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Proceedings Paper

Calculation of the joint distribution of stack filters
Author(s): Olli P. Yli-Harja
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Paper Abstract

In this paper it is shown how to calculate the joint distribution function of two different stack filters sharing the same arguments. The input signal is modeled as a sequence of independent, but not necessarily identical, random variables. Supposing that the input signal is filtered with stack filter, we apply the derived formula to find the joint distribution function of any two samples in the output signal. In the paper we first go through the derivation of the formula starting with real-valued stack filters and the definition of the joint distribution function of their outputs. After that we change into binary domain where the enumeration of the possible cases turns out to be quite a straightforward task. It also allows reasonably compact expression of the final formula. The joint distribution formula for stack filters has many possible applications. For example it allows the analytic computation of the autocorrelation functions of these filters. It may also be useful in system reliability studies where the failure of a system is derived as a function of its components states. Often this function can be composed of solely min- and max-operations, i.e., it possesses the weak superposition property called stack decomposition. The paper includes interesting examples where the joint distribution function is obtained in a particularly neat form. Also a special symmetry class of stack filters is characterized.

Paper Details

Date Published: 28 March 1995
PDF: 6 pages
Proc. SPIE 2424, Nonlinear Image Processing VI, (28 March 1995); doi: 10.1117/12.205209
Show Author Affiliations
Olli P. Yli-Harja, Helsinki Univ. of Technology (Finland)


Published in SPIE Proceedings Vol. 2424:
Nonlinear Image Processing VI
Edward R. Dougherty; Jaakko T. Astola; Harold G. Longbotham; Nasser M. Nasrabadi; Aggelos K. Katsaggelos, Editor(s)

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