Designing robust binary filters

An optimal binary-image filter estimates an ideal random set by means of an observed random set. A fundamental and practically important question regards the robustness of a designed filter: to what extent does performance degrade when the filter is applied to a different model than the one for which it has been designed? By parameterizing the ideal and observation random sets, one can analyze the robustness of filter design relative to parameter states. Based on a prior distribution for the states, a robustness mesure is defined for each state in terms of how well its optimal filter performs on models for different states. Not only is filter performance on other states taken into account, but so too is the contribution of other states in terms of their mass relative to the prior state distribution. This paper characterizes maximally robust states, derives performance bounds, treats mean robustness (as opposed to robustness by state), introduces a global filter that is applied across all states, particularizes the entire analysis to a sparse noise model for which there are analytic robustness expressions, and proposes a simplified model for determination of robust states from data. Sufficient conditions are given under which the global filter is uniformly more robust than all state-specific optimal filters.

An analytic solution for real optimal filters is known, and the special case of optimal binary phase-only filters can be solved by a fast binning algorithm but no analytic solution is known. We establish a geometric solution for the design of optimal binary amplitude filters (OBAF's) and optimal binary phase-only filters (OBPOF's) for any object. The optimal filter is found in terms of maximizing the field strength at the origin in the correlation plane. We found that it is possible to construct a unique convex polygon by using an ordered set of phasors from the filter object's Fourier transform. This process leads eventually to an exact solution for the filter-design problem. We show that the maximum distance across the polygon divides the phasors into two groups: For the OBAF, it determines the group that is passed or blocked; for the OBPOF, it determines which group is passed with a zero or a pi phase shift. The shape of the convex polygon gives qualitative information on the criticalness and the tightness needed in the design process. It provides good insight into the binning-process algorithm and permits us to bound the error in the binning process. Design examples through computer simulation and applications in fingerprint identification are presented.

The practical issues in the design and implementation of the optimal binary filters limit the observation windows down to a size that is usually much smaller than the characteristic features found in document images. To overcome this drawback, a new composite binary filtering method is developed. A preprocessing stage based on linearly separable Boolean functions is used to gather information from a very large window. The pre-filtering results together with the pixel values from a smaller window are then faded into an optimal estimator. The proposed filter structure can be viewed either as a two stage binary filter with linearly separable preprocessing or as a locally adaptive binary filter where the local adaptation is based on the characteristic features extracted from a large window. Both software and hardware implementations of the filter exhibit reasonable complexity even for large windows. Some properties of the filter and a closed form expression of the mean-absolute-error are derived. It is shown that, because there are no restrictions in the second stage, the whole composite structure can be optimally designed. The paper develops a practical design procedure that uses an efficient gradient method. Computer simulations are used to test the proposed filter against the optimal binary filter.

We derive robust linear filtering and experimental design for systems governed by stochastic differential equations (SDEs) under model uncertainty. Given a model of signal and observation processes, an optimal linear filter is found by solving the Wiener-Hopf equation; with model uncertainty, it is desirable to derive a corresponding robust filter. This article assumes that the physical process is modeled via a SDE system with unknown parameters; the signals are degraded by blurring and additive noise. Due to time-dependent stochasticity in SDE systems, the system is nonstationary; and the resulting Wiener-Hopf equation is difficult to solve in closed form. Hence, we discretize the problem to obtain a matrix system to carry out the overall procedure. We further derive an intrinsically Bayesian robust (IBR) linear filter together with an optimal experimental design framework to determine the importance of SDE parameter(s). We apply the theory to an SDE-based pharmacokinetic two-compartment model to estimate drug concentration levels.

For binary window-based filters, the optimal increasing filter is often derived from the optimal unconstrained (nonincreasing) filter by iteratively switching the filter values at pixels from 0 to 1 or from 1 to 0 so as to make the resulting filter be the optimal increasing filter. This paper gives a corresponding switching algorithm for gray-scale nonlinear filters, and it does so in the context of finite lattices, which makes the algorithm applicable to computational morphology on lattices. The algorithm is minimal in the sense that it involves a minimal search if one wishes to be certain to obtain the optimal increasing filter when beginning with the optimal unconstrained filter.

This paper considers robust fault‐detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well‐recognized robust fault‐detection problems, such asℋ−/ℋ∞,ℋ2/ℋ∞, andℋ∞/ℋ∞problems, are the same and can be obtained by solving a standard algebraic Riccati equatio n. Optimal filters are also derived for many other optimization criteria and it is shown that some well‐studied and seeming‐sensible optimization criteria for fault‐detection filter design could lead to (optimal) but useless fault‐detection filters.

Use of the Magneto-Optic Spatial Light Modulator (MOSLM) in the filter plane of optical correlatorsis attractive because it is capable of high frame rates. This has led to the design of several differenttypes of Binary Phase-Only Filters (BPOFs) and Ternary Filters matched to a single reference. Tofurther increase the throughput of an optical correlator employing the MOSLM, attempts at designingBinary Phase-Only Composite Filters have been made. In this paper, we introduce a new iterativetechnique to design such Composite Filters in which we simultaneously maximize the peak sharpnessand minimize the deviation of the actual correlation peak intensities from their desired values. 1 Introduction Binary Phase-Only Filters have received much attention in the past ten years [1-9]. Most of this research has focused on the design of filters matched to a single reference image. These filters have beendesigned to optimize many different figures of merit. Among these are Signal-to-Noise Ratio, Peak-to-Correlation Energy and light efficiency. Now, the focus appears to be shifting to the design of Binary Phase-Only Composite Filters (BPOCFs) [10,11]. If we desire real-time implementation, then binary phase-onlycomposite filters, which are used to recognize many distortions of an image, should be considered sincethey require fewer filters.In this paper, we present a new algorithm for designing BPOCFs. The advantage of this new algorithmover the previous ones is that it allows us to not only approach the desired correlation peak value, butit also maximizes the peak sharpness produced by the filter. The remainder of this paper is organized asfollows. Section 2 introduces composite filters or synthetic discriminant functions (SDFs) [12,13] and setsup the notation we use. Section 3 develops the new algorithm for designing BPOCFs. Section 4 presentssome initial results and Section 5 gives our conclusions.

Considers the filtering problem for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The unknown nonlinearities in the system are time-varying and norm-bounded. First, we show the equivalence of the norm bounded linear and nonlinear uncertainty sets. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.

This paper presents an alternative approach for the design of linear phase digital high pass FIR filter using Particle Swarm Optimization with Constriction Factor and Inertia Weight Approach (PSOCFIWA). FIR filter design is a multi-modal optimization problem. The conventional gradient based optimization techniques are not efficient for digital filter design. Given the filter specifications to be realized, PSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency characteristic. In this paper, for the given problem, the realization of the optimal FIR high pass filters of different orders has been performed. The simulation results have been compared to those obtained by the well accepted evolutionary algorithm such as genetic algorithm (GA). The results justify that the proposed optimal filter design approach using PSOCFIWA outperforms GA, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

Optimal and adaptive design of logical granulometric filters

Compressed Raman methods allow classification between known chemical species with only a few measurements through binary filters. We propose a methodology for binary filter optimization, in which filters are modified at each pixel so that classification can still be achieved pixel by pixel with a few measurements acquired in parallel, while retaining the ability to reconstruct a full spectrum when combining measurements from several pixels. This approach is robust to intensity variations between pixels. It relies on a generalized Bhattacharyya bound and on the Cramér-Rao bound to tailor filters with optimized performance.

The experimental and theoretical operation of the dc-blocked phase-only filter correlator is studied for obscured inputs. The performance of the nearly optimal filter is compared with the performances of other varieties of simple optimal filters that are capable of real-time implementation with spatial light modulators. Uses of these correlation filters in associative memories is investigated.

An algorithm for detection and identification of image clusters or {open_quotes}blobs{close_quotes} based on color information for an autonomous mobile robot is developed. The input image data are first processed using a crisp color fuszzyfier, a binary smoothing filter, and a median filter. The processed image data is then inputed to the image clusters detection and identification program. The program employed the concept of {open_quotes}elastic rectangle{close_quotes}that stretches in such a way that the whole blob is finally enclosed in a rectangle. A C-program is develop to test the algorithm. The algorithm is tested only on image data of 8x8 sizes with different number of blobs in them. The algorithm works very in detecting and identifying image clusters.

An efficient method is proposed for the design of finite impulse response (FIR) filter with arbitrary pass band edge, stop band edge frequencies and transition width. The proposed FIR band stop filter is designed using craziness based particle swarm optimization (CRPSO) approach. Given the filter specifications to be realized, the CRPSO algorithm generates a set of optimal filter coefficients and tries to meet the ideal frequency response characteristics. In this paper, for the given problem, the realizations of the optimal FIR band pass filters of different orders have been performed. The simulation results have been compared with those obtained by the well accepted evolutionary algorithms, such as Parks and McClellan algorithm (PMA), genetic algorithm (GA) and classical particle swarm optimization (PSO). Several numerical design examples justify that the proposed optimal filter design approach using CRPSO outperforms PMA and PSO, not only in the accuracy of the designed filter but also in the convergence speed and solution quality.

In this paper, the robust recursive filtering problem is investigated for a class of uncertain multi-rate systems in sensor networks. Each sensor node receives signals from its neighboring node according to a given network topology. The uncertain multi-rate system under consideration is first transformed into a singular uncertain single-rate system by recurring to the lifting technique. Then, an optimal robust recursive filter is designed for the resulting singular uncertain single-rate system via a solution to an optimization problem. Moreover, the convergence of the filtering algorithm is also discussed. Finally, a simulation example is presented to verify the effectiveness of the proposed design approach.