Abstract
In this paper, we present some deterministic properties of separable and cross median filters. It is proved that in the absence of vertical binary oscillations, the roots of a separable median filter are included in a subset of root signals of the corresponding cross median filter. Moreover, the sufficient and necessary condition is given for a point to be invariant to cross median filtering. On the root structures of cross median filters, we indicate that there exist three different types of regions based on the one-dimensional features of rows and columns. Finally, an application example is discussed where the roots of separable and cross median filters are used in block truncation coding (BTC) for image compression.
Similar content being viewed by others
References
B.I. Justusson, “Median Filtering: Statistical Properties,” inTopics in Applied Physics, Two-Dimensional Digital Signal Processing II, T.S. Huang, ed., Berlin: Springer, pp. 161–196, 1981.
S.G. Tyan, “Median Filtering: Deterministic Properties,” inTopics in Applied Physics, Two-Dimensional Digital Signal Processing II. T.S. Huang, ed., Berlin: Springer, pp. 197–217, 1981.
N.C. Gallagher, Jr., and G.L. Wise, “A Theoretical Analysis of the Properties of Median Filters,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-29, pp. 1136–1141, 1981.
J.P. Fitch, E.J. Coyle, and N.C. Gallagher, Jr., “Root Properties and Convergence Rates of Median Filters,”IEEE Transaction on Acoustics, Speech, and Signal Processing, vol. ASSP-33, pp. 230–240, 1985.
J. Astola, P. Heinonen, and Y. Neuvo, “On Root Structures of Median and Median-Type Filters,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-35, pp. 1199–1201, 1987.
T.A. Nodes and N.C. Gallagher, Jr., “Median Filters: Some Modifications and Their Properties,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-30, pp. 739–746, 1982.
P.M. Narendra, “A Separable Median Filter for Image Noise Smoothing,”IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-3, pp. 20–29, 1981.
T.A. Nodes and N.C. Gallagher, “Two-Dimensional Root Structures and Convergence Properties of the Separable Median Filter,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-31, pp. 1350–1365, 1983.
M.P. McLoughlin and G.R. Arce, “Deterministic Properties of the Recursive Separable Median Filter,”IEEE Transactions on Acoustic, Speech, and Signal Processing, vol. ASSP-35, pp. 98–106, 1987.
G. Liao, T.A. Nodes, and N.C. Gallagher, Jr., “Output Distributions of Two-Dimensional Median Filters,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-33, pp. 1280–1295, 1985.
G.R. Arce and M.P. McLoughlin, “Theoretical Analysis of the Max/Median Filter,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-35, pp. 60–69, 1987.
Q. Wang and Y. Neuvo, “On Two-Dimensional Root Structures of Separable and Cross Median Filters,” inProc. 1991 Int. Symp. Circuits and Systems, Singapore, pp. 104–107, 1991.
Q. Wang and Y. Neuvo, “Application of Median-Type Filtering to Image Segmentation in Electrophoresis,” inProc. SPIE/SPSE Conf. Biomedical Image Processing II, San Jose, CA, pp. 47–58, 1991.
H.U. Döhler, “Generation of Root Signals of Two-Dimensional Median Filters,”Signal Processing, vol. 18, pp. 269–276, 1989.
E.J. Delp and O.R. Mitchell, “Image Compression Using Block Truncation Coding,”IEEE Transactions on Communications, vol. COM-27, pp. 1335–1342, 1979.
G.R. Arce and N.C. Gallagher, “BTC Image Coding Using Median Filter Roots,”IEEE Transactions on Communications, vol. COM-31, pp. 784–793, 1983.
G.R. Arce and N.C. Gallagher, “State Description for the Root-Signal Set of Median Filters,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-30, pp. 894–902, 1982.
B. Zeng, Q. Wang, and Y. Neuvo, “BTC Image Coding Using Two-Dimensional Median Filter Roots,” inProc., 1991 Int. Symp. Circuits and Systems, Singapore, pp. 400–403, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, Q., Neuvo, Y. Deterministic properties of separable and cross median filters with an application to block truncation coding. Multidim Syst Sign Process 4, 23–38 (1993). https://doi.org/10.1007/BF00986004
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00986004