Multidimensional Image Models and Processing

Krasheninnikov, V. R.; Васильев, Константин Константинович

doi:10.1007/978-3-319-67516-9_2

Cited by 19 publications

(4 citation statements)

References 15 publications

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“…Let us consider the RF wave model [12] that generalizes a number of other models and helps to solve the tasks of analysis and synthesis effectively. This model is simple enough and can serve as a basis for simulating images and their sequences with given covariance function (CF) without increasing the number of model parameters.…”

Section: Basic Wave Model Of a Random Fieldmentioning

confidence: 99%

“…Therefore, it is rather difficult to solve the problems of image imitation, descriptions of inhomogeneous images, correlation analysis and synthesis. A wave model of a random field was proposed in [12][13][14], which makes it possible to describe homogeneous images and their sequences defined on regions and surfaces of any dimension with small computational costs for simulation. In this model, the RF is the result of the influence of perturbations (waves) that occur at random times in random places and have random shapes.…”

Section: Introductionmentioning

confidence: 99%

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Double stochastic wave models of multidimensional random fields

Krasheninnikov

Subbotin

2019

Proceedings of the v International Conference Information Technology and Nanotechnology 2019

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The paper deals with the development of mathematical models of random fields to describe and simulate images. In the wave model, a random field is the result of the influence of perturbations (waves) that occur at random times in random places and have random shapes. This model allows representing and simulate isotropic and anisotropic images (and their temporal sequences) defined on arbitrary areas of multidimensional space, as well as on any surfaces. The problems of correlation analysis and synthesis can be relatively easily solved. However, this model allows representing only homogeneous fields. In this paper, we consider «double stochastic» wave models, when the first wave random field (control field) sets the parameters of the second (controlled field). As a result, the controlled field becomes nonuniform, since its parameters vary randomly. We also consider options when two fields mutually influence each other. These models allow us to represent and simulate multidimensional inhomogeneous images (and their temporal sequences), as well as systems of such images with mutual correlations.

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Section: Basic Wave Model Of a Random Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Double stochastic wave models of multidimensional random fields

Krasheninnikov

Subbotin

2019

Proceedings of the v International Conference Information Technology and Nanotechnology 2019

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“…It is required to evaluate the informative image X using observations Z. To solve this problem, we apply following adaptive pseudogradient analogue of Kalman filter (Krasheninnikov et al, 2017):…”

Section: Identification and Filtrationmentioning

confidence: 99%

“…Among these models there are autoregressive, polynomial, Gibbs, canonical decompositions, and so on (Gimel'farb, 1999, Soifer, 2009, Vizilter et al, 2015, Woods, 1981. There are also works on fields defined on a sphere and other curved surfaces (Krasheninnikov et al, 2017). In some practical situations, the images have a circular, radial or radial-circular structure.…”

Section: Introductionmentioning

confidence: 99%

Models of Images With Radial-Circular Structure

Krasheninnikov

Malenova

Subbotin

2019

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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<p><strong>Abstract.</strong> The overwhelming majority of known image models are varieties of random fields defined on rectangular two-dimensional grids or grids of higher dimension, for example. In some practical situations, the images have an annular, radial or radial-circular structure. For example, images of the facies (thin film) of dried biological fluid, eyes, cut of a tree trunk or a fruit, blood vessel, erythrocyte, blast pattern, end face detail, etc. In addition, radar and other images are physically obtained in polar or spherical coordinates. These features of images require their consideration in their mathematical models. In this paper, an autoregressive models of homogeneous and inhomogeneous random fields defined on a circle or oval are considered as representations of images with radial or radial-circular structure.</p>

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