Digital Filters Based On Threshold Decomposition And Boolean Functions

In this paper we discuss certain limitations which are inherent in filters that are based on threshold decomposition and Boolean functions. We also define a generalization of stack filters by dropping the requirement of positivity in the defining Boolean function. We show that while some of the nice properties of stack filters are lost the extra design freedom makes it possible to construct filters which have certain attractive properties that are not attainable with stack filters.

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

[2]  Saburo Muroga,et al.  Threshold logic and its applications , 1971 .

[3]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

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

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

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