Approximation of planar point sets by point configurations
https://doi.org/10.25206/1813-8225-2023-186-55-59
Abstract
The paper is devoted to planar linear point sets having hierarchical structure. Point configurations arise naturally in several areas of computational geometry. In the paper, the linear approximation of planar point configurations is discussed. Planar point configuration is considered as a fuzzed and deformed image of some ideal configuration. Also, it may be considered as random realizations of ideal one. Pure images and deformed ones are described by the same hierarchical structures. The structure of approximating configuration is determined a priory. Image approximation is realized by mean of least square restoration. The correspondence of the structures is one of the parameters of approximation. Identification procedure is realized by linear transformations. Similarity transformations as general ones are used in the calculations.
About the Author
V. Yu. Yurkov V. Yu.
Omsk State Technical University
Russian Federation
Russian Federation
YURKOV Viktor Yuryevich, Doctor of Technical Sciences, Professor, Professor of Design and Technology of Light Industry Product Manufacture Department
Omsk
References
1. Yurkov V. Yu. Odnoparametricheskaya approksimatsiya ploskikh semeystv pryamykh [One-parameter approximation of planar families of straight lines] // Problemy mashinovedeniya. Problems of Mechanical Engineering. Omsk, 2019. P. 363–368. (In Russ.).
2. Podolak J., Shilane P., Giesen J., Gross M. [et al.]. Examplebased 3D scan completion // Proc. Symposium on Geometry Proceeding. 2005. P. 23–32. (In Engl.).
3. Karkishchenko A. N., Grechukhin I .A. Lokalizatsiya kharakternykh tochek na osnove estestvennoy simmetrii [Localisation of characteristic points based on natural image symmetry] // Intellektual’nyye sistemy upravleniya na zheleznodorozhnom transporte. Intelligent Control Systems for Railway Transport. Moscow, 2012. P. 261–265. (In Russ.).
4. Simari P., Kalogerakis E., Singh K. Folding meshes: Hierarchical mesh segmentation based on planar symmetry // Eurographics Symposium on Geometry Processing Proceedings. 2006. P. 111–119. DOI: 10.1145/1281957.1281972. (In Engl.).
5. Mikhlyayev S. V. Issledovaniye neiteratsionnogo metoda naimen’shikh kvadratov dlya otsenivaniya parametrov approksimiruyushchey okruzhnosti [A study of a non iterative least squares method for estimating the parameters of an approximating circle] // Vychislitel’nyye tekhnologii. Computational Technologies. 2008. Vol. 13, no. 5. P. 41–50. (In Russ.).
6. Prikhach I. V., Mamchits M. V., Gundina M. A. Priblizheniye okruzhnost’yu dannykh, poluchennykh pri obrabotke promyshlennykh izobrazheniy [Circle Approximation of industrial image processing data] // Х Masherovskiye chteniya. X Masherov Readings. Vitebsk, 2016. P. 25–27. ISBN 978-985-517-548-4. (In Russ.).
7. Efimov Yu. S., Matveyev I. A. Vydeleniye tochnykh granits raduzhki na izobrazhenii glaza [Iris image segmentation by paired gradient method with pupil boundary refinement] // Informatsionnyye tekhnologii. Information Technologies. 2017. Vol. 23, no. 4. P. 300–309. (In Russ.).
8. Konovalenko I. A., Kokhan V. V., Nikolayev D. P. Optimal’naya affinnaya approksimatsiya proyektivnogo preobrazovaniya izobrazheniy [Optimal affine approximation of image projective transformation] // Sensornyye sistemy. Sensory Systems. 2019. Vol. 33, no. 1. P. 7–14. DOI: 10.1134/S02350092190100629. (In Russ.).
9. Kozlovskiy A. N. Algoritm obnaruzheniya vershiny ugla na izobrazhenii na osnove approksimatsii kontura binarnogo izobrazheniya [Vertex detection algorithm in image processing based on binary image contour approximation] // Mezhdunarodnyy nauchnyy zhurnal. International Scientific Journal. 2016. No. 9. P. 63–73. (In Russ.).
Review
For citations:
Yurkov V. Yu. VY. Approximation of planar point sets by point configurations. Omsk Scientific Bulletin. 2023;(2):55-59. (In Russ.) https://doi.org/10.25206/1813-8225-2023-186-55-59
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