Fuzzy Ordering Theory and Its Use in Filter Generalization

Abstract

<p/> <p>The rank ordering of samples is widely used in robust nonlinear signal processing. Recent advances in nonlinear filtering algorithms have focused on combining spatial and rank (SR) order information into the filtering process to allow spatial correlations to be exploited while retaining the robust characteristics of strict rank order methods. Further generalization can be achieved by replacing the crisp, or binary, SR information utilized by most methods with more general fuzzy SR information. Indeed, by exploiting fuzzy methodologies real valued SR orderings can be defined that not only relate the spatial and rank orderings of samples, but also includes information on sample spread. This paper utilizes this approach to define fuzzy ranking and fuzzy order statistics. Properties of these concepts are discussed and several previously defined filters are generalized by including fuzzy concepts. Specifically, the fuzzy median, fuzzy rank conditioned rank selection, and fuzzy weighted median filters are defined. Optimization of the parameters for these filters are discussed. Simulation results are presented to show the advantages of these fuzzy filters over their crisp counterparts.</p

Defective point data reconstruction based on improved process of morphological operations

“…(9) amplifies the noise influence, it is much suitable for weighted vector median filter to reduce the noise in functions v in and v out , which is more effective and robust to denoise in image process [45]. The algorithm needs to define the matrix and the relationship between the elements in neighbor grid region.…”

Surface Reconstruction of Defective Point Clouds Based on Dual Off-Set Gradient Functions

“…(2) Although the computation of Eq. (3) amplifies the noise influence, it is much suitable of weighted vector median filter to reduce the noise in function in v and out v , which is more effective and robust to denoise in image process (Barner et al 2001). The algorithm needs to define the metric and the relationship between the elements in neighbor grid region.…”

Fuzzy weighted median filters

“…The fuzzy SR matrix, samples and fuzzy order statistic possess powerful properties that are useful in relating sam ple ordering and values [2,6]. The following will be utilized to incorporate fuzzy ordering into WM filter framework: for the samples in the same-filter window, the elements of the correspon ding fuzzy spatial vector and those of fuzzy rank order vector (i.e., fuzzy order statistics) form the same set Specifically, if Xi is the j'th order statistic, i.e., Xi = xli), then Xi = z(j).…”

“…The FWM filter proposed in this paper is based on fuzz y ordering theory [2,6]. By introducing the concept of fuzzy relationship between samples and incorporating it into the SR ordering framework, sample rank ordering information, spatial rank ordering information as well as sample spread information can be represented and utilized simultaneously.…”