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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

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