Rotationally invariant pattern recognition by use of linear and nonlinear cascaded filters

We discuss the merits of using single-layer (linear and nonlinear) and multiple-layer (nonlinear) filters for rotationally invariant and noise-tolerant pattern recognition. The capability of each approach is considered with reference to a two-class, rotation-invariant, character recognition problem. The minimum average correlation energy (MACE) filter is a linear filter that is generally accepted to be optimal for detecting signals that are free from noise. Here it is found that an optimized MACE filter cannot differentiate between the characters E and F in a rotation-invariant manner. We have found, however, that this task is possible when a single optimized linear filter is used to achieve the required response when a nonlinear threshold function is included after the filter. We show that this structure can be cascaded to form a multiple-layer, cascaded filter and that the capability of such a system is enhanced by its increased noise tolerance in the character recognition problem. Finally, we show the capability of a two-layer cascade as a means to detect different species of bacteria in images obtained from a phase-contrast microscope.     

Distortion-invariant pattern recognition with Fourier-plane nonlinear filters

The use of nonlinear techniques in the Fourier plane of pattern-recognition correlators can improve the correlators' performance in terms of discrimination against objects similar to the target object, correlation-peak sharpness, and correlation noise robustness. Additionally, filter designs have been proposed that provide the linear correlator with invariance properties with respect to input-signal distortions and rotations. We propose simple modifications to presently known distortion-invariant correlator filters that enable these filter designs to be used in a nonlinear correlator architecture. These Fourier-plane nonlinear filters can be implemented electronically, or they may be implemented optically with a nonlinear joint transform correlator. Extensive simulation results are presented that illustrate the performance enhancements that are gained by the unification of nonlinear techniques with these filter designs.     

Optical correlation of images with signal-dependent noise using constrained-modulation filter devices

Images with signal-dependent noise present challenges beyond those of images with additive white or colored signal-independent noise in terms of designing the optimal 4-? correlation filter that maximizes correlation-peak signal-to-noise ratio, or combinations of correlation-peak metrics. Determining the proper design becomes more difficult when the filter is to be implemented on a constrained-modulation spatial light modulator device. The design issues involved for updatable optical filters for images with signal-dependent film-grain noise and speckle noise are examined. It is shown that although design of the optimal linear filter in the Fourier domain is impossible for images with signal-dependent noise, proper nonlinear preprocessing of the images allows the application of previously developed design rules for optimal filters to be implemented on constrained-modulation devices. Thus the nonlinear preprocessing becomes necessary for correlation in optical systems with current spatial light modulator technlogy. These results are illustrated with computer simulations of images with signal-dependent noise correlated with binary-phase-only filters and ternary-phase-amplitude filters.     

Schlieren systems with coherent illumination for quantitative measurements

Schlieren systems with a coherent light source were investigated by the Fourier optics technique. The imaging properties of the systems with various cutoff filters were studied. Systems with a graded piecewise linear filter and a Gaussian step function convolution (graded) filter are considered, demonstrating that the image can be approximated by the geometrical-optics theory of conventional schlieren systems. A nonlinear phase contribution was estimated, allowing for the measurement of strong phase objects. Within the framework of linear approximation the results are described by the phase derivative point-spread function, introduced in this paper as the schlieren point-spread function. In addition, modification of the Lopez cutoff filter is proposed, demonstrating its superiority over the piecewise linear and the Gaussian step convolution filters. Simulations of coherent schlieren imaging as well as phase derivative measurements were performed. Finally, the imaging properties of the schlieren systems with the different filters are compared.     

闪光CCD图像的中值-非线性扩散滤波

根据闪光CCD图像的特点,提出了一种中值-非线性扩散滤波(Median-NonlinearDiffusionFiltering,简称MNDF)方法。该方法采用中值预滤波来估计图像的真实边缘,通过求解偏微分方程(PartialDifferentialEquation,简称PDE)来进行非线性扩散滤波,充分发挥了中值滤波和非线性扩散滤波的优势,能更好地消除噪声、保护边缘。实验结果表明,在高斯噪声和脉冲噪声同时存在的情况下,MNDF方法取得的滤波效果较P-M方案和Catte方案要好,信噪比改善因子提高3~5倍,均方误差减小1.3~2.7倍。对闪光照相CCD图像取得了很好的消噪声结果,保护了边缘信息。     

A generalized shaping filter method for higher order statistics

The shaping filter method has been a valuable tool for computing the stochastic response of linear dynamical systems to Gaussian stochastic inputs that are not delta-correlated. A straightforward extension of this method to the non-Gaussian case involves determining shaping filters that “match” higher order cumulant functions of the stochastic noise input. However it is easy to find simple examples of input signals for which this will not work because their cumulant functions cannot be realized as cumulant functions of the output of a linear system with delta-correlated input. This paper proposes an alternative shaping filter and it shows that it is applicable to an entire class of input signals for which the original shaping filter method fails.

A further extension of the shaping filter method is suggested, that involves the introduction of the concept of generalized moments that includes as particular cases both the moments and the cumulants.     

Noise robustness of nonlinear filters for image recognition

We analyze the performance of the Fourier plane nonlinear filters in terms of signal-to-noise ratio (SNR). We obtain a range of nonlinearities for which SNR is robust to the variations in input-noise bandwidth. This is shown both by analytical estimates of the SNR for nonlinear filters and by experimental simulations. Specifically, we analyze the SNR when Fourier plane nonlinearity is applied to the input signal. Using the Karhunen-Loève series expansion of the noise process, we obtain precise analytic expressions of the SNR for Fourier plane nonlinear filters in the presence of various types of additive-noise processes. We find a range of nonlinearities that need to be applied that keep the output SNR of the filter stable relative to changes in the noise bandwidth.     

一种新的自适应非线性卡尔曼滤波算法

为避免由于系统噪声统计特性不准确所导致的滤波性能下降问题,改进了一种基于新息的系统噪声方差调整方法,并将其与扩展卡尔曼滤波、Unscented 卡尔曼滤波和差分滤波相结合,形成自适应非线性卡尔曼滤波.将此方法应用到非线性测量光电跟踪系统中,并与采用基本非线性卡尔曼滤波进行性能对比.仿真实验结果证明该方法可以实时调整系统噪声方差,有效地避免由于系统噪声统计特性不准确所带来的滤波性能下降的问题,而且其性能明显优于基本非线性卡尔曼滤波.     

Nonlinear filtering for recognition of phase-encoded images

We investigate the use of Fourier plane nonlinear filtering for phase-encoded images. We investigate the performance of the nonlinear joint transform correlator and the nonlinearly transformed matched filter for phase-encoded images with different types of input noise. We use the peak-to-output-energy ratio, peak-to-sidelobe ratio, and discrimination ratio as the metrics for measuring the performances. We mathematically analyze the peak-to-output-energy ratio of the nonlinearly transformed matched filter for phase-encoded images with spatially nonoverlapping white noise. Computer simulations are provided to show the performance improvements of the nonlinear filtering techniques for the phase-encoded images. In comparison with linear filtering techniques, we find that the nonlinear filtering techniques substantially improve the performance metrics. From the computer-simulation results it can be seen that the nonlinear joint transform correlator performs better than the nonlinearly transformed matched filter in detecting phase-encoded targets in the presence of different types of noise, such as additive overlapping white noise, spatially nonoverlapping white background noise, spatially nonoverlapping colored background noise, and nontarget objects.     

Filter for biomedical imaging and image processing

Image filtering techniques have numerous potential applications in biomedical imaging and image processing. The design of filters largely depends on the a priori, knowledge about the type of noise corrupting the image. This makes the standard filters application specific. Widely used filters such as average, Gaussian, and Wiener reduce noisy artifacts by smoothing. However, this operation normally results in smoothing of the edges as well. On the other hand, sharpening filters enhance the high-frequency details, making the image nonsmooth. An integrated general approach to design a finite impulse response filter based on Hebbian learning is proposed for optimal image filtering. This algorithm exploits the interpixel correlation by updating the filter coefficients using Hebbian learning. The algorithm is made iterative for achieving efficient learning from the neighborhood pixels. This algorithm performs optimal smoothing of the noisy image by preserving high-frequency as well as low-frequency features. Evaluation results show that the proposed finite impulse response filter is robust under various noise distributions such as Gaussian noise, salt-and-pepper noise, and speckle noise. Furthermore, the proposed approach does not require any a priori knowledge about the type of noise. The number of unknown parameters is few, and most of these parameters are adaptively obtained from the processed image. The proposed filter is successfully applied for image reconstruction in a positron emission tomography imaging modality. The images reconstructed by the proposed algorithm are found to be superior in quality compared with those reconstructed by existing PET image reconstruction methodologies.     

Polynomial distance classifier correlation filter for pattern recognition

We introduce what is to our knowledge a new nonlinear shift-invariant classifier called the polynomial distance classifier correlation filter (PDCCF). The underlying theory extends the original linear distance classifier correlation filter [Appl. Opt. 35, 3127 (1996)] to include nonlinear functions of the input pattern. This new filter provides a framework (for combining different classification filters) that takes advantage of the individual filter strengths. In this new filter design, all filters are optimized jointly. We demonstrate the advantage of the new PDCCF method using simulated and real multi-class synthetic aperture radar images.     

Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra

Nonnegative color analysis filters are obtained by using an invertible linear transformation of characteristic spectra, which are orthogonal vectors from a principal component analysis (PCA) of a representative ensemble of color spectra. These filters maintain the optimal compression properties of the PCA scheme. Linearly constrained nonlinear programming is used to find a transformation that minimizes the noise sensitivity of the filter set. The method is illustrated by computing analysis and synthesis filters for an ensemble of measured Munsell color spectra.     

Particle Filtering for State Estimation in Nonlinear Industrial Systems

State estimation is a major problem in industrial systems, particularly in industrial robotics. To this end, Gaussian and nonparametric filters have been developed. In this paper, the extended Kalman filter, which assumes Gaussian measurement noise, is compared with the particle filter, which does not make any assumption on the measurement noise distribution. As a case study, the estimation of the state vector of an industrial robot is used when measurements are available from an accelerometer that was mounted on the end effector of the robotic manipulator and from the encoders of the joints' motors. It is shown that, in this kind of sensor fusion problem, the particle filter outperforms the extended Kalman filter, at the cost of more demanding computations.     

Estimation of parameters for plasma glucose regulation in type‐2 diabetics in presence of meal

In this study, the authors propose a methodology for the estimation of glucose masses in stomach (both in solid and liquid forms), intestine, plasma and tissue; insulin masses in portal vein, liver, plasma and interstitial fluid using only plasma glucose measurement. The proposed methodology fuses glucose–insulin homoeostasis model (in the presence of meal intake) and plasma glucose measurement with a Bayesian non‐linear filter. Uncertainty of the model over individual variations has been incorporated by adding process noise to the homoeostasis model. The estimation is carried out over 24 h for the healthy people as well as a type II diabetes mellitus patients. In simulation, the estimator follows the truth accurately for both the cases. Moreover, the performances of two non‐linear filters, namely the unscented Kalman filter (KF) and cubature quadrature KF are compared in terms of root mean square error. The proposed methodology will be helpful in future to: (i) observe a patient''s insulin–glucose profile, (ii) calculate drug dose for any hyperglycaemic patients and (iii) develop a closed‐loop controller for automated insulin delivery system.Inspec keywords: blood, diseases, biochemistry, parameter estimation, biological tissues, liver, Bayes methods, nonlinear filters, Kalman filters, drugs, drug delivery systems, medical signal processingOther keywords: automated insulin delivery system, closed‐loop controller, hyperglycaemic patients, drug dose, root mean square error, cubature quadrature KF, Kalman filter, type II diabetes mellitus, process noise, Bayesian nonlinear filter, glucose‐insulin homoeostasis model, interstitial fluid, liver, portal vein, insulin mass, biological tissues, intestine, stomach, glucose mass, meal intake, type‐2 diabetics, plasma glucose regulation, parameter estimation     

Evaluation of bistable systems for binary signal detection in symmetric non-Gaussian noise

For detecting binary signals in symmetric noise with unknown probability density functions (PDF), a nonlinear receiver is proposed based on the bistable systems with autoregressive models of order 1 [AR(1)]. The bistable systems are utilized to pre-process the noisy observations ahead of the linear correlation (LC) detector. The permutations of the observations are utilized to bypass the design of the optimal LC vector which depends on the noise PDF. The detection performances, in the form of probabilities of error, in some non-Gaussian noise are evaluated versus the matched filter (MF) and Volterra filter (VF) through numerical simulations. The results show that the bistable receiver performs better than MF receiver when the noise deviates from Gaussian distribution, and seems more robust compared to the VF receiver.     

A neural network‐based nonlinear filter for image enhancement

This paper explores a novel neural network‐based nonlinear filter that has the ability to remove mixed noises and sharpen the edges in noise‐corrupted digital images. The noise is assumed to be a mixture of both Gaussian and impulse types. Initially, a nonlinear filter is used to reduce the noise. The smoothed image is then combined with the output of an edge detector using a synthesizer to provide the effect of noise reducing and edge sharpening. The smoother and synthesizer are designed by using layered neural networks. Simulation results show that the proposed filter can effectively remove the mixed Guassian and impulsive noises and sharpen the edges. It can adapt itself to the various noise environments by learning during the training process. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 56–62, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10009     

Monte Carlo filters for identification of nonlinear structural dynamical systems

The problem of identification of parameters of nonlinear structures using dynamic state estimation techniques is considered. The process equations are derived based on principles of mechanics and are augmented by mathematical models that relate a set of noisy observations to state variables of the system. The set of structural parameters to be identified is declared as an additional set of state variables. Both the process equation and the measurement equations are taken to be nonlinear in the state variables and contaminated by additive and (or) multiplicative Gaussian white noise processes. The problem of determining the posterior probability density function of the state variables conditioned on all available information is considered. The utility of three recursive Monte Carlo simulation-based filters, namely, a probability density function-based Monte Carlo filter, a Bayesian bootstrap filter and a filter based on sequential importance sampling, to solve this problem is explored. The state equations are discretized using certain variations of stochastic Taylor expansions enabling the incorporation of a class of non-smooth functions within the process equations. Illustrative examples on identification of the nonlinear stiffness parameter of a Duffing oscillator and the friction parameter in a Coulomb oscillator are presented. This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

Importance sampling for reliability assessment of dynamic systems under general random process excitation

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally efficient approach intended for dynamic systems driven by Gaussian white noise, and this approach can be extended to random process inputs that can be represented as transformations of Gaussian white noise. In practice, dynamic systems may be subjected to inputs that may be better modeled as non-Gaussian and/or non-stationary random processes, which are not easily transformable to Gaussian white noise. We propose a computationally efficient scheme, based on importance sampling, which can be implemented directly on a general class of random processes — both Gaussian and non-Gaussian, and stationary and non-stationary. We demonstrate that this approach is in fact equivalent to Girsanov transformation when the uncertain inputs are Gaussian white noise processes. The proposed approach is demonstrated on a linear dynamic system driven by Gaussian white noise and Brownian bridge processes, a multi-physics aero-thermo-elastic model of a flexible panel subjected to hypersonic flow, and a nonlinear building frame subjected to non-stationary non-Gaussian random process excitation.     

Kalman filter tracking in a Cherenkov neutrino telescope

The reconstruction of tracks in underwater Cherenkov neutrino telescopes is strongly complicated due to large background counting rate originates from ⁴⁰K beta decay and to the electromagnetic showers accompanying high energy muons together with the effects of light propagation in the water, in particular the photon scattering. These two effects lead to a non-linear problem with a non-Gaussian measurement noise. A method for track reconstruction based on Kalman filter approach in this situation is presented. We use Gaussian Sum Filter algorithm to take into account non-Gaussian process noise. While usual Kalman filter estimators based on linear least-square method are optimal in case all observations are Gaussian distributed, the Gaussian Sum Filter offers a better treatment of non-Gaussian process noise and/or measurement errors when these are modeled by Gaussian mixtures. As an example of the application, the results of muon track reconstruction in NEMO underwater neutrino telescope are presented as well as the comparison of its capability with other standard track reconstruction methods.     

一种自适应的图像双边滤波方法

提出一种利用双边滤波的图像平滑滤波方法,即在滤除图像中高频噪声的同时,按照图像亮度变化保持图像中处于高频部分的边缘信息的自适应滤波过程。该滤波方法将传统的Gauss滤波器的权系数优化成Gauss函数和图像的亮度信息乘积的形式,优化后的权系数再与图像作卷积运算。这样,滤波时就可以考虑到图像的亮度信息,在滤除图像噪声的同时尽量保持了图像的边缘。由于双边滤波的方法可以使滤波器的权系数随着图像的亮度变化而改变,所以在滤波过程中能达到自适应滤波的目的。