Geodesic
Algorithm for interpretation of phase images for measuring the three-dimensional geometry of dynamic objects
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 53-59.

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The problem of decoding phase images is relevant for a wide range of problems in the field of optical diagnostics of three-dimensional geometry of objects in thermophysical and fluid dynamics applications. In systems based on triangulation and structured illumination or interferometric systems, a three-dimensional profile of the measured object is restored from phase images. When measuring complex-profile objects with varying surface geometry, it is important, on the one hand, to perform measurements as quickly as possible, and on the other hand, to decode the received data as quickly as possible. In this paper, we propose an algorithm for decoding phase images, which has an algorithmic complexity of O(NlogN). The method is based on an iterative search for the minimum deviation of the model function from the measurement results. The use of the interval search algorithm made it possible to significantly reduce the computational complexity of the algorithm. The error of the proposed method is comparable to the error of the phase image decoding method based on the analytical solution of the system of equations de-scribing the intensity in the phase images.
Keywords: decoding of phase images, three-dimensional geometry, fast algorithm. 
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     author = {S. V. Dvoynishnikov and D. V. Kulikov and V. G. Meledin and V. V. Rakhmanov},
     title = {Algorithm for interpretation of phase images for measuring the three-dimensional geometry of dynamic objects},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {53--59},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a4/}
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S. V. Dvoynishnikov; D. V. Kulikov; V. G. Meledin; V. V. Rakhmanov. Algorithm for interpretation of phase images for measuring the three-dimensional geometry of dynamic objects. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 2, pp. 53-59. http://geodesic.mathdoc.fr/item/SJIM_2023_26_2_a4/

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