Klyachin V.A., Grigorieva E.G. Uniqueness Theorem of Reconstruction of Preimage by Its Image Under Degenerate Mapping

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https://doi.org/10.15688/mpcm.jvolsu.2022.2.2

Vladimir A. Klyachin
Doctor of Physical and Mathematical Sciences,
Head of the Computer Science and Experimental Mathemetics Department,
Volgograd State University
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https://orcid.org/0000000319227849 
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Elena G. Grigorieva
Candidate of Physical and Mathematical Sciences,
Associate Professor of the Computer Science and Experimental Mathemetics
Department, Volgograd State University
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https://orcid.org/000000018303262X 
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. One of the urgent problems in the construction of computer vision systems is the problem of determining the spatial orientation and spatial position of an object from a photograph. For example, this task is especially important for autonomous driving systems, where the positioning of nearby vehicles is a key issue for autonomous vehicles in an urban environment. In this regard, for example, in 2019, the Baidu Robotics and Autonomous Driving Laboratory together with Peking University, set an appropriate task for the Kaggle community (https://www.kaggle.com/c/pkuautonomousdriving) and provided more than 60,000 copies of threedimensional cars marked from 5,277 real images. In this article, we formulate some results that are the mathematical basis for substantiating methods for solving the abovementioned reconstruction problems in computer vision systems.

Key words: central projection, degenerate maps, preimage restoration, transformation groups, computer vision systems.

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Uniqueness Theorem of Reconstruction of Preimage by Its Image Under Degenerate Mapping by Klyachin V.A., Grigorieva E.G. is licensed under a Creative Commons Attribution 4.0 International License.

 

Citation in English: Mathematical Physics and Computer Simulation .  Vol. 25 No. 2 2022, pp. 17-22

 

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