

[4]  Gonzalo R. Arce,et al.  Deterministic properties of the recursive separable median filter , 1987, IEEE Trans. Acoust. Speech Signal Process..

[5]  Arthur R. Butz.  A class of rank order smoothers , 1986, IEEE Trans. Acoust. Speech Signal Process..

[6]  Lawrence R. Rabiner,et al.  Applications of a nonlinear smoothing algorithm to speech processing , 1975 .

[7]  John W. Tukey,et al.  Nonlinear (nonsuperposable) methods for smoothing data , 1974 .

[8]  N. Gallagher,et al.  Two-dimensional root structures and convergence properties of the separable median filter , 1983 .

[9]  G. Wise,et al.  A theoretical analysis of the properties of median filters , 1981 .

[10]  Donald L. Snyder,et al.  Random point processes , 1975 .

[11]  N. Gallagher,et al.  An application of median filters to digital television , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  Petros Maragos,et al.  Morphological skeleton representation and coding of binary images , 1984, IEEE Trans. Acoust. Speech Signal Process..

[13]  Edward J. Coyle,et al.  Some convergence properties of median filters , 1986 .

[14]  Thomas S. Huang,et al.  A generalization of median filtering using linear combinations of order statistics , 1983 .

[15]  Gonzalo R. Arce,et al.  Theoretical analysis of the max/Median filter , 1987, IEEE Trans. Acoust. Speech Signal Process..

[16]  Petros Maragos,et al.  Morphological filters-Part II: Their relations to median, order-statistic, and stack filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[17]  E. Gilbert.  Lattice Theoretic Properties of Frontal Switching Functions , 1954 .

[18]  Petros Maragos,et al.  A unification of linear, median, order-statistics and morphological filters under mathematical morphology , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

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

[21]  G. Arce,et al.  State description for the root-signal set of median filters , 1982 .

[22]  Yong Hoon Lee,et al.  Generalized median filtering and related nonlinear filtering techniques , 1985, IEEE Trans. Acoust. Speech Signal Process..

[23]  Edward J. Coyle,et al.  Stack filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[24]  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..

[25]  Thomas S. Huang,et al.  The Effect of Median Filtering on Edge Estimation and Detection , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[26]  Edward J. Coyle,et al.  Root properties and convergence rates of median filters , 1985, IEEE Trans. Acoust. Speech Signal Process..

[27]  Alan C. Bovik,et al.  Edge detection using median comparisons , 1986, Comput. Vis. Graph. Image Process..

[28]  Yrjö Neuvo,et al.  FIR-median hybrid filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[29]  C. Peterson,et al.  MODE, MEDIAN, AND MEAN AS OPTIMAL STRATEGIES. , 1964, Journal of experimental psychology.

[30]  T. Nodes,et al.  Median filters: Some modifications and their properties , 1982 .