Klyachin A.A., Klyachin V.A. Algorithm for restoring the surface of an object from its image

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https://doi.org/10.15688/mpcm.jvolsu.2021.1.2

Aleksey A. Klyachin
Doctor of Physical and Mathematical Sciences, Head Of Department of Mathematical
Analysis and Function Theory,
Volgograd State University
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https://orcid.org/0000-0003-3293-9066 
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Vladimir A. Klyachin
Doctor of Physical and Mathematical Sciences, Head Of the Department of Computer
Science and Experimental Mathematics,
Volgograd State University
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https://orcid.org/0000-0003-1922-7849 
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. This paper describes an algorithm for constructing a surface based on the projection of a triangular mesh applied to this surface. In this case, the angles of the mesh triangles are assumed to be known. This algorithm can be applied to determining the orientation of a three-dimensional object from its snapshot, if the object surface has triangular elements with known angles in advance. In addition to the description of the algorithm, the article gives examples of surface restoration (see figures 2–4), calculates the calculation error for them and examples of the algorithm application in the problem of determining
the orientation of buildings from a photograph. As a result, a spatial triangular mesh was reconstructed from a given flat grid (see figure ref fig: fig1), and the calculation error was 6.21e-05. Measurements of the coordinates of a point in the images and calculations using the formulas (2) and (3) gave an error on average of 0.84°.

Key words: surface triangulation, central projection, object spatial orientation, system of quadratic equations .

Algorithm for restoring the surface of an object from its image by Klyachin A.A., Klyachin V.A. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 24 No. 1 2021, pp. 16-24

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