Order Statistic Filters Research Articles

Detection of Cardiac Boundaries in Echocardiographic Images Using a Customized Order Statistics Filter

Order statistics filters are nonlinear filters that suppress impulsive and Gaussian noise while preserving edges. These features are particularly useful for cardiac boundary detection in ultrasound images. Based on these facts, we have analyzed performance of a combined ranked order statistics filter. The filter subtracts ranks of ordered highest and lowest intensity values of pixels encompassed in a filter window. The rank extent and window size selection allow adjustment of filter properties for a particular application. Increasing the rank fosters the low-pass characteristics of the filter. Increasing the window size supports noise removal but reduces anatomic selectivity. The filter highlights cardiac boundaries in clinical echocardiograms with intensity proportional to the local probability of a presence of the boundary.

ディジタル放送 動き補正テレビ方式変換の改善

Recent years have seen the development of methods for motion-compensated television standards conversion (MC-TSC) in which motion information in the picture is utilized for conversion between TV standards that have different numbers of scanning lines and fields. Motion information used for standards conversion should contain true movement, which is not always a requirement in motion-compensated predictive coding. In conventional motion estimation methods for MC-TSC, however, the trueness has been insufficient, which has led to degradation of the converted picture. The authors therefore have improved the motion estimation scheme, utilizing a DOG (Difference of Gaussian) preprocessing filter for motion estimation, the iterative gradient method with improved high-precision, and the AOSF (Absolute Order Statistics Filter) for post-processing of motion vectors. A new high-quality motion-compensated television standards converter has been developed adopting the improved motion estimation scheme. This converter now makes it possible to greatly suppress degradation of the converted picture which has been difficult up until now.

A new representation of weighted order statistic filters

The Weighted Order Statistic Filters (WOSF) are useful tools in digital signal processing. Their standard representation is not canonical, which is a major drawback in comparison or design issues. A new representation is proposed, which is based on the statistical study of the WOSF. Efficient conversion algorithms are presented. This representation is of interest for analyzing, comparing and designing WOSF.

Nonlinear multiresolution decomposition with applications in image restoration

This paper addresses a nonlinear multiresolution decomposition scheme based on order statistic (OS) filters with applications in image restoration. In this scheme the input signal is decomposed into multiresolution bands using OS filters of different parameter values. We present the deterministic and statistical properties of the decomposed signals. As an application of the proposed scheme, we consider the restoration of images in the presence of Gaussian and non-Gaussian noise. In the image restoration, nonlinear filtering is performed on decomposed signal components using denoising techniques. Simulations show that this method has better edge and sharp feature preservation and better noise reduction properties than other OS filter based techniques.

Order statistic filter banks

Filter banks play a major role in multirate signal processing where these have been successfully used in a variety of applications. In the past, filter banks have been developed within the framework of linear filters. It is well known, however, that linear filters may have less than satisfactory performance whenever the underlying processes are non-Gaussian. We introduce the nonlinear class of order statistic (OS) filter banks that exploit the spectral characteristics of the input signal as well as its rank-ordering structure. The attained subband signals provide frequency and rank information in a localized time interval. OS filter banks can lead to significant gains over linear filter banks, particularly when the input signals contain abrupt changes and details, as is common with image and video signals. OS filter banks are formed using traditional linear filter banks as fundamental building blocks. It is shown that OS filter banks subsume linear filter banks and that the latter are obtained by simple linear transformations of the former. To illustrate the properties of OS filter banks, we develop simulations showing that the learning characteristics of the LMS algorithm, which are used to optimize the weight taps of OS filters, can be significantly improved by performing the adaptation in the OS subband domain.

Extended permutation filters and their application to edge enhancement

Extended permutation (EP) filters are defined and analyzed. In particular, we focus on extended permutation rank selection (EPRS) filters. These filters are constrained to output an order statistic from an extended observation vector. This extended vector includes N observation samples and K statistics that are functions of the observation samples. The rank permutations from selected samples in this extended observation vector are used as the basis for selecting an order statistic output. We show that by including the sample mean in the extended observation vector, the filters exhibit excellent edge enhancement properties. We also show that several previously defined classes of rank-order-based edge enhancers (CS, LUM, and WMMR sharpeners) can be formulated as subclasses of EPRS filters. These sharpening subclasses are in addition to the smoothing subclasses, which include rank conditioned rank selection, permutation stack, and weighted order statistic filters. Thus, this novel class of filters provides a broad framework within which many rank-order-based smoothers and edge enhancers can be unified. Edge enhancement properties are developed and an L(n) norm EPRS filter optimization procedure is presented. Finally, extensive computer simulation results are presented, comparing the performance of EPRS and other sharpening filters in edge enhancement applications.

Linear combination of weighted order statistic filters: canonical structure and optimal design

A new class of filters, called linear combination of weighted order statistic (LWOS) filters, is introduced. This filter is a combination of L-filters and weighted order statistic (WOS) filters. Based on the observation that this filter possesses the threshold decomposition property, a representation of LWOS filters, named the canonical representation, is developed. It is shown that most nonrecursive filters having the threshold decomposition property can be thought of as special cases of the canonical LWOS filter. This result indicates that this class of LWOS filters encompasses a variety of filters which include median-type nonlinear filters and linear FIR filters. A procedure for designing an optimal canonical LWOS filter under the mean square error (MSE) criterion has been developed. The optimization of LWOS filters yields an FIR Wiener filter when the input is zero-mean Gaussian and a median-type nonlinear filter for non-Gaussian inputs. Experimental results in image restoration are presented to compare the relative performances of the LWOS and existing filters.

A note on "On the VLSI implementation of real-time order statistic filters"

This note proposes further simplification for the architecture given in a paper by Murthy and Swamy (see ibid., vol.40, no.5, p.1241, 1992). The Boolean expression in the m-array algorithm is simplified such that the number of AND operators is significantly reduced for the 8-bit order statistic filter.

Image enhancement using the modified ICM method

A generalized version of the iterative conditional modes (ICM) method for image enhancement is developed. The proposed algorithm utilizes the characteristic of Markov random fields (MRF) in modeling the contextual information embedded in image formation. To cope with real images, a new local MRF model with a second-order neighborhood is introduced. This model extracts contextual information not only from the intensity levels but also from the relative position of neighboring cliques. Also, an outlier rejection method is presented. In this method, the rejection depends on each candidate's contribution to the local variance. To cope with a mixed noise case, a hypothesis test is implemented as part of the restoration procedure. The proposed algorithm performs signal adaptive, nonlinear, and recursive filtering. In comparing the performance of the new procedure with several well-known order statistic filters, the superiority of the proposed algorithm is demonstrated both in the mean-square-error (MSE) and the mean-absolute-error (MAE) senses. In addition, the new algorithm preserves the details of the images well. It should be noted that the blurring effect is not considered.

Realization of an alpha-trimmed mean filter on the threshold decomposition architecture

The realization of the α-trimmed mean filter on the threshold decomposition architecture is described. The threshold decomposition architecture is developed for facilitating realization of nonlinear, order-statistic filters. In this architecture, an input sequence is thresholded at different levels to form a number of binary sequences. The filter output is formed by combining the decision results made at various levels; at each level it is determined whether the signal should be above the associated threshold level. The decision rule used is the distinguishing feature of an individual filter; the current implementation of the α-trimmed mean filter is based on using a threshold logic function as the decision rule, thus allowing the decision rule to output multiple values. The statistical properties and performance of the a-trimmed mean filter are analyzed on the basis of this realization.

Soft morphological filtering

Stack filters are widely used nonlinear filters based on threshold decomposition and positive Boolean functions. They have shown to form a very large class of filters which includes rank-order operations as well as standard morphological operations. The stack filter representation of an order statistic filter provides an efficient tool for the theoretical analysis of the filter. Soft morphological filters form a large subclass of stack filters. They were introduced to improve the behavior of standard morphological filters in noisy conditions. In this paper, different properties of soft morphological filters are analysed and illustrated. Their connection to stack filters is established, and that connection is used in the statistical analysis of soft morphological filters. Soft morphological filters are less sensitive to additive noise than standard morphological filters. The deterministic properties of soft morphological filters are also analysed and it is shown that soft morphological filters form a class of filters with many desirable properties. For example, they preserve well details of images.

Morphological representation of order-statistics filters

We propose a comprehensive theory for the morphological bounds on order-statistics filters (and their repeated iterations). Conditions are derived for morphological openings and closings to serve as bounds (lower and upper, respectively) on order-statistics filters (and their repeated iterations). Under various assumptions, morphological open-closings and close-openings are also shown to serve as (tighter) bounds (lower and upper, respectively) on iterations of order-statistics filters. Simulations of the application of the results presented to image restoration are finally provided.

Permutation weighted order statistic filter lattices

We introduce and analyze a new class of nonlinear filters called permutation weighted order statistic (PWOS) filters. These filters extend the concept of weighted order statistic (WOS) filters, in which filter weights associated with the input samples are used to replicate the corresponding samples, and an order statistic is chosen as the filter output. PWOS filters replicate each input sample according to weights determined by the temporal-order and rank-order of samples within a window. Hence, PWOS filters are in essence time-varying WOS filters. By varying the amount of temporal-rank order information used in selecting the output for a given observation window size, we obtain a wide range of filters that are shown to comprise a complete lattice structure. At the simplest level in the lattice, PWOS filters reduce to the well-known WOS filter, but for higher levels in the lattice, the obtained selection filters can model complex nonlinear systems and signal distortions. It is shown that PWOS filters are realizable by a N! piecewise linear threshold logic gate where the coefficients within each partition can be easily optimized using stack filter theory. Simulations are included to show the advantages of PWOS filters for the processing of image and video signals.

Colour image interpolation for high resolution acquisition and display devices

Spatial interpolation is an important technique that is often used to perform an image zoom or to simply recover an original image from its downsampled version. The rapid advancements in hardware, both in acquisition and display devices, has made it possible to process high resolution digital colour images. However, the multichannel nature of colour images demands sophisticated signal processing algorithms that take into account the existing interchannel correlations when performing image expansion. Many conventional linear approaches exist. Nevertheless, these produce artifacts in the form of blockiness, jagged lines, and blurring in the interpolated image. In addition to this, these methods perform independently in each colour plane, thereby neglecting the colour component correlation. A set of nonlinear vector FIR-median hybrid (VFMH) filters are applied to the interpolation problem. These schemes are based on the class of vector order statistic filters which have desirable properties, such as the preservation of edges and image details, and the preservation of interchannel correlations. Colour images are interpolated from their downsampled versions and all of the techniques are compared, both, quantitatively as well as qualitatively. Experimental results indicate that VFMH filters produce better quantitative, and visually pleasing results than linear techniques.

On the convergence and roots of order-statistics filters

We propose a comprehensive theory of the convergence and characterization of roots of order-statistics filters. Conditions for the convergence of iterations of order-statistics filters are proposed. Criteria for the morphological characterization of roots of order-statistics filters are also proposed. >

Input compression and efficient VLSI architectures for rank order and stack filters

Rank-order-based filters include rank-order filters, stack filters, and weighted order statistic filters. The output of a rank-order-based filter is always one of the sample points in its input window; which one is chosen depends only upon the ranks and positions of the samples within the window. This paper introduces new architectures for rank-order-based filters. They all achieve fast, efficient operation by exploiting an algorithm called input compression. Under this algorithm, the sample points in the input window are first mapped to their relative ranks — the sample points in a window of size N + 1 would thus be mapped to the integers 0− N. The rank-order-based filter to be implemented is then applied directly to this compressed input, and the rank chosen is then mapped back to the sample of that rank in the original data to obtain the final output. This approach has been used to implement rank-order filters, in which case the same rank is always chosen from the compressed data. In this paper, which rank is chosen also depends on the positions of the ranks in the compressed data. Implementations employing input compression have several advantages. They are computationally efficient like running order sorters, yet can be pipelined to a fine degree like sorting networks. In stack filter implementations, the threshold decomposition circuitry can be eliminated when input compression is combined with unary encoding of the ranks. Weighted order statistic filter implementations based on input compression can support programmable, noninteger weights.

Adaptive L-filters with applications in signal and image processing

Adaptive order statistic filter ( L-filters) based on local statistics of signals are introduced in this paper. Such estimators are particularly effective in filtering signals which are corrupted by more than one type of noise, e.g., additive Gaussian noise plus impulses. In order to further improve the filtering performance (detail preserving ability), adaptive L-filtering structures have been combined with weighted median operations, exploiting temporal information which is lost by ordering in L-filtering. Simulation results are included to assess the performance of the proposed adaptive structures for one and two dimensional signals.

Fast adaptation and performance characteristics of FIR-WOS hybrid filters

Fast adaptive algorithms are developed for training weighted order statistic (WOS) filters and FIR-WOS hybrid (FWH) filters under the mean absolute error (MAE) criterion. These algorithms are based on the threshold decomposition of real-valued signals introduced in this paper. With this method an N-length WOS filter can be implemented by thresholding the input signals at most N times independent of the accuracy used. Beside saving in computations, the proposed algorithms can be applied to process arbitrary real-valued signals directly. Performance characteristics of FWH filters in 1-D and 2-D signal restoration are investigated through computer simulations. We show that both in restoration of signals containing edges and in the case of heavy tailed nonGaussian noise, considerable improvement in performance can be achieved with FWH filters over WOS filters, Ll filters, and adaptive linear filters. Two new FWH filter design strategies are found for removal of impulsive noise and for restoration of a square wave, respectively.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

CMOS threshold gate and networks for order statistic filtering

The threshold gate is a very good candidate in the realization of order statistic filtering. In this paper, a simple procedure is developed to determine the circuit parameters for a set of output-wired CMOS inverters in order to implement threshold functions for order statistic filtering. Weighted and nonweighted order statistic filters in either binary or integer domain can be easily realized in similar architectures. An incremental scheme is also proposed to construct threshold gate networks for general or multi-stage order statistic filters. >

Parametric analysis of weighted order statistics filters

The authors study the convergence properties of weighted order statistics filters. Based on a set of parameters, weighted order statistics filters are divided into five categories making their convergence properties easily understood. They show that any symmetric weighted order statistics filters will make the input sequence converge to a root or oscillate in a cycle of period 2. This result is significant since a restriction imposed by an earlier research is eliminated making the result applicable for the whole class of symmetric weighted order statistics filters. A condition to guarantee convergence of symmetric weighted order statistics filters is also derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>