Journal ArticleDOI
Median filtering by threshold decomposition
TLDR
It is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals, filtering each binary signal to a root with a binary median filter, and then reversing the decomposition.Abstract:
Median filters are a special class of ranked order filters used for smoothing signals Repeated application of the filter on a quantized signal of finite length ultimately results in a sequence, termed a root signal, which is invariant to further passes of the median filter In this paper, it is shown that median filtering an arbitrary level signal to its root is equivalent to decomposing the signal into binary signals, filtering each binary signal to a root with a binary median filter, and then reversing the decomposition This equivalence allows problems in the analysis and the implementation of median filters for arbitrary level signals to be reduced to the equivalent problems for binary signals Since the effects of median filters on binary signals are well understood, this technique is a powerful new toolread more
Citations
More filters
Journal ArticleDOI
Morphological filters--Part I: Their set-theoretic analysis and relations to linear shift-invariant filters
Petros Maragos,R. Schafer +1 more
TL;DR: The representation of classical linear filters in terms of morphological correlations, which involve supremum/infimum operations and additions, are introduced and demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal-shaping strategies.
Journal ArticleDOI
Weighted median filters: a tutorial
TL;DR: Weighted median (WM) filters have the robustness and edge preserving capability of the classical median filter and resemble linear FIR filters in certain properties as discussed by the authors, which enables the use of the tools developed for the latter class in characterizing and analyzing the behavior and properties of WM filters.
Journal Article
Stack filters
TL;DR: This investigation of the properties of stack filters produces several new, useful, and easily implemented filters, including two which are named asymmetric median filters.
Journal ArticleDOI
From Boolean to probabilistic Boolean networks as models of genetic regulatory networks
TL;DR: The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions and its relationships to nonlinear digital filters.
Journal ArticleDOI
Morphological filters--Part II: Their relations to median, order-statistic, and stack filters
Petros Maragos,R. Schafer +1 more
TL;DR: This paper extends the theory of median, order-statistic (OS), and stack filters by using mathematical morphology to analyze them and by relating them to those morphological erosions, dilations, openings, closings, and open-closings that commute with thresholding.
References
More filters
Journal ArticleDOI
A theoretical analysis of the properties of median filters
Neal C. Gallagher,G. Wise +1 more
TL;DR: In this article, the authors derived necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering and proved that the form of successive median filtering of a signal (i.e., the filtered output is itself again filtered) eventually reduces the original signal to an invariant signal called a root signal.
Journal ArticleDOI
Median filters: Some modifications and their properties
T. Nodes,Neal C. Gallagher +1 more
TL;DR: It is proved that the output of a recursive median filter is invariant to subsequent passes by the same filter and that for nonmedian nth ranked-order operations, repeated application of the operation will reduce any signal to a constant.
Journal ArticleDOI
Applications of a nonlinear smoothing algorithm to speech processing
TL;DR: A nonlinear smoothing algorithm recently proposed by Tukey is described and evaluated for speech processing applications and the concept of double smoothing is introduced as a refinement on the smoothing algorithms.
Journal ArticleDOI
State description for the root-signal set of median filters
TL;DR: A tree structure for the root signal set of median filters, where signals invariant to median filters are called roots of the signal, is obtained for binary signals.
Journal ArticleDOI
Root properties and convergence rates of median filters
TL;DR: The theory is developed both for determining the cardinality of the root signal space of arbitrary window width filters applied to signals with any number of quantization levels and for counting or estimating the number of passes required to produce a root for binary signals.