Autoregressive Random Field Research Articles

Threshold Autoregressive Nearest-Neighbour Models for Claims Reserving

Motivated by claims reserving in run-off triangles, a class of threshold autoregressive nearest-neighbour (TAR-NN) models extending a major class of parametric nonlinear time series models, namely threshold autoregressive (TAR) models, is introduced. The proposed class of models also introduces a flexible regime-switching mechanism to nearest-neighbour models. Attention is given to a sub-class of TAR-NN models, namely self-exciting threshold autoregressive nearest-neighbour models (SETAR-NN), for uses in claims reserving. The (strict) stationarity and geometric ergodicity of the SETAR-NN model, and more generally, a two-dimensional nonlinear autoregressive random field, are discussed. The conditional least-square (CLS) method is used to estimate the SETAR-NN model and some of its nested models. Simulation studies on the parameter estimates from the CLS method are conducted. Using real insurance claims data and stochastic simulations, the applications of the SETAR-NN model and the nested models for projecting future claims liabilities are discussed. Comparisons of those models with the Bootstrap-Chain-Ladder (BCL) model for claims reserving are provided.

Lognormal Random Field models to identify temporal Land cover changes using full polarimetric L-Band SAR imagery

Multiplicative Autoregressive Random Field (MAR) based texture models have been identified as one of the most appropriate models for SAR intensity images to capture the stochastic spatial interaction among neighboring pixels. But very few studies have tested their viability particularly in disaster applications. In this paper, we analyse the MAR texture models for their advantageous in land cover change detection compared to the changes resulting from logarithm of SAR image intensity and speckle filtered SAR imagery. The paper shows that lognormal random fields with multiplicative spatial interactions in the form of MAR models can be an effective alternative to suppress speckle noise and model SAR image intensity in time series data analysis. The pre and post disaster observational data of the Tohoku earthquake, in the east coast of Japan, acquired by the Advanced Land Observation Satellite (ALOS)/phased array type L-band synthetic aperture radar (PALSAR) were synthesized using MAR model based texture measures. Two of the main texture descriptors of the MAR model were considered primarily in this study. Those are the neighborhood weighting and the noise variance parameters. A 2nd order neighborhood configuration was used to estimate them. We present a variogram based analysis, structural similarity index measure (SSIM), and the mean ratio detector (MRD) as three different approaches to analyse the changes in land cover using radar texture. The change detection results of the MRD were further tested using area error proportion (AEP), root mean square error (RMSE) and correlation coefficient (CC), keeping normalized ratio, principle component analysis (PCA) and adaptive Lee filtered polarimetric intensity based change as the references.

Autoregressive Models of the Random fields—A Survey

Autoregressive (AR) random fields are widely use to describe changes in the status of real-physical objects and implemented for analyzing linear & non-linear models. AR models are Markov processes with a higher order dependence for one-dimensional time series. Actually, various estimation methods were used in order to evaluate the autoregression parameters. Although in many applications background knowledge can often shed light on the search for a suitable model, but other applications lack this knowledge and often require the type of trial errors to choose a model. This article presents a brief survey of the literatures related to the linear and non-linear autoregression models, including several extensions of the main mode models and the models developed. The use of autoregression to describe such system requires that they be of sufficiently high orders which leads to increase the computational costs.

Investigation of the algorithm for detecting deterministic anomalies in complex structure images using a doubly stochastic model

The article proposes an algorithm for detecting deterministic anomalies against the background of satellite images with a complex structure, containing a combination of several natural objects. To describe such images, doubly stochastic models of random fields are proposed, which provide the formation of inhomogeneous images. The effectiveness of the algorithm is estimated by the probability of correct detection under various conditions of the interference. The dependences of the probability of the correct detection on the signal-to-noise ratio at various thresholds are presented. We present the detection efficiency studies on simulated and real images. The results are compared with the algorithm based on autoregressive random fields. We demonstrate that the proposed algorithm provides the efficacy in reducing the signal-to-noise ratio to achieve the given probability of the correct detection. Andriyanov N. A., Gavrilina Yu. N. Investigation of the algorithm for detecting deterministic anomalies in complex structure images using a doubly stochastic model. Ural Radio Engineering Journal . 2020;4(1):18–32. DOI: 10.15826/urej.2020.4.1.002

Prediction of random fields with incomplete quarter-plane past

Let be a zero mean weakly stationary random field and consider the problem of predicting X(0, 0) based on the incomplete quarter-plane past. An explicit formula is obtained for the prediction error of a future value of weakly stationary random fields when the quarter-plane is altered by some missing observations. Some properties for autoregressive (AR) random fields and for moving average (MA) are established.

A Random Matrix Approach to the Forensic Analysis of Upscaled Images

The forensic analysis of resampling traces in upscaled images is addressed via subspace decomposition and random matrix theory principles. In this context, we derive the asymptotic eigenvalue distribution of sample autocorrelation matrices corresponding to genuine and upscaled images. To achieve this, we model genuine images as an autoregressive random field and we characterize upscaled images as a noisy version of a lower dimensional signal. Following the intuition behind Marcenko-Pastur law, we show that for upscaled images, the gap between the eigenvalues corresponding to the low-dimensional signal and the ones from the background noise can be enhanced by extracting a small number of consecutive columns/rows from the matrix of observations. In addition, using bounds provided by the same law for the eigenvalues of the noise space, we propose a detector for exposing traces of resampling. Finally, since an interval of plausible resampling factors can be inferred from the position of the gap, we empirically demonstrate that by using the resulting range as the search space of existing estimators (based on different principles), a better estimation accuracy can be attained with respect to the standalone versions of the latter.

Aggregation of autoregressive random fields and anisotropic long-range dependence

We introduce the notions of scaling transition and distributional long-range dependence for stationary random fields $Y$ on $\mathbb {Z}^2$ whose normalized partial sums on rectangles with sides growing at rates $O(n)$ and $O(n^{\gamma})$ tend to an operator scaling random field $V_{\gamma}$ on $\mathbb {R}^2$, for any $\gamma>0$. The scaling transition is characterized by the fact that there exists a unique $\gamma_0>0$ such that the scaling limits $V_{\gamma}$ are different and do not depend on $\gamma$ for $\gamma>\gamma_0$ and $\gamma<\gamma_0$. The existence of scaling transition together with anisotropic and isotropic distributional long-range dependence properties is demonstrated for a class of $\alpha$-stable $(1<\alpha\le2)$ aggregated nearest-neighbor autoregressive random fields on $\mathbb{Z}^2$ with a scalar random coefficient $A$ having a regularly varying probability density near the "unit root" $A=1$.

Fused Lasso and rotation invariant autoregressive models for texture classification

Anisotropic, rotation invariant, autoregressive random fields, realised by considering local radial sampling, are flexible models which have been considered for texture classification. Unfortunately, owing to the strong correlations present in the neighbourhood covariate matrix, parameter estimation is complicated by the dichotomy between ill-conditionedness and rotation invariance. Exploiting the Fused Lasso framework, we here propose a compromise which incorporates two regularisers. The ℓ1-norm induces stability and performs variable selection amongst strongly correlated radial samples; the total variation seminorm encourages clustering and promotes parsimony. Experiments confirm the potential utility. Parallels are drawn within the texture classification literature and beyond.

Double random field models for remote sensing image segmentation

By incorporating the local statistics of an image, a semi-causal non-stationary autoregressive random field can be applied to a non-stationary image for segmentation. Because this non-stationary random field can provide a better description of the image texture than the stationary one, an image can be better segmented. Besides low-order dependence among pixels in image for above-mentioned texture random field, the paper also introduces high-order dependence as a new classification feature to recognize the real object. Entropy rate that depicts the high-order dependence feature can also be estimated by using random field model. The proposed technique is applied to extract urban areas from a Landsat image.

Spatial autoregression and related spatio-temporal models

We propose a spatial autoregressive random field of order p on the spatial domain R d for p⩾2 in this paper, whose univariate margins are the continuous-time autoregression of order p on the real line, and introduce a class of semiparametric spatio-temporal covariance models stationary in space with the spatial autoregressive margin.

Color image retrieval using multispectral random field texture model and color content features

This paper describes a color-texture-based image retrieval system for query of an image database to find similar images to a target image. The color-texture information is obtained via modeling with the multispectral simultaneous autoregressive (MSAR) random field model. The general color content characterized by ratios of sample color means is also used. The retrieval process involves segmenting the image into regions of uniform color texture using an unsupervised histogram clustering approach that utilizes the combination of MSAR and color features. The color-texture content, location, area and shape of the segmented regions are used to develop similarity measures describing the closeness of a query image to database images. These attributes are derived from the maximum fitting square and best fitting ellipse to each of the segmented regions. The proposed similarity measure combines all these attributes to rank the closeness of the images. The performance of the system is tested on two databases containing synthetic mosaics of natural textures and natural scenes, respectively.

Rotation-invariant texture classification using feature distributions

A distribution-based classification approach and a set of recently developed texture measures are applied to rotation-invariant texture classification. The performance is compared to that obtained with the well-known circular-symmetric autoregressive random field (CSAR) model approach. A difficult classification problem of 15 different Brodatz textures and seven rotation angles is used in experiments. The results show much better performance for our approach than for the CSAR features. A detailed analysis of the confusion matrices and the rotation angles of misclassified samples produces several interesting observations about the classification problem and the features used in this study.

A spatial correlation based method for neighbor set selection in random field image models

Random field (RF) models have widespread application in image modeling and analysis. The effectiveness of these models is largely dependent on the choice of neighbor sets, which determine the spatial interactions that are represented by the model. We consider the problem of selecting these neighbor sets for simultaneous autoregressive and Gauss-Markov random field models, based on the correlation structure of the image to be modeled. A procedure for identifying appropriate neighbor sets is proposed, and experimental results which demonstrate the viability of this method are presented.

An evaluation of Landsat TM spectral data and SAR-derived textural information for lithological discrimination in the Red Sea Hills, Sudan

The effectiveness of spectral and textural information in the identification of surface rock types in an arid region, the Red Sea Hills of Sudan, is evaluated using spectral information from the six Landsat TM optical bands and textural features derived from Shuttle Imaging Radar-C (SIR-C) C-band HH polarization data. An initial classification is derived from Landsat TM data alone using three classification algorithms, Gaussian maximum likelihood, a multi-layer feed-forward neural network and a Kohonen self-organizing feature map (SOM), to generate lithological maps, with classification accuracy being measured using a confusion matrix approach. The feed-forward neural net produced the highest overall classification accuracy of 57 per cent and was, therefore, selected for the second experiment, in which texture measures from SIR-C C-band HH-polarized synthetic aperture radar (SAR) data are added to selected TM spectral features. Four methods of measuring texture are employed, based on the Fourier power spectrum, grey level co-occurrence matrix (GLCM), multi-fractal measures, and the multiplicative autoregressive random field (MAR) model. The use of textural information together with a subset of the TM spectral features leads to an increase in classification accuracy to almost 70 per cent. Both the MAR model and the GLCM matrix approach perform better than Fourier and multi-fractal based methods of texture characterization.

Some properties of the quasihomogeneous autoregressive random fields

The problem of the classification, description by the difference equations and possible models of quasihomogeneous autoregressive random fields, existing in one-dimensional space Rl, is considered. The properties of the quasihomogeneous areas as well as of the parameters changing by not the jumps areas of such fields are considered also. The quasihomogeneous areas determination algorithm is proposed.

Texture in skin images: Comparison of three methods to determine smoothness

Smooth texture, a critical feature in skin tumor diagnosis, is analyzed using three texture measurement methods. A dermatologist classified 1290 small blocks within 42 tumor images as smooth, partially smooth, or nonsmooth. Texture discriminatory power of three methods were compared: the neighboring gray-level dependence matrix (NGLDM) method of Sun and Wee, the circular symmetric autoregressive random field model of Kashyap and Khotanzad, and a new peak-variance method. The texture analysis method that allows best prediction of smoothness for our tumor domain is the NGLDM method, affording 98% correct prediction of a smooth block with 21% false positives. We discuss applicability of texture analysis to dermatology.

Image segmentation based on composite random field models

The problem of region segmentation is examined and a new algorithm for maximum a posteriori (MAP) segmentation is introduced. The observed image is modeled as a composite of two processes: a high-level process that describes the various regions in the images and a low-level process that describes each particular region. A Gibbs-Markov random field model is used to describe the high-level process and a simultaneous autoregressive random field model is used to describe the low-level process. The MAP segmentation algorithm is formulated from the two models and a recursive implementation forthe algorithm is presented. Results of the algorithm on various synthetic and natural textures clearly indicate the effectiveness of the approach to texture segmentation.

Inhomogeneous Gaussian image models for estimation and restoration

Two inhomogeneous Gaussian-image models are presented for estimation and restoration. By incorporating the local statistics of an image, a homogeneous autoregressive (AR) random field can be extended to an inhomogeneous AR field. This inhomogeneous random field can provide a better description of the image than the homogeneous one. As a consequence of this improved modeling, a minimum-mean-square-error estimator (MMSE), based on the inhomogeneous Gaussian model, can produce good results in both subjective and objective criteria. Two image models are proposed for use in image estimation and restoration: a residual image model (original image minus the space-variant mean) and a normalized image model (residual image divided by space-variant standard variation). The novel aspect of these models is the use of an autoregressive dynamical model for residual and normalized images. Some aspects of parameter estimation are discussed and simulation results are presented. >

Mapping and Forecasting Soil Erosion Patterns from Landsat on a Microcomputer-based Image Processing Facility.

The paper summarises recent work in the development and implementation of broad scale conceptual and mathematical models of the soil erosion process in flat arid lands. The conceptual model is based on erosion cell behaviour. Its mathematical counterpart is the simultaneous autoregressive random field model recently developed for image modelling.The data used in the mathematical model are derived by transforming standard Landsat MSS data to produce a soil stability index. Practical application of the methods requires the appropriate computer software and an image processing facility. The erosion modelling routines have therefore been implemented as part of a user- friendly microcomputer based image processing package which is now available commercially. The package runs on an IBM XT or AT computer using a Vectrix graphics board and the hardware includes high resolution display and hard copy facilities. Both hardware and software cost less than $30,000 making it ~ossible to decentralise image processing technology to branch offices of government departments or to agricultural consultants.

A unilateral representation for autoregressive random field models

This paper discusses autoregressive random field (ARF) models and derives a unilateral representation driven by uncorrelated noise. The representation is in terms of a stochastic differential equation involving the spectral representation of the model.