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Papers by Alexey Chulichkov

IOP Conference Series: Earth and Environmental Science, 2020

The paper presents the results of applying the continuous wavelet analysis method to assess the c... more The paper presents the results of applying the continuous wavelet analysis method to assess the cyclic components of discrete time series. The work is based on an analysis of a long-term series of data on observations of air temperature in the south-west of the Valdai Upland, as well as analysis of data on observations of CO2 concentration in the canopy of the tropical monsoon forest in southern Vietnam. The patterns of wavelet coefficients and integral spectra have been studied for all considered time series. Additionally, the cyclicities contained in the studied series were revealed.

Journal of Physics: Conference Series, 2019

The paper presents two approaches to subjective modelling incomplete and uncertain information ab... more The paper presents two approaches to subjective modelling incomplete and uncertain information about possible shape of images. The shape is understood as a set of images of the scene, recorded under all possible conditions (lighting, exposure, etc.). To simulate the likelihood, the measure of likelihood introduced by Yu.P. Pytyev is used. This measure is a function defined on a set of statements and ordering them according to plausibility. The obtained subjective models of shapes allow using the theory of optimal strategies for solving morphological problems.

The comparison and classification of images can be carried out by means of numerous methods. In t... more The comparison and classification of images can be carried out by means of numerous methods. In this study we develop the approach based on object boundary curve analysis. In general, object boundaries can be extracted from the image in two following ways: 1) Segmentation followed by the extraction of segmented areas boundaries. In this case each object in a scene can be represented by a single closed contour. Usually such contours have not branches and can be represented by piecewise smooth curves. For description of such objects we propose to use curvature as significantly invariant curve characteristic: curvature is invariant to affine transforms and the proportional scaling leads only to its linear change. 2) The detection of the object boundary by means of segmentation is not always possible (for example, for objects with strongly nonuniform brightness characteristics). Nevertheless, object boundary still can be quite distinct even if segmentation fails, and it is possible to e...

Sensors, Jan 4, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Moscow University Physics Bulletin, 2015

An urgent problem of the optimization of automated optical microscopy is considered. An approach ... more An urgent problem of the optimization of automated optical microscopy is considered. An approach is suggested during which variations in the brightness of a Gaussian beam in microscope optics are analyzed. A discrete (digital) model, which correlates with the continuous one, is introduced. An analytical approach to finding the maximum of a discrete function that estimates the measure of optical system focusing is suggested; it is based on a discrete model of Gaussian beam behavior and requires a much smaller number of optical microscope images, which speeds up the process of the automated focusing of an optical microscope.

The estimation of function values at specified points in its domain of definition based on the me... more The estimation of function values at specified points in its domain of definition based on the measurement results of the finite set of functionals is posed and solved. The measurements are distorted by a finite error. It is shown that with the finite error can be estimated only finitedimensional component of unknown function. Exact finite-dimensional model, underlying the construction of required assessments is proposed. Two methods for estimation are discussed. The first method minimizes the maximal error of the estimation of each value of the function at a given point. It is believed that the measurement error of each linear functional may take any value within a given interval. For each of the estimated value of a function the interval that contains this value was constructed. The minimax estimate is the midpoint of this interval, and the error is the half of its length. The ends of each interval are determined

Pure and Applied Geophysics

Pure and Applied Geophysics

Moscow University Physics Bulletin, 2014

The possibility of estimating the values of a function at given points of its domain is investiga... more The possibility of estimating the values of a function at given points of its domain is investigated. The estimation uses results of the measurements of a finite number of linear functionals; the results of the measurements are distorted by an error. It is shown that only the component of the functions from the linear finite-dimensional subspace can be estimated with a finite error. A method for estimating this component with accuracy control is proposed. The mathematical methods of measurement reduction proposed by Yu.P. Pyt’ev are used. An example of the estimation of an emission spectrum that is measured by a double-slit spectrometer is described.

Measurement Techniques, 1998

We present the elements of a theory for computer aided measurement systems with superhigh resolut... more We present the elements of a theory for computer aided measurement systems with superhigh resolution. We present the concept of an ideal measurement instrument that does not distort the parameters of an object of study.

Journal of Applied Crystallography, 1989

The model of the instrumental function of a four-circle X-ray diffractometer suggested earlier [C... more The model of the instrumental function of a four-circle X-ray diffractometer suggested earlier [Chulichkov et al. (1987). Kristallografiya, 32, 1107–1114] is complemented by the introduction of the crystal mosaicity. This improved model is used to develop a method for the reconstruction of the mosaicity function profile f(ω) from the experimental intensity profile I(ω) measured on a diffractometer. The method consists of the reduction of the experimental I(ω) distribution to the form it would have if it were measured on a diffractometer with an instrumental function close to the δ function. The suggested method for determining f(ω) is tested on Si crystals with dislocation densities Nd = 3 × 1010 and 2 × 1011 m−2.

Moscow University Physics Bulletin, 2007

Time delays between signals emitted by an unknown source are estimated on the basis of the shape ... more Time delays between signals emitted by an unknown source are estimated on the basis of the shape analysis of their fragments detected by spatially separated sensors operated under unknown and different conditions [1]. The estimates minimize the maximal error in the time delay of the detected signals with a guaranteed reliability of the estimate [2, 3]. The signal shape is determined as an invariant of the class of transformations modeling the variety of the signal detection conditions.

Computer Vision in Control Systems-1, 2014

Some original and novel morphological concepts and tools are presented in this chapter as well as... more Some original and novel morphological concepts and tools are presented in this chapter as well as required amount of mathematical morphological basics. The continuous binary morphology based on a computational geometry is presented as a very fast approach to shape representation via real-time computation of figures' skeletons. A skeletal representation of the figure is formed as a skeleton graph, and the radial function is determined in skeleton points. The proposed morphological spectrum is the multi-scale morphological shape description and analysis tools based on granulometry. It is shown how the tasks of change detection and shape matching in images can be solved using a morphological image analysis. The projective morphology as a generalized framework based on the mathematical morphology and the morphological image analysis provides fast and efficient solutions of morphological segmentation problem in complex images.

Moscow University Physics Bulletin, 2021

IOP Conference Series: Earth and Environmental Science, 2020

The paper presents the results of applying the continuous wavelet analysis method to assess the c... more The paper presents the results of applying the continuous wavelet analysis method to assess the cyclic components of discrete time series. The work is based on an analysis of a long-term series of data on observations of air temperature in the south-west of the Valdai Upland, as well as analysis of data on observations of CO2 concentration in the canopy of the tropical monsoon forest in southern Vietnam. The patterns of wavelet coefficients and integral spectra have been studied for all considered time series. Additionally, the cyclicities contained in the studied series were revealed.

Journal of Physics: Conference Series, 2019

The paper presents two approaches to subjective modelling incomplete and uncertain information ab... more The paper presents two approaches to subjective modelling incomplete and uncertain information about possible shape of images. The shape is understood as a set of images of the scene, recorded under all possible conditions (lighting, exposure, etc.). To simulate the likelihood, the measure of likelihood introduced by Yu.P. Pytyev is used. This measure is a function defined on a set of statements and ordering them according to plausibility. The obtained subjective models of shapes allow using the theory of optimal strategies for solving morphological problems.

The comparison and classification of images can be carried out by means of numerous methods. In t... more The comparison and classification of images can be carried out by means of numerous methods. In this study we develop the approach based on object boundary curve analysis. In general, object boundaries can be extracted from the image in two following ways: 1) Segmentation followed by the extraction of segmented areas boundaries. In this case each object in a scene can be represented by a single closed contour. Usually such contours have not branches and can be represented by piecewise smooth curves. For description of such objects we propose to use curvature as significantly invariant curve characteristic: curvature is invariant to affine transforms and the proportional scaling leads only to its linear change. 2) The detection of the object boundary by means of segmentation is not always possible (for example, for objects with strongly nonuniform brightness characteristics). Nevertheless, object boundary still can be quite distinct even if segmentation fails, and it is possible to e...

Sensors, Jan 4, 2023

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Moscow University Physics Bulletin, 2015

An urgent problem of the optimization of automated optical microscopy is considered. An approach ... more An urgent problem of the optimization of automated optical microscopy is considered. An approach is suggested during which variations in the brightness of a Gaussian beam in microscope optics are analyzed. A discrete (digital) model, which correlates with the continuous one, is introduced. An analytical approach to finding the maximum of a discrete function that estimates the measure of optical system focusing is suggested; it is based on a discrete model of Gaussian beam behavior and requires a much smaller number of optical microscope images, which speeds up the process of the automated focusing of an optical microscope.

The estimation of function values at specified points in its domain of definition based on the me... more The estimation of function values at specified points in its domain of definition based on the measurement results of the finite set of functionals is posed and solved. The measurements are distorted by a finite error. It is shown that with the finite error can be estimated only finitedimensional component of unknown function. Exact finite-dimensional model, underlying the construction of required assessments is proposed. Two methods for estimation are discussed. The first method minimizes the maximal error of the estimation of each value of the function at a given point. It is believed that the measurement error of each linear functional may take any value within a given interval. For each of the estimated value of a function the interval that contains this value was constructed. The minimax estimate is the midpoint of this interval, and the error is the half of its length. The ends of each interval are determined

Pure and Applied Geophysics

Pure and Applied Geophysics

Moscow University Physics Bulletin, 2014

The possibility of estimating the values of a function at given points of its domain is investiga... more The possibility of estimating the values of a function at given points of its domain is investigated. The estimation uses results of the measurements of a finite number of linear functionals; the results of the measurements are distorted by an error. It is shown that only the component of the functions from the linear finite-dimensional subspace can be estimated with a finite error. A method for estimating this component with accuracy control is proposed. The mathematical methods of measurement reduction proposed by Yu.P. Pyt’ev are used. An example of the estimation of an emission spectrum that is measured by a double-slit spectrometer is described.

Measurement Techniques, 1998

We present the elements of a theory for computer aided measurement systems with superhigh resolut... more We present the elements of a theory for computer aided measurement systems with superhigh resolution. We present the concept of an ideal measurement instrument that does not distort the parameters of an object of study.

Journal of Applied Crystallography, 1989

The model of the instrumental function of a four-circle X-ray diffractometer suggested earlier [C... more The model of the instrumental function of a four-circle X-ray diffractometer suggested earlier [Chulichkov et al. (1987). Kristallografiya, 32, 1107–1114] is complemented by the introduction of the crystal mosaicity. This improved model is used to develop a method for the reconstruction of the mosaicity function profile f(ω) from the experimental intensity profile I(ω) measured on a diffractometer. The method consists of the reduction of the experimental I(ω) distribution to the form it would have if it were measured on a diffractometer with an instrumental function close to the δ function. The suggested method for determining f(ω) is tested on Si crystals with dislocation densities Nd = 3 × 1010 and 2 × 1011 m−2.

Moscow University Physics Bulletin, 2007

Time delays between signals emitted by an unknown source are estimated on the basis of the shape ... more Time delays between signals emitted by an unknown source are estimated on the basis of the shape analysis of their fragments detected by spatially separated sensors operated under unknown and different conditions [1]. The estimates minimize the maximal error in the time delay of the detected signals with a guaranteed reliability of the estimate [2, 3]. The signal shape is determined as an invariant of the class of transformations modeling the variety of the signal detection conditions.

Computer Vision in Control Systems-1, 2014

Some original and novel morphological concepts and tools are presented in this chapter as well as... more Some original and novel morphological concepts and tools are presented in this chapter as well as required amount of mathematical morphological basics. The continuous binary morphology based on a computational geometry is presented as a very fast approach to shape representation via real-time computation of figures' skeletons. A skeletal representation of the figure is formed as a skeleton graph, and the radial function is determined in skeleton points. The proposed morphological spectrum is the multi-scale morphological shape description and analysis tools based on granulometry. It is shown how the tasks of change detection and shape matching in images can be solved using a morphological image analysis. The projective morphology as a generalized framework based on the mathematical morphology and the morphological image analysis provides fast and efficient solutions of morphological segmentation problem in complex images.

Moscow University Physics Bulletin, 2021