Engineering and Technology
| Open Access |
DOI: Algorithm Of Generalization Based On The Minimum Quadrates Method
Shaxislam Batirovich Joldasov , Tashkent University of Information Technologies named after Muhammad Al- Khwarizmi, 105, A. Temur, Tashkent, 100142, Uzbekistan Saida Safibullayevna Beknazarova , Tashkent University of Information Technologies named after Muhammad Al- Khwarizmi, 105, A. Temur, Tashkent, 100142, UzbekistanAbstract
The article proposes an algorithm based on the least squares method for solving problems of simplifying and generalizing many lines. The proposed approach, unlike classical polyline simplification algorithms, does not require the location of the generated nodes at the points of the initial polyline, which increases the generality of the algorithm and improves the accuracy of geometric approximation. It was shown that the algorithm can be used for flexible simplification of contours at different accuracy levels, reduction of noise effects, and optimization of the number of nodes. The research results confirm that the method can be effectively applied in the fields of cartography, computer graphics, and image vectorization.
Keywords
Least squares method, polyline generalization, contour simplification
References
Canny, J. (1986). A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8 (6), 679-698.
Douglas, D., & Peucker, T. (1973). Algorithms for reducing the number of points required to represent a digitized line. The Canadian Cartographer, 10 (2), 112-122.
Unser, M. (1999). Splines: Perfect fit for signal and image processing. IEEE Signal Processing Magazine, 16 (6), 22-38.
Szeliski, R. (2010). Computer Vision: Algorithms and Applications. Springer.
Suzuki, S., & Abe, K. (1985). Topological structural analysis of digitized binary images by border following. Computer Vision, Graphics, and Image Processing.
Achanta, R., et al. (2012). SLIC superpixels compared to state-of-the-art superpixel methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34 (11), 2274-2282.
Freeman, H. (1974). Computer processing of line drawing images. ACM Computing Surveys, 6 (1), 57-97.
Xu, C., & Prince, J. (1998). Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing, 7 (3), 359-369.
Beknazarova, S., Abdullayeva, O., Abdullayev, S., Abdullayev, Z. Image processing: Face recognition by neural networks/E3S Web of Conferences 587
Beknazarova, S., Abdullayev, S., Abdullayeva, O., Abdullayev, Z. Machine Learning Method for Predicting Human Movements/AIP Conference Proceedings 3244 (1)
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Copyright (c) 2026 Shaxislam Batirovich Joldasov, Saida Safibullayevna Beknazarova
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