METHOD FOR DETECTING CORNER POINTS IN IMAGES USING A COROTATIONAL BEAM SPLINE
DOI:
https://doi.org/10.20535/kpisn.2026.1.349268Keywords:
corner points, corner identification, local integral work, corner dummy point, corotational beam spline, contour point renumberingAbstract
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.
References
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Eubank, R. L. (1999). Nonparametric regression and spline smoothing. CRC press. https://doi.org/10.1201/9781482273144
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
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
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
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
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
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
Alberg, J. H., Nilson, E. N., & Walsh, J. L. (1967). The theory of splines and their applications. New York: Academic Press.
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
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