Two-dimensional Filters Research Articles

Implementation of image median filters using programmable logic devices

A two-dimensional median filter structure, oriented at implementation in programmable logic devices and ensuring ultrafast determination of a median of data in a two-dimensional window owing to the parallel execution of comparison and ordering operations is presented. This approach ensures the cost-effective implementation is suitable for filtering both stationary and movable images, and allows one to expand the application area of the median filtering.

Wavefront-modulated four-wave mixing interferometry with silicon checkerboard gratings

Nonlinear optical FWM generation was studied using a wavefront-modulated beam to understand how emissions adapt under additional interference. Size-dependent circular π-phase-modulated masks were applied to create stepwise, z-directionally elongated, bottleneck-shaped FWM foci as schematic interference conditions. The polarizing FWM features varied dramatically as the circular mask size approached 0.35 times the beam barrel, resulting in the convergence of two inherently paired emissions without significant contrast at the edges. The results were reproduced through kernel-type filtering using two-dimensional nonlinear spatial filters with computationally efficient focal field calculations.

Condition of the elimination of overflow oscillations in two‐dimensional digital filters with external interference

This study is concerned with the problem of the elimination of overflow oscillations (EOOs) for two-dimensional (2D) digital filters with external interference. The main purpose is the presentation of a new unified criterion such that the underlying 2D digital filter is stable with a positive prescribed interference attenuation level. A performance index is proposed for the first time, which is referred to as generalised dissipativity property. By using this index and two harmonic slack matrices, a novel criterion is established, which can be used to solve ℋ∞ EOOs, passive EOOs and l 2–l ∞ EOOs for 2D digital filters with external interference in a unified framework, and reduce the conservatism of the existing results. The effectiveness of the criterion is demonstrated by a numerical example.

Overflow Oscillation Elimination of 2-D Digital Filters in the Roesser Model with Wiener Process Noise

Recently, Ahn's criteria were proposed for dealing with deterministic external interference with finite energy in two-dimensional (2-D) digital filters. However, these criteria fail for cases where the 2-D filters have stochastic noise. In this letter, we propose a new criterion for overflow oscillation elimination of 2-D digital filters in the Roesser model with Wiener process noise. The criterion guarantees the asymptotic stability as well as a 2-D expected power bound. Thus, it can ascertain the attenuation of the effect of Wiener process noise to a prescribed level. This criterion is also expressed by linear matrix inequality (LMI). A numerical example is provided to show the usefulness of the proposed result.

GPR data noise attenuation on the curvelet transform

Signal extraction is critical in GRP data processing and noise attenuation. When the target depth is shallow, its reflection echo signal will overlap with the background noise, affecting the detection of arrival time and localization of the target. Thus, we propose a noise attenuation method based on the curvelet transform. First, the original signal is transformed into the curvelet domain, and then the curvelet coefficients of the background noise are extracted according to the distribution features that differ from the effective signal. In the curvelet domain, the coarse-scale curvelet atom is isotropic. Hence, a two-dimensional directional filter is designed to estimate the high-energy background noise in the coarsescale domain, and then, attenuate the background noise and highlight the effective signal. In this process, we also use a subscale threshold value of the curvelet domain to filter out random noise. Finally, we compare the proposed method with the average elimination and 2D continuous wavelet transform methods. The results show that the proposed method not only removes the background noise but also eliminates the coherent interference and random noise. The numerical simulation and the real data application suggest and verify the feasibility and effectiveness of the proposed method.

Spatial–Spectral Information-Based Semisupervised Classification Algorithm for Hyperspectral Imagery

Semisupervised learning has shown its great potential in land cover mapping. It exploits the information of unlabeled training samples and converts those samples to labeled training samples to enhance classification. In this paper, the spatial information extracted by a two-dimensional (2-D) Gabor filter was stacked with spectral information first, and then the spatial neighborhood information of labeled training samples was combined with active learning (AL) algorithm to select the most useful and informative samples, which were used as the unlabeled set to aid the probability model-based supervised support vector machine (SVM). Experiments on two hyperspectral datasets showed that the spatial-spectral information-based semisupervised classification algorithm ($\bf{S}^{\bf{2}} \bf{ISC}$) can produce high classification accuracy with a small number of labeled samples, and outperformed the compared semisupervised algorithms.

$l_{2}-l_{\infty}$ Suppression of Limit Cycles in Interfered Two-Dimensional Digital Filters: A Fornasini–Marchesini Model Case

Recently, Ahn proposed an l 2 -l ∞ stability criterion for interfered two-dimensional (2-D) digital filters described by the Roesser model. However, until now, no criteria for interfered 2-D digital filters in the Fornasini-Marchesini (FM) model have been studied. As a continuation of the results, this brief proposes a new criterion for the l 2 -l ∞ suppression of limit cycles in interfered 2-D digital filters in the FM model. The proposed criterion ensures the asymptotic stability and l 2 -l ∞ performance of 2-D digital filters. The effectiveness of the proposed criterion is demonstrated using numerical examples. The work in this brief and that of the Roesser model provide, as an integrity, systematic results on limit cycle suppression for 2-D digital filters in the l 2 -l ∞ sense.

Biometric feature extraction using local fractal auto-correlation

Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach.

Adaptive genetic algorithm‐based approach to improve the synthesis of two‐dimensional finite impulse response filters

The design of finite impulse response (FIR) filters can be formulated as a non-linear optimization problem reputed to be difficult for conventional approaches. The constraints are high and a large number of parameters have to be estimated, especially when dealing with two-dimensional FIR filters. In order to improve the performance of conventional approaches, the authors explore several stochastic methodologies capable of handling large spaces. The authors specifically propose a new genetic algorithm (GA) in which some innovative concepts are introduced to improve the convergence and make its use easier for practitioners. The algorithm is globally improved by adapting the mutation and crossover and selection operators with the genetic advances. A dynamic ranking selection scheme is introduced to limit the promotion of extraordinary chromosomes. A refreshing mechanism is investigated to manage the trade-off between diversity and elitism. The key point of the proposed approach stems from the capacity of the GA to adapt the genetic operators during the genetic life while remaining simple and easy to implement. Most of the parameters and operators are changed by the GA itself. From an initial calibration, the GA performs the design problem while calibrating and repeatedly re-calibrating itself for solving it. The authors demonstrate on various cases of filter design a significant improvement in performance.

Label free high throughput screening for apoptosis inducing chemicals using time-lapse microscopy signal processing.

Label free time-lapse microscopy has opened a new avenue to the study of time evolving events in living cells. When combined with automated image analysis it provides a powerful tool that enables automated large-scale spatiotemporal quantification at the cell population level. Very few attempts, however, have been reported regarding the design of image analysis algorithms dedicated to the detection of apoptotic cells in such time-lapse microscopy images. In particular, none of the reported attempts is based on sufficiently fast signal processing algorithms to enable large-scale detection of apoptosis within hours/days without access to high-end computers. Here we show that it is indeed possible to successfully detect chemically induced apoptosis by applying a two-dimensional linear matched filter tailored to the detection of objects with the typical features of an apoptotic cell in phase-contrast images. First a set of recorded computational detections of apoptosis was validated by comparison with apoptosis specific caspase activity readouts obtained via a fluorescence based assay. Then a large screen encompassing 2,866 drug like compounds was performed using the human colorectal carcinoma cell line HCT116. In addition to many well known inducers (positive controls) the screening resulted in the detection of two compounds here reported for the first time to induce apoptosis.

Design of 1-D and 2-D recursive filters using crossover bacterial foraging and Cuckoo search techniques

Recently, there has been an increasing interest on the application of the evolutionary algorithms in order to solve the drawbacks of traditional filter design methods. Unlike classical methods, they offer the advantage of not requiring a good initial estimate of filter parameters to proceed. This paper presents design of one-dimensional (1-D) and two-dimensional (2-D) recursive filters using crossover bacterial foraging (COBFO) and Cuckoo Search (CS) techniques. Design of 1-D and 2-D recursive filters is considered here as a constrained optimization problem to ensure stability. The solution is obtained through convergence of a biased random search using crossover bacterial foraging optimization technique to ensure quality. A faster solution is also obtained through the convergence of a meta heuristic search technique called the Cuckoo search technique. Inbuilt constraint handling capability makes our proposal attractive in the design of recursive filters. Results are compared with genetic algorithm (GA) and bacteria foraging optimization (BFO) techniques.

An improved criterion for the global asymptotic stability of 2-D state-space digital filters with finite wordlength nonlinearities

This paper investigates the problem of global asymptotic stability of fixed-point state-space two-dimensional (2-D) digital filters described by the Roesser model in the presence of finite wordlength nonlinearities. The class of nonlinearities under consideration captures the combined effects of quantization (except value truncation) and overflow arithmetic employed in practice. A new criterion for the limit cycle-free realization of 2-D digital filters is proposed. The criterion is based on a more precise sector-based characterization of the nonlinearities which exploits the information of the wordlength available in the digital processor. The criterion is compared with the previously reported criteria.

New passivity criterion for limit cycle oscillation removal of interfered 2D digital filters in the Roesser form with saturation nonlinearity

The passivity concept plays an important role in circuit theory, signal processing, and control, but no criteria have yet been established for two-dimensional (2D) digital filters. In this article, we propose a new and first criterion for 2D digital filters in the Roesser form, to ensure passivity from the interference vector to the output vector with a certain storage function. The proposed criterion also guarantees the asymptotic stability of 2D digital filters in the Roesser form without interference. This criterion is described by linear matrix inequality, making it computationally attractive. A simulation example is presented, which demonstrates the usefulness of the 2D passivity criterion.

Two-dimensional slant filters for beam steering

The concept of a two-dimensional digital “slant” filter is introduced. If the input and output of the slant filter are represented by matrices whose row and column indices denote discrete time and discrete space, respectively, then each diagonal of the output matrix is equal to the linear convolution of the corresponding diagonal of the input matrix with a common one-dimensional sequence. This sequence may be considered as the impulse response of a one-dimensional shift-invariant filter. The transfer function of the slant filter has the form H(z1,z2) = G(z1z2) where G(z) is the transfer function of the one-dimensional filter. It is shown that the slant filter is capable of forming and steering a beam using pressure samples from a linear array. The output of the beamformer is equal to the last column of the output matrix of the slant filter. One interesting feature is the possibility that two beamformers can have the same beamwidth but steer the beam to different angles. Another is that though the slant filter is two-dimensional, it can be designed by utilizing well-developed one-dimensional techniques. An example is presented to illustrate the theoretical concepts.

Real-Time Lane Detection on Suburban Streets Using Visual Cue Integration

The detection of lane boundaries on suburban streets using images obtained from video constitutes a challenging task. This is mainly due to the difficulties associated with estimating the complex geometric structure of lane boundaries, the quality of lane markings as a result of wear, occlusions by traffic, and shadows caused by road-side trees and structures. Most of the existing techniques for lane boundary detection employ a single visual cue and will only work under certain conditions and where there are clear lane markings. Also, better results are achieved when there are no other on-road objects present. This paper extends our previous work and discusses a novel lane boundary detection algorithm specifically addressing the abovementioned issues through the integration of two visual cues. The first visual cue is based on stripe-like features found on lane lines extracted using a two-dimensional symmetric Gabor filter. The second visual cue is based on a texture characteristic determined using the entropy measure of the predefined neighbourhood around a lane boundary line. The visual cues are then integrated using a rule-based classifier which incorporates a modified sequential covering algorithm to improve robustness. To separate lane boundary lines from other similar features, a road mask is generated using road chromaticity values estimated from CIE L*a*b*colour transformation. Extraneous points around lane boundary lines are then removed by an outlier removal procedure based on studentized residuals. The lane boundary lines are then modelled with Bezier spline curves. To validate the algorithm, extensive experimental evaluation was carried out on suburban streets and the results are presented.

A new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with interference

Stability criteria have been proposed previously by Ahn for two-dimensional (2-D) digital filters described by the Roesser model with external interference. However, no stability criteria have yet been established for 2-D digital filters described by the Fornasini–Marchesini second model. In this paper, we propose a new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with saturation arithmetic and external interference. This new criterion guarantees that 2-D digital filters in this model are asymptotically stable with a guaranteed H∞ performance. The criterion is described by linear matrix inequalities (LMIs). Illustrative examples show the effectiveness of the proposed new criterion.

Edge Detection from High Resolution Remote Sensing Images using Two-Dimensional log Gabor Filter in Frequency Domain

Edges are vital features to describe the structural information of images, especially high spatial resolution remote sensing images. Edge features can be used to define the boundaries between different ground objects in high spatial resolution remote sensing images. Thus edge detection is important in the remote sensing image processing. Even though many different edge detection algorithms have been proposed, it is difficult to extract the edge features from high spatial resolution remote sensing image including complex ground objects. This paper introduces a novel method to detect edges from the high spatial resolution remote sensing image based on frequency domain. Firstly, the high spatial resolution remote sensing images are Fourier transformed to obtain the magnitude spectrum image (frequency image) by FFT. Then, the frequency spectrum is analyzed by using the radius and angle sampling. Finally, two-dimensional log Gabor filter with optimal parameters is designed according to the result of spectrum analysis. Finally, dot product between the result of Fourier transform and the log Gabor filter is inverse Fourier transformed to obtain the detections. The experimental result shows that the proposed algorithm can detect edge features from the high resolution remote sensing image commendably.

Design and Application of Digital Filter Based on Calculus Computing Concept

Calculus has been widely applied in engineering fields. The development of Integer order calculus theory is more mature in the project which can obtain fractional calculus theory through the promotion of integration order. It extends the flexibility of calculation and achieves the engineering analysis of multi-degree of freedom. According to fractional calculus features and the characteristics of fractional calculus, this paper treats the frequency domain as the object of study and gives the fractional calculus definition of the frequency characteristics. It also designs the mathematical model of fractional calculus digital filters using Fourier transform and Laplace transform. At last, this paper stimulates and analyzes numerical filtering of fractional calculus digital filter circuit using matlab general numerical analysis software and FDATool filter toolbox provided by matlab. It obtains the one-dimensional and two-dimensional filter curves of fractional calculus method which achieves the fractional Calculus filter of complex digital filter.

Mixed-Media Filter System for Removal of Multiple Contaminants from Urban Storm Water: Large-Scale Laboratory Testing

Urban storm water runoff consists of unacceptable levels of nutrients and heavy metals, and a mixed-media filter system is proposed to treat such storm water with multiple contaminants. In this study, a two-dimensional filter simulation test apparatus was constructed to examine the effectiveness of mixed media for the removal of multiple contaminants from synthetic storm water. The mixed media, selected based on several series of batch and column experiments in previous studies, consisted of a mixture of calcite, zeolite, sand, and iron filings. The mixed media was tested for removal of coexisting nitrate, phosphate, Ni, Cu, Cd, Cr, Pb, and Zn at concentrations and conditions relevant for typical urban storm water. Results show that the mixed-media filter was able to maintain high flow rates without any clogging issues, with an average hydraulic conductivity around 30 cm/min. No significant initial release or final desorption of the contaminants was observed. The filter system proved effective for the simultaneous removal of nutrients and heavy metals from the storm water, except for Ni, which had significantly lower removal efficiency than the other metals. Overall, the study indicated that a mixed-media filter can be designed with high contaminants removal capacity, but additional studies are recommended for evaluating long-term performance of the mixed-media filter under variable storm water field conditions.

Two-Dimensional IIR Filter Design Using Simulated Annealing Based Particle Swarm Optimization

We present a novel hybrid algorithm based on particle swarm optimization (PSO) and simulated annealing (SA) for the design of two-dimensional recursive digital filters. The proposed method, known as SA-PSO, integrates the global search ability of PSO with the local search ability of SA and offsets the weakness of each other. The acceptance criterion of Metropolis is included in the basic algorithm of PSO to increase the swarm’s diversity by accepting sometimes weaker solutions also. The experimental results reveal that the performance of the optimal filter designed by the proposed SA-PSO method is improved. Further, the convergence behavior as well as optimization accuracy of proposed method has been improved significantly and computational time is also reduced. In addition, the proposed SA-PSO method also produces the best optimal solution with lower mean and variance which indicates that the algorithm can be used more efficiently in realizing two-dimensional digital filters.