Calculation of the joint distribution of stack filters

Olli P. Yli-Harja

doi:10.1117/12.205209

28 March 1995 Calculation of the joint distribution of stack filters

Olli P. Yli-Harja

Proceedings Volume 2424, Nonlinear Image Processing VI; (1995) https://doi.org/10.1117/12.205209
Event: IS&T/SPIE's Symposium on Electronic Imaging: Science and Technology, 1995, San Jose, CA, United States

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.

Citation Download Citation

Olli P. Yli-Harja "Calculation of the joint distribution of stack filters", Proc. SPIE 2424, Nonlinear Image Processing VI, (28 March 1995); https://doi.org/10.1117/12.205209

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
6 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Digital filtering

Iterated function systems

Nonlinear filtering

Electronic filtering

Failure analysis

Reliability

Superposition

Show All Keywords

Keywords/Phrases

Search In:

Publication Years