Modeling of radiopaque angiographic images for determining vessel parameters using dual spectral scanning

The purpose of the study is to develop a methodology for cognitive determination of medical halftone images’ parameters based on dual spectral scanning methods. The mathematical model of radiopaque images of vessels is described in this work. Based on this model, the method for determining the vessel parameters using spectral scanning was developed. The model is based on the representation of oriented brightness differences using Walsh functions. This vessel model was convolved with wavelets based on the first Walsh functions. The result of the convolution will yield extremes at the points of brightness differences. We can use this result as an informative parameter for the presence of a vessel contour. Information from many such parameters in a local area is aggregated and gives an averaged characteristic of this area. This leads to a significant decrease in the influence of noise on the final result due to an acceptable decrease in the resolution of localization of significant arterial occlusions. The averaged results of the convolution of Walsh functions are recommended to be calculated using a two-dimensional spectral Walsh transform in a sliding window with subsequent frequency selection. The method is illustrated by the example of classifying the contour of the boundary of a vessel model and a real radiopaque image of an artery with a high noise level. A comparison of theoretical and practical approaches to solving the problem of detecting the contour of arteries is carried out. Experimental studies of the proposed method have shown the possibility of estimating informative parameters even under conditions of analyzing images with unsatisfactory contrast and with a low signal-to-noise ratio. The use of the dual spectral scanning method in systems for automatic analysis of radiopaque angiographic images allows obtaining informative parameters in conditions of high noise in the images.

1. Fraz M.M., Remagnino P., Hoppe A., et al. Blood Vessel Segmentation Methodologies in Retinal Images – A Survey. Computer Methods and Programs in Biomedicine. 2012;108(1):407–433. https://doi.org/10.1016/j.cmpb.2012.03.009

2. Yu J., Jiang Q. Asymmetric Up-Down Sampling and Complementary-Fusion Network for Coronary Artery Segmentation on Coronary Angiography Images. Biomedical Signal Processing and Control. 2025;105. https://doi.org/10.1016/j.bspc.2025.107633

3. Zhao Ch., Vij A., Malhotra S., et al. Automatic Extraction and Stenosis Evaluation of Coronary Arteries in Invasive Coronary Angiograms. Computers in Biology and Medicine. 2021;136. https://doi.org/10.1016/j.compbiomed.2021.104667

4. Nasr-Esfahani E., Samavi S., Karimi N., Soroushmehr S.M.R., Ward K., Jafari M.H. Vessel Extraction in X-Ray Angiograms Using Deep Learning. In: 2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 16–20 August 2016, Orlando, FL, USA. IEEE; 2016. P. 643–646. https://doi.org/10.1109/EMBC.2016.7590784

5. Danilov V.V., Klyshnikov K.Yu., Gerget O.M., et al. Real-Time Coronary Artery Stenosis Detection Based on Modern Neural Networks. Scientific Reports. 2021;11. https://doi.org/10.1038/s41598-021-87174-2

6. Paulauskaite-Taraseviciene A., Siaulys J., Jankauskas A., Jakuskaite G. A Robust Blood Vessel Segmentation Technique for Angiographic Images Employing Multi-Scale Filtering Approach. Journal of Clinical Medicine. 2025;14(2). https://doi.org/10.3390/jcm14020354

7. Liu I., Sun Y. Recursive Tracking of Vascular Networks in Angiograms Based on the Detection-Deletion Scheme. IEEE Transactions on Medical Imaging. 1993;12(2):334–341. https://doi.org/10.1109/42.232264

8. Freeman W.T., Adelson E.H. The Design and Use of Steerable Filters. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1991;13(9):891–906. https://doi.org/10.1109/34.93808

9. Weiler M., Hamprecht F.A., Storath M. Learning Steerable Filters for Rotation Equivariant CNNs. In: 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 18–23 June 2018, Salt Lake City, UT, USA. IEEE; 2018. P. 849–858. https://doi.org/10.1109/CVPR.2018.00095

10. Krig S. Computer Vision Metrics: Textbook Edition. Cham: Springer; 2016. 637 p. https://doi.org/10.1007/978-3-319-33762-3

11. Krasnobaev A.A. Simple Image Feature Detector Algorithms Survey and Estimation of Hardware Realization Ability. Keldysh Institute Preprints. 2005;(114):1–20. (In Russ.).

12. Bobyr M.V., Khrapova N.I. A Cognitive Model for Making a Decision about the Presence of Object Boundaries in an Image. In: Programmnaya inzheneriya: sovremennye tendentsii razvitiya i primeneniya (PI-2024): sbornik materialov VIII Vserossiiskoi nauchno-prakticheskoi konferentsii s mezhdunarodnym uchastiem, 17 October 2024, Kursk, Russia. Kursk: ZAO "Universitetskaya kniga"; 2024. P. 102–105. (In Russ.).

13. Ahmed N., Rao K.R. Orthogonal Transforms for Digital Signal Processing. Berlin, Heidelberg: Springer; 1975. 264 p. https://doi.org/10.1007/978-3-642-45450-9

14. Kekre H.B., Athawale A., Sadavarti D. Algorithm to Generate Wavelet Transform from an Orthogonal Transform. International Journal of Image Processing. 2010;4(4):444–455.

15. Farkov Yu.A., Manchanda P., Siddiqi A.H. Construction of Wavelets Through Walsh Functions. Singapore: Springer; 2019. 381 p. https://doi.org/10.1007/978-981-13-6370-2

16. Korenevsky N.A., Ionescu F., Kuzmin A.A., Al-Kasasbeh R.T. Synthesis of the Combined Fuzzy Rules for Medical Applications with Using Tools of Exploration Analysis. Biomedical Radioelectronics. 2009;(5):65–75. (In Russ.).

17. Kuzmin A., Sukhomlinov A., Filist S., Zhilin I. Double Spectral Scanning Method for Determining Arterial Contours on Coronary Angiography Images. Vestnik Kazanskogo gosudarstvennogo energeticheskogo universiteta. 2024;16(4):13–24. (In Russ.).

18. Malyutina I.A., Kuzmin A.A., Shatalova O.V. Methods and Algorithms of Analyzing Chest Radiographs Using Local Windows for Pathology Detection. Prikaspiiskii zhurnal: upravlenie i vysokie tekhnologii. 2017;(3):131–138. (In Russ.).

19. Kudryavtsev P.S., Kuzmin A.A., Savinov D.Yu., Filist S.A., Shatalova O.V. Modeling Morphological Structures on Radiography of Thorax in Intelligent Diagnostic Systems for Medical Purposes. Prikaspiiskii zhurnal: upravlenie i vysokie tekhnologii. 2017;(3):109–120. (In Russ.).

20. Canny J. A Computational Approach to Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986;PAMI-8(6):679–698. https://doi.org/10.1109/TPAMI.1986.4767851