Convergence properties of multidimensional stack filters

Wendt, Peter

doi:10.1117/12.19610

Cited by 5 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The final field related to median-type filters is the field of neural networks, although this connection has only begun to be exploited [32], [53], [135], [136], [141], [146], [147]. The fields are similar since they are both based on threshold logic operators--every binary rank-order operator is a thres-hold logic gate.…”

Section: Generalization Of Median-type Filters : Theoretical Analysismentioning

confidence: 99%

“…Wendt [135], [136] studied the convergence behavior of those nonrecursive and recursive one-dimensional stack filters and multidimensional stack filters which can be represented by symmetric threshold functions for binary inputs. Based on similar theorems on the convergence of neural networks, he showed that any n-dimensional signal, when surrounded by an arbitrary fixed boundary, will be filtered to either a root or will oscillate between two signals when filtered by any n-dimensional stack filter in this class in a finite number of passes.…”

Section: Theoretical Advancesmentioning

confidence: 99%

“…Median-type filters, and particularly stack filters, start from a more global point of view--the threshold logic gates are buried inside positive Boolean functions and are thus subject to an important restriction on their operation. Results on the convergence properties of symmetric threshold functions have been very helpful in analyzing the convergence behavior of a large subclass of stack filters [135], [-136].…”

Section: Generalization Of Median-type Filters : Theoretical Analysismentioning

confidence: 99%

“…The convergence behavior of stack filters has been extensively studied in [52], [105], [135], [136], and [145]. In [52] stack filters were partitioned into four different types, namely type-0 through type-3, based on the structure of the on-set and the off-set of the positive Boolean function defining the stack filter.…”

Section: Theoretical Advancesmentioning

confidence: 99%

See 3 more Smart Citations

An overview of median and stack filtering

Coyle

Gallagher

Gabbouj

1992

Circuits Systems and Signal Process

108

View full text Add to dashboard Cite

Abstract. Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the median-related filters known as rank-order filters, order-statistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since the days of Fourier, Laplace, and "Convolute."We trace the development of this theory of nonlinear filtering from its beginnings in the study of noise-removal properties and structural behavior of the median filter to the recently developed theory of optimal stack filtering.The theory of stack filtering provides a point of view which unifies many different filter classes, including morphological filters, so it is discussed in detail. Of particular importance is the way this theory has brought together, in a single analytical framework, both the estimation-based and the structural-based approaches to the design of these filters.Some recent applications of median and stack filters are provided to demonstrate the effectiveness of this approach to nonlinear filtering. They include: the design of an optimal stack filter for image restoration; the use of vector median filters to attenuate impulsive noise in color images and to eliminate cross luminance and cross color in TV images; and the use of median-based filters for image sequence coding, reconstruction, and scan rate conversion in normal TV and HDTV systems.

show abstract