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Data Analysis and Interpretation: Methods of Computer-Aided Measuring Transducer Theory, Morphological Analysis, Possibility Theory, and Subjective Mathematical Modeling

  • SCIENTIFIC SCHOOLS OF THE LOMONOSOV MOSCOW STATE UNIVERSITY (MSU), MOSCOW, THE RUSSIAN FEDERATION
  • Faculty of Physics Yu.P. Pyt’ev’s Scientific School
  • Published:
Pattern Recognition and Image Analysis Aims and scope Submit manuscript

Abstract

This article provides an overview of the fundamental research directions being pursued at the Faculty of Physics of Lomonosov Moscow State University under the guidance of Professor Yuri Petrovich Pyt’ev. These research directions can be categorized into three primary areas: methods of morphological analysis of images and signals, theory of computer-aided measuring systems, and methods related to the theory of possibilities and subjective mathematical modeling. The article elucidates the foundational ideas and concepts of these directions, contemplates alternative approaches to address similar challenges, and offers both model-based and application-driven examples utilizing the methods corresponding to these directions and their combinations.

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Notes

  1. An ideal MT is an MT interacting with the measured object in the same way as an MT in a CAMT, whose output signal is equal to the Uf value of the characteristic of the SO of interest.

  2. A measurement model is a mathematical model of the MT interacting with the measured object and with the environment, linking its input and output signals. The model of interpretation of the input signal of the MT is the mathematical model linking its input signal and CIMR of the object under study undisturbed by measurement.

  3. \({{B}^{ - }}\) and \(B{\kern 1pt} \text{*}\) are the operators pseudoinverse to \(B\) and conjugate to \(B\), \({{B}^{ - }}\) = \(\mathop {\lim }\limits_{\alpha \to 0} B{\kern 1pt} \text{*}{\kern 1pt} {{(BB{\kern 1pt} \text{*} + \;\alpha I)}^{{ - 1}}}\) = \(\mathop {\lim }\limits_{\alpha \to 0} {{(B{\kern 1pt} \text{*}{\kern 1pt} B + \alpha I)}^{{ - 1}}}B{\kern 1pt} \text{*}\) [148].

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Funding

This study was supported by grant no. 19-29-09044 of the Science Foundation of the Russian Federation.

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Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russian Federation

    Yu. P. Pyt’ev, A. I. Chulichkov, O. V. Falomkina & D. A. Balakin

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  1. Yu. P. Pyt’ev
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  2. A. I. Chulichkov
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  3. O. V. Falomkina
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  4. D. A. Balakin
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Correspondence to Yu. P. Pyt’ev, A. I. Chulichkov, O. V. Falomkina or D. A. Balakin.

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Yuri Petrovich Pyt’ev (born in 1935). Graduated from the Faculty of Physics at Lomonosov Moscow State University in 1959. He received his Candidate’s degree in theoretical and mathematical physics from Lomonosov Moscow State University in 1963 and Doctoral degree in 1976. He was head of the Mathematical Modeling and Computer Science Department (earlier, Computer Methods in Physics) at the Faculty of Physics, Lomonosov Moscow State University, from 1995 to 2018. He has been a Professor of the Mathematical Modeling and Computer Science Department since 2018. Scientific interests: fuzzy and uncertain fuzzy mathematics, theory of possibilities, subjective modeling, mathematical modeling, image processing, pattern recognition and image analysis. He is the author of more than 400 papers and 36 books.

Alexey Ivanovich Chulichkov (born in 1954). Graduated from the Faculty of Physics at Lomonosov Moscow State University in 1978. He received his Candidate’s degree in physics and mathematics from Lomonosov Moscow State University in 1983 and Doctoral degree in 1993. He was a Professor of the Mathematical Modeling and Computer Science Department (earlier, Computer Methods in Physics) at the Faculty of Physics, Lomonosov Moscow State University, from 1994 to 2019. He has been head of the Mathematical Modeling and Computer Science Department (earlier, Computer Methods in Physics) since 2020. Scientific interests: morphological methods of image analysis, fuzzy and uncertain fuzzy mathematics, and analysis and interpretation of experimental data. He is the author of more 200 papers and 14 books.

Olesya Vladimirovna Falomkina (born in 1979). Graduated from the Faculty of Physics at Lomonosov Moscow State University in 2002. She received her Candidate’s degree in mathematical modeling, numerical methods, and software development from Lomonosov Moscow State University in 2006. She has been a senior researcher of the Mathematical Modeling and Computer Science Department (earlier, Computer Methods in Physics) at the Faculty of Physics, Lomonosov Moscow State University, since 2005. Scientific interests: fuzzy and uncertain fuzzy mathematics, theory of possibilities, mathematical modeling, image processing, pattern recognition, and image analysis. She is the author of more than 35 papers and 1 book.

Dmitriy Aleksandrovich Balakin (born in 1991). Graduated from the Faculty of Physics of Lomonosov Moscow State University in 2014. He has worked as a junior researcher at the Mathematical Modeling and Computer Science Department (formerly, the Department of Computer Methods in Physics) of the Faculty of Physics of Lomonosov Moscow State University since 2019. Scientific interests: computer-aided measuring systems, subjective modeling, image and signal processing, possibility theory, and image analysis. Author of 30 articles.

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Pyt’ev, Y.P., Chulichkov, A.I., Falomkina, O.V. et al. Data Analysis and Interpretation: Methods of Computer-Aided Measuring Transducer Theory, Morphological Analysis, Possibility Theory, and Subjective Mathematical Modeling. Pattern Recognit. Image Anal. 33, 1515–1563 (2023). https://doi.org/10.1134/S1054661823040351

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