Abstract
The article deals with the problem of determining the spatial position and spatial orientation of an object from its image. The task is reduced to 3D reconstruction in space of a finite set of points from its central projection. Simple mathematical reasoning allows us to conclude that with a small motion in the space of a finite set of points, its central projection remains unique. This provides a theoretical basis for developing an algorithm for the above reconstruction. The article proposes an algorithm for reconstructing a finite set of points in space based on minimizing the Hausdorff distance function between a given flat set and an auxiliary finite set of a 3D model of an object. To minimize this function, a combined method for the numerical calculation of the minimum point is proposed, in which each subsequent method uses the calculated point as the initial one. In addition, the article proposes an algorithm for choosing the starting point of the iterative minimization algorithm, based on the known spatial dimensions of the object under study.
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Acknowledgments
This work was supported by the Ministry of Education and Science of Russia (the project “Development of Virtual 3D Reconstruction of Historical Objects Technique”, scientific theme code 2019-0920, project number in the research management system FZUU-0633-2020-0004).
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Klyachin, A.A., Klyachin, V.A. (2022). Geometric Fitting in Problem of Spatial Position of Object Determination by Image. In: Arai, K. (eds) Proceedings of the Future Technologies Conference (FTC) 2021, Volume 2. FTC 2021. Lecture Notes in Networks and Systems, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-030-89880-9_16
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DOI: https://doi.org/10.1007/978-3-030-89880-9_16
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