Iterative Behavior Of Symmetric Weighted Threshold Filter For Bounded Sequences With Infinite Support
نویسنده
چکیده
The symmetric weighted median filter is a natural extension of the median filter and has the same advantages as the median filter: edge preservation and efficient suppression of impulsive noise [1]. The symmetric weighted threshold filter is a generalization of the symmetric weighted median filter. It is natural to iterate the symmetric weighted threshold filter in order to reduce the noise still further. An interesting question to be asked is what iterative behavior the the symmetric weighted threshold filter has if we apply iteratively the symmetric weighted threshold filter to a fixed sequence. For sequences with finite support, it was shown that the iterated sequences of the symmetric threshold automaton converges or gets trapped in a periodic orbit of period 2 ([2,3]). P. D. Wendt [4] applied the fact to analyze the iterative behavior of stack filters and proposed a method to transform a symmetric weighted threshold filter into a symmetric threshold automaton if this symmetric weighted threshold filter preserves roots of median filter. But for sequences with infinite the method above does not work. In this paper, for bounded sequences with infinite support, we give a thorough answer to the question. On one hand, in our result we cancel the restrictive condition for symmetric weighted threshold filter to preserve roots of median filter. On the other hand, a sequence with finite support may be transferred into a sequence with infinite support by appending two ends of the original sequence or by expending periodically the original sequence. Specifically, for the original sequence with finite support xL = {xL(1), xL(2), · · · , xL(L)}, the corresponding sequence with infinite support x = {x′(n)}n∈Z is defined either by
منابع مشابه
MIXED VARIATIONAL INCLUSIONS INVOLVING INFINITE FAMILY OF FUZZY MAPPINGS
In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.
متن کاملA PRACTICAL APPROACH TO REAL-TIME DYNAMIC BACKGROUND GENERATION BASED ON A TEMPORAL MEDIAN FILTER
In many computer vision applications, segmenting and extraction of moving objects in video sequences is an essential task. Background subtraction, by which each input image is subtracted from the reference image, has often been used for this purpose. In this paper, we offer a novel background-subtraction technique for real-time dynamic background generation using color images that are taken fro...
متن کاملAsymptotic Behavior of Weighted Sums of Weakly Negative Dependent Random Variables
Let be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let be other sequence of positive random variables independent of and for some and for all . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy...
متن کاملSubspace-diskcyclic sequences of linear operators
A sequence ${T_n}_{n=1}^{infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...
متن کامل