Image Representation and Processing Using Autoregressive Random Fields with Multiple Roots of Characteristic Equations

2019 ◽  
pp. 11-52 ◽  
Author(s):  
Konstantin K. Vasil’ev ◽  
Nikita A. Andriyanov
Keyword(s):  
Random Fields ◽  
Image Representation ◽  
Multiple Roots ◽  
Characteristic Equations

scholarly journals Optimal filtering of multidimensional random fields generated by autoregressions with multiple roots of characteristic equations

2019 ◽  
pp. 72-78 ◽  
Author(s):  
N A Andriyanov ◽  
K K Vasiliev
Keyword(s):  
Random Fields ◽  
Model Parameters ◽  
Multiple Roots ◽  
Optimal Filtering ◽  
Characteristic Equations ◽  
Relative Variance ◽  
Filtering Efficiency ◽  
Simulation Results ◽  
Simulated Images ◽  
Use Of Models

The use of mathematical models allows to compare the theoretical expressions and simulation results. Autoregressive random fields can be used for description of the images, however, such models have pronounced anisotropy, and the simulated images are too sharp. The elimination of this drawback is possible through the use of models with multiple roots of characteristic equations. The analysis shows that using models with multiple roots in filtering images with smoothly varying brightness provides smaller errors than the use of autoregressive random fields. However, studies of the dependences of filtering efficiency on various model parameters and signal-to-noise ratios for multidimensional autoregressive random fields were almost not carried out. The article discusses the solution of the problem of optimal filtering of images based on models with multiple roots of characteristic equations. Theoretical dependences of the relative variance of the filtering error on the dimension of random fields are obtained. Furthermore, it was presented some results of filtering real images by such model in comparison with autoregressive model.

scholarly journals Solution for the problem of the parameters identification for autoregressions with multiple roots of characteristic equations

2019 ◽  
pp. 79-85 ◽  
Author(s):  
N A Andriyanov ◽  
M N Sluzhivyi
Keyword(s):  
Mathematical Model ◽  
Model Selection ◽  
Parameters Identification ◽  
Autoregressive Models ◽  
Model Parameters ◽  
Multiple Roots ◽  
Real Image ◽  
Optimal Parameters ◽  
Characteristic Equations ◽  
Identification Of Parameters

When describing a real image using a mathematical model, the problem of model parameters identification is of importance. In this case the identification itself is easier to perform when a particular type of model is known. In other words, if there is a number of models characterized by different properties, then if there is a correspondence with the type of suitable images, then the model to be used can be determined in advance. Therefore, in this paper, we do not consider the criteria for model selection, but perform the identification of parameters for autoregressive models, including those with multiple roots of characteristic equations. This is due to the fact that the effectiveness of identification is verified by the images generated by this model. However, even using this approach where the model is known, one must first determine the order of the model. In this regard, on the basis of YuleWalker equations, an algorithm for determining the order of the model is investigated, and the optimal parameters of the model are also found. In this case the proposed algorithm can be used when processing real images.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

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