2-D iteratively reweighted least squares lattice algorithm and its application to defect detection in textured images

In this paper, a 2-D iteratively reweighted least squares lattice algorithm, which is robust to the outliers, is introduced and is applied to defect detection problem in textured images. First, the philosophy of using different optimization functions that results in weighted least squares solution in the theory of 1-D robust regression is extended to 2-D. Then a new algorithm is derived which combines 2-D robust regression concepts with the 2-D recursive least squares lattice algorithm. With this approach, whatever the probability distribution of the prediction error may be, small weights are assigned to the outliers so that the least squares algorithm will be less sensitive to the outliers. Implementation of the proposed iteratively reweighted least squares lattice algorithm to the problem of defect detection in textured images is then considered. The performance evaluation, in terms of defect detection rate, demonstrates the importance of the proposed algorithm in reducing the effect of the outliers that generally correspond to false alarms in classification of textures as defective or nondefective

Wave modelling - the state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered. The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments

Prediction and Estimation of Random Fields

For a stationary two dimensional random field, we utilize the classical Kolmogorov-Wiener theory to develop prediction methodology which requires minimal assumptions on the dependence structure of the random field. We also provide solutions for several non-standard prediction problems which deals with the "modified past," in which a finite number of observations are added to the past. These non-standard prediction problems are motivated by the network site selection in the environmental and geostatistical applications. Unlike the time series situation, the prediction results for random fields seem to be expressible only in terms of the moving average parameters, and attempts to express them in terms of the autoregressive parameters lead to a new and mysterious projection operator which captures the nature of edge-effects. We put forward an approach for estimating the predictor coefficients by carrying out an extension of the exponential models. Through simulation studies and real data example, we demonstrate the impressive performance of our prediction method. To the best of our knowledge, the proposed method is the first to deliver a unified framework for forecasting random fields both in the time and spectral domain without making a subjective choice of the covariance structure. Finally, we focus on the estimation of the hurst parameter for long range dependence stationary random fields, which draws its motivation from applications in the environmental and atmospheric processes. Current methods for estimation of the Hurst parameter include parametric models like fractional autoregressive integrated moving average models, and semiparametric estimators which are either inefficient or inconsistent. We propose a novel semiparametric estimator based on the fractional exponential spectrum. We develop three data-driven methods which can automatically select the optimal model order for the fractional exponential models. Extensive simulation studies and analysis of Mercer and Hall?s wheat data are used to illustrate the performance of the proposed estimator and model order selection criteria. The results show that our estimator outperforms existing estimators, including the GPH (Geweke and Porter-Hudak) estimator. We show that the proposed estimator is consistent, works for different definitions of long range dependent random fields, is computationally simple and is not susceptible to model misspecification or poor efficiency

Essays on spatial autoregressive models with increasingly many parameters

Much cross-sectional data in econometrics is blighted by dependence across units. A solution to this problem is the use of spatial models that allow for an explicit form of dependence across space. This thesis studies problems related to spatial models with increasingly many parameters. A large proportion of the thesis concentrates on Spatial Autoregressive (SAR) models with increasing dimension. Such models are frequently used to model spatial correlation, especially in settings where the data are irregularly spaced. Chapter 1 provides an introduction and background material for the thesis. Chapter 2 develops consistency and asymptotic normality of least squares and instrumental variables (IV) estimates for the parameters of a higher-order spatial autoregressive (SAR) model with regressors. The order of the SAR model and the number of regressors are allowed to approach infinity with sample size, and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied. An alternative to least squares or IV is to use the Gaussian pseudo maximum likelihood estimate (PMLE), studied in Chapter 3. However, this is plagued by finitesample problems due to the implicit definition of the estimate, these being exacerbated by the increasing dimension of the parameter space. A computationally simple Newton type step is used to obtain estimates with the same asymptotic properties as those of the PMLE. Chapters 4 and 5 of the thesis deal with spatial models on an equally spaced, d dimensional lattice. We study the covariance structure of stationary random fields defined on d-dimensional lattices in detail and use the analysis to extend many results from time series. Our main theorem concerns autoregressive spectral density estimation. Stationary random fields on a regularly spaced lattice have an infinite autoregressive representation if they are also purely non-deterministic. We use truncated versions of the AR representation to estimate the spectral density and establish uniform consistency of the proposed spectral density estimate

From thin plates to Ahmed bodies: linear and weakly non-linear stability of rectangular prisms

We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$, while the length-to-height ratio $1/6<L/H<3$ covers a wide range of geometries from thin plates to elongated Ahmed bodies. First, global linear stability analysis yields a series of pitchfork and Hopf bifurcations: (i) at lower Reynolds numbers $Re$, two stationary modes, $A$ and $B$, become unstable, breaking the top/bottom and left/right planar symmetries, respectively; (ii) at larger $Re$, two oscillatory modes become unstable and, again, each mode breaks one of the two symmetries. The critical $Re$ of these four modes increase with $L/H$, qualitatively reproducing the trend of stationary and oscillatory bifurcations in axisymmetric wakes (e.g. thin disk, sphere and bullet-shaped bodies). Next, a weakly non-linear analysis based on the two stationary modes $A$ and $B$ yields coupled amplitude equations. For Ahmed bodies, as $Re$ increases state $(A,0)$ appears first, followed by state $(0,B)$. While there is a range of bistability of those two states, only $(0,B)$ remains stable at larger $Re$, similar to the static wake deflection (across the larger base dimension) observed in the turbulent regime. The bifurcation sequence, including bistability and hysteresis, is validated with fully non-linear direct numerical simulations, and is shown to be robust to variations in $W$ and $L$ in the range of common Ahmed bodies

Aeronautical engineering: A special bibliography with indexes, supplement 82, April 1977

This bibliography lists 311 reports, articles, and other documents introduced into the NASA scientific and technical information system in March 1977

Acoustics Division recent accomplishments and research plans

The research program currently being implemented by the Acoustics Division of NASA Langley Research Center is described. The scope, focus, and thrusts of the research are discussed and illustrated for each technical area by examples of recent technical accomplishments. Included is a list of publications for the last two calendar years. The organization, staff, and facilities are also briefly described

Numerical solution of three-dimensional incompressible unsteady viscous flows

Issued as Semi-annual progress reports [nos. 1-7], and Final report, Project E-16-61