Skip to content
KPI Science News
ISSN 2617-5509 · e‑ISSN 2663-7472 Open Access · CC BY 4.0
Vol. 142 · Issue 1 · 2026 Mar 30, 2026 article

METHOD FOR DETECTING CORNER POINTS IN IMAGES USING A COROTATIONAL BEAM SPLINE

IO
Igor Orynyak Corresponding Faculty of Applied Mathematics, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine Ukraine
DK
Dmytro Koltsov Faculty of Applied Mathematics, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine Ukraine
DT
Danylo Tavrov Faculty of Applied Mathematics, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine Ukraine
PublishedMar 30, 2026
PDF (Ukrainian)
KPISN 1 VOL 142 · 1
VOL 142 · ISS 1 · 2026 View issue

Abstract

Background. The detection of corner points in images is of great importance for object identification and has numerous applications in computer vision and pattern recognition. Typically, this task is performed using geometric analysis of black-and-white contours, to which Gaussian smoothing is subsequently applied in order to identify points of maximum curvature. Functional minimization is then applied to these regions to determine the angle magnitude between adjacent contour segments. A drawback of this approach lies in the difficulty of accounting for artifacts, as well as in the fact that increased smoothing leads to a reduction in the effective scale (size) of the image. Objective. To develop a method for detecting corner points in a digitized grayscale image using the corotational beam spline (CBS) method. Methods. Application of the CBS method using the proposed corner dummy points, for which the angular continuity condition is not satisfied; instead, zero curvature is postulated, resulting in a discontinuity (jump) in the tangent direction at that point. Results. The CBS method is applied to smooth the contour of a black-and-white image according to the length of a contour segment rather than the number of points on that segment, thereby preserving the overall image scale. Special corner dummy points are proposed that allow for a loss of angular continuity. Candidates for corner points are identified based on the local extrema of the curvature graph. For each point, the work is defined as the square of the distance between the point and its corresponding location on the contour, multiplied by the length of the segment associated with that point. The concept of integral work is introduced as the sum of individual works within the region of maximum curvature. A criterion for the existence of a corner point is developed based on the analysis of the ratio of individual works obtained in the absence and in the presence of a corner dummy point. Conclusions. The application of adaptive smoothing according to the distance between points on the contour, which are projections (correspondences) of the measured points, enables the method to be applied to datasets with varying point densities, thereby improving the quality of the reconstructed contour. The use of corner dummy points that allow for a loss of angular continuity makes it possible to more accurately reproduce the target contour, in particular sharp angle changes. Furthermore, the use of the ratio of individual works obtained in the absence and in the presence of a dummy point serves as a reliable criterion for corner point detection. The ratio of work values demonstrates an improvement by a factor of 8–30 for corner points, whereas for curved regions this value deteriorates or remains nearly unchanged.

Keywords

#corner points #corner identification #local integral work #corner dummy point #corotational beam spline #contour point renumbering

References

  1. Кольцов Д. Р., Ориняк І. В. (2025). Укладання неточно оцифрованого безколiрного пазла по кривизнi контурiв за допомогою коротацiйного балкового сплайна. Журнал обчислювальної та прикладної математики, (2), 5–32. https://doi.org/10.17721/2706-9699.2025.2.01
  2. Magnier, B., & Hayat, K. (2023). Revisiting mehrotra and nichani’s corner detection method for improvement with truncated anisotropic gaussian filtering. Sensors, 23(20), 8653. https://doi.org/10.3390/s23208653
  3. Andreopoulos, A., & Tsotsos, J. K. (2013). 50 years of object recognition: Directions forward. Computer vision and image understanding, 117(8), 827-891. https://doi.org/10.1016/j.cviu.2013.04.005
  4. Mokhtarian, F., & Mohanna, F. (2006). Performance evaluation of corner detectors using consistency and accuracy measures. Computer Vision and Image Understanding, 102(1), 81-94. https://doi.org/10.1016/j.cviu.2005.11.001
  5. Rodehorst, V., & Koschan, A. (2006, March). Comparison and evaluation of feature point detectors. In 5th international symposium Turkish-German joint geodetic days. Berlin, Germany, 29–31 March 2006.
  6. Jing, J., Liu, C., Zhang, W., Gao, Y., & Sun, C. (2023). ECFRNet: Effective corner feature representations network for image corner detection. Expert Systems with Applications, 211, 118673. https://doi.org/10.1016/j.eswa.2022.118673
  7. Song, W., Zhong, B., & Sun, X. (2019). Building corner detection in aerial images with fully convolutional networks. Sensors, 19(8), 1915. https://doi.org/10.3390/s19081915
  8. Bansal, M., & Daniilidis, K. (2014). Geometric urban geo-localization. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 3978-3985). https://doi.org/10.1109/CVPR.2014.508
  9. Zheng, Y., Li, X., & Weng, Y. (2024). Reunion helper: an edge matcher for sibling fragment identification of the Dunhuang manuscript. Heritage Science, 12(1). https://doi.org/10.1186/s40494-024-01150-3
  10. Zhang, H., Xiao, L., & Xu, G. (2020, August). A novel tracking method based on improved FAST corner detection and pyramid LK optical flow. In 2020 Chinese control and decision conference (CCDC) (pp. 1871-1876). IEEE. https://doi.org/10.1109/CCDC49329.2020.9164332
  11. Zhang, Y., Li, G., Xie, X., & Wang, Z. (2017, May). A new algorithm for accurate and automatic chessboard corner detection. In 2017 IEEE International Symposium on Circuits and Systems (ISCAS) (pp. 1-4). IEEE. https://doi.org/10.1109/ISCAS.2017.8050637
  12. Kerstein, T., Roth, H., & Wahrburg, J. (2014, March). Accurate X-corner Fiducial Marker Localization in Image Guided Surgery (IGS). In Proceedings of the International Conference on Pattern Recognition Applications and Methods, Angers, France, 6–8 March 2014; pp. 471–478. https://doi.org/10.5220/0004751904710478
  13. Xia, Y., Wu, H., Zhu, L., Qi, W., Zhang, S., & Zhu, J. (2024). A multi-sensor fusion framework with tight coupling for precise positioning and optimization. Signal Processing, 217, 109343. https://doi.org/10.1016/j.sigpro.2023.109343
  14. Tang, Y., Huang, Z., Chen, Z., Chen, M., Zhou, H., Zhang, H., & Sun, J. (2023). Novel visual crack width measurement based on backbone double-scale features for improved detection automation. Engineering Structures, 274, 115158. https://doi.org/10.1016/j.engstruct.2022.115158
  15. Benam, A., Drew, M. S., & Atkins, M. S. (2017, April). A CBIR system for locating and retrieving pigment network in dermoscopy images using dermoscopy interest point detection. In 2017 IEEE 14th International Symposium on Biomedical Imaging (ISBI 2017) (pp. 122-125). IEEE. https://doi.org/10.1109/ISBI.2017.7950483
  16. Yazdi, R., Khotanlou, H., & Khademfar, H. (2024). Robust Corner Detection Using Local Extrema Differences. International Journal of Web Research, 7(1), 69-84. https://doi.org/10.22133/ijwr.2024.458246.1217
  17. Rosten, E., Porter, R., & Drummond, T. (2008). Faster and better: A machine learning approach to corner detection. IEEE transactions on pattern analysis and machine intelligence, 32(1), 105-119. https://doi.org/10.1109/TPAMI.2008.275
  18. Gao, C., Panetta, K., & Agaian, S. (2015, May). Robust template based corner detection algorithms for robotic vision. In 2015 IEEE International Conference on Technologies for Practical Robot Applications (TePRA) (pp. 1-6). IEEE. https://doi.org/10.1109/TePRA.2015.7219683
  19. Morevec, H. P. (1977, August). Towards automatic visual obstacle avoidance. In Proceedings of the 5th international joint conference on Artificial intelligence-Volume 2 (pp. 584-584).
  20. Wang, J., & Zhang, W. (2018, March). A survey of corner detection methods. In 2018 2nd International Conference on Electrical Engineering and Automation (ICEEA 2018) (pp. 214-219). Atlantis Press. https://doi.org/10.2991/iceea-18.2018.47
  21. Harris, C., & Stephens, M. (1988, August). A combined corner and edge detector. In Alvey vision conference (Vol. 15, No. 50, pp. 10-5244). https://doi.org/10.5244/C.2.23
  22. Wang, M., Sun, C., & Sowmya, A. (2022). Efficient corner detection based on corner enhancement filters. Digital Signal Processing, 122, 103364. https://doi.org//10.1016/j.dsp.2021.103364
  23. Sun, X., & Zhong, B. (2023). A rotation-invariant corner detector based on the median of subpixelized triangle. Journal of King Saud University-Computer and Information Sciences, 35(8), 101645. https://doi.org/10.1016/j.jksuci.2023.101645
  24. Canny, J. (1986). A Computational Approach to Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6), 679-698 https://doi.org/10.1109/TPAMI.1986.4767851
  25. Zhang, S., Li, B., Zhang, Z., Ma, J., Li, P., & Wang, H. (2020). Robust corner finding based on multi-scale k-cosine angle detection. IEEE Access, 8, 66741-66748. https://doi.org/10.1109/ACCESS.2020.2984566
  26. Han, J. H., & Poston, T. (2001). Chord-to-point distance accumulation and planar curvature: a new approach to discrete curvature. Pattern Recognition Letters, 22(10), 1133-1144. https://doi.org/10.1016/S0167-8655(01)00063-0
  27. Awrangjeb, M., & Lu, G. (2008). Robust image corner detection based on the chord-to-point distance accumulation technique. IEEE transactions on multimedia, 10(6), 1059-1072. https://doi.org/10.1109/TMM.2008.2001384
  28. Chen He, X., & Yung, N. H. (2008). Corner detector based on global and local curvature properties. Optical engineering, 47(5), 057008-057008-12. https://doi.org/10.1117/1.2931681
  29. Rattarangsi, A., & Chin, R. T. (1992). Scale-Based Detection of Corners of Planar Curves. IEEE Transactions on Pattern Analysis & Machine Intelligence, 14(04), 430-449. https://doi.org/10.1109/ICPR.1990.118242
  30. Zhong, B., Ma, K. K., & Liao, W. (2008). Scale-space behavior of planar-curve corners. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(8), 1517-1524. https://doi.org/10.1109/TPAMI.2008.295
  31. Mokhtarian, F., & Mackworth, A. (1986). Scale-based description and recognition of planar curves and two-dimensional shapes. IEEE transactions on pattern analysis and machine intelligence, (1), 34-43. https://doi.org/10.1109/TPAMI.1986.4767750
  32. Mokhtarian, F., & Mackworth, A. K. (1992). A theory of multiscale, curvature-based shape representation for planar curves. IEEE transactions on pattern analysis and machine intelligence, 14(8), 789-805. https://doi.org/10.1109/34.149591
  33. Ohrhallinger, S., & Wimmer, M. (2018). Stretchdenoise: Parametric curve reconstruction with guarantees by separating connectivity from residual uncertainty of samples. arXiv preprint arXiv:1808.07778. https://doi.org/10.48550/arXiv.1808.07778
  34. Eubank, R. L. (1999). Nonparametric regression and spline smoothing. CRC press. https://doi.org/10.1201/9781482273144
  35. Bertolazzi, E., Frego, M., & Biral, F. (2020). Point data reconstruction and smoothing using cubic splines and clusterization. Mathematics and Computers in Simulation, 176, 36-56. https://doi.org/10.1016/j.matcom.2020.04.002
  36. Lee, E. T. (1989). Choosing nodes in parametric curve interpolation. Computer-Aided Design, 21(6), 363-370. https://doi.org/10.1016/0010-4485(89)90003-1
  37. Orynyak, I., Koltsov D., Chertov O., Mazuryk R. (2022). Application of beam theory for the construction of twice differentiable closed contours based on discrete noisy points. System Research and Information Technologies. 2022, N4, p.119-140. https://doi.org/10.20535/SRIT.2308-8893.2022.4.10
  38. Orynyak, I., Yablonskyi, P., Koltsov D., Chertov O., Mazuryk R. (2024) Fairness of 2D corotational beam spline as compared with Geometrically nonlinear elastic beam. System Research and Information Technologies, N3, p.119-140 https://doi.org/10.20535/SRIT.2308-8893.2024.3.07
  39. Orynyak, I., Kuznetsov, Y., & Mazuryk, R. (2025). Controllable Curvature Smoothing of the Pipeline Positions by 2D Corotational Beam Spline. Journal of Pipeline Systems Engineering and Practice, 16(3), 04025047. https://doi.org/10.1061/JPSEA2.PSENG-1739
  40. Orynyak, I., Kuznetsov, Y., & Tavrov, D. (2026). Efficient construction of clothoidal splines using corotational beam splines. Journal of Computational and Applied Mathematics, 117318. https://doi.org/10.1016/j.cam.2025.117318
  41. Alberg, J. H., Nilson, E. N., & Walsh, J. L. (1967). The theory of splines and their applications. New York: Academic Press.
  42. Levien, R., & Séquin, C. H. (2009). Interpolating splines: Which is the fairest of them all? Computer-Aided Design and Applications, 6(1), 91-102. https://doi.org/10.3722/cadaps.2009.91-102
§ 06 — Related

Similar articles in this journal

Related peer-reviewed studies published in this journal.
View all issues

Similar Articles

You may also start an advanced similarity search for this article.