E.N. Afanasyev1, S.V. Vasilyev2, I.V. Zhigulina3

1-3 MESC AF «N.E. Zhukovsky and Y.A. Gagarin Air Force Academy» (Voronezh, Russia)

1 egor88jj@gmail.com; 2 p-digim@mail.ru; 3 ira_zhigulina@mail.ru

One of the primary tasks in video data preprocessing for machine vision systems involves detecting objects within images. For this purpose, two-dimensional discrete filtering can be employed. However, its effectiveness decreases significantly when an image contains multiple objects within similar shapes, since each object requires an individually optimized filter. Single-reference two-dimensional discrete filtering does not allow the simultaneous use of multiple reference templates for synthesizing a unified filter.

This problem can be addressed through polyreference two-dimensional filtering, where a single filter is synthesized while being simultaneously adjusted to multiple reference templates or different segments of a single reference. The goal of this study is to develop a two-dimensional discrete filtering procedure capable of generating a unified filter for a set of references while maintaining sensitivity to object shapes.

The study demonstrates how the filter’s response to image regions containing objects can be improved by explicitly accounting for reference samples during filter synthesis. To enable the simultaneous detection of all similar objects using a single filter, the proposed method utilizes multiple reference templates containing characteristic contour segments. The concept of ‘reference segments’ is introduced, where each segment corresponds to a distinct part of an object’s contour. When multiple reference segments are applied, constraints are imposed on the filter’s response, resulting in a conditional minimum of the quadratic energy form instead of a strict extremum. The filter is synthesized by determining the conditional minimum of the Lagrangian function.

The structure of the Lagrangian function is defined in this work. It incorporates not only the quadratic form but also a collection of filter samples obtained from different reference templates or segments of a single reference (if partitioned). The Langrangian function includes a filter performance metric for each reference template or reference segment, calculated as the dot product of the filter’s impulse response vector and the reference sample vector. For critical reference segments, this product equals one; otherwise, it is zero. The study shows that this approach remains valid even when synthesizing a unified filter for detecting multiple objects with differing shapes.

Processing examples of test and real-world images demonstrate that the proposed method is highly sensitive to reference image selection, but significantly improves computational efficiency by enabling the use of a single small-aperture filter for multiple references. Polyreference two-dimensional discrete filtering allows a single filter to simultaneously identify regions containing objects of varying shapes, reducing computational overhead and minimizing false alarms in subsequent image processing stages. The results are directly applicable to automated video processing in machine vision systems.

Afanasyev E.N., Bogoslovsky A.V., Zhigulina I.V. Polyreference discrete 2D filtering. Radiotekhnika. 2026. V. 90. № 1. P. 38−44. DOI: https://doi.org/10.18127/j00338486-202601-04 (In Russian)

1. Gruzman I.S., Kirichuk V.S., Kosyh V.P., Peretjagin G.I., Spektor A.A. Cifrovaja obrabotka izobrazhenij v informa-cionnyh sistemah: Uchebnoe posobie. Novosibisrk: Izd-vo NGTU. 2002. 352 s. (in Russian).
2. Davies R., Turk M. Komp'ternoe zrenie. Sovremennye metody i perspektivy razvitija. M.: DMK Press. 2022. 690 s. (in Russian).
3. Gonsales R., Vuds R. Cifrovaja obrabotka izobrazhenij. Izd. 3-e, ispr. i dop. M.: Tehnosfera. 2019. 1104 s. (in Russian).
4. Shapiro L, Stokmann Dzh. Komp'juternoe zrenie. M.: Laboratorija znanij. 2020. 763 s. (in Russian).
5. Novikov A.I., Pron'kin A.V. Linejnye operatory s vektornymi maskami v zadachah cifrovoj obrabotki izobrazhenij. Komp'juternaja optika. 2023. T. 47. № 4. S. 596-604. DOI: 10.18287/2412-6179-SO-1241 (in Russian).
6. Gaj V.E., Domnina N.A., Barinov R.O., Poljakov I.V., Golubenko V.A., Kuznecov G.D. Model' i algoritmy obnaruzhenija ob’ektov na izobrazhenii s ispol'zovaniem lokal'nogo priznakovogo opisanija. Informacionnye i matematicheskie tehnologii v nauke i upravlenii. 2023. № 1(29) S. 33-43. DOI: 10.38028/ESI/2023.29.1.003 (in Russian).
7. Honina S.N., Porfir'ev A.P., Horin A.P., Dzjuba A.P., Serafimovich R.V., Skidanov R.V. Mnogoporjadkovye opticheskie prostranstvennye vihrevye fil'try dlja odnovremennogo vydelenija konturov razlichnyh chastej ob’ekta. Komp'juternaja optika. 2024. T. 48. № 4. S. 525-534. DOI: 10.18287/2412-6179-SO-1497 (in Russian).
8. Egorova E.V., Aksjaitov M.H., Rybakov A.N. Verojatnostnaja procedura raspoznavanija i identifikacija prostranstvennyh ob’ektov. Uspehi sovremennoj radiojelektroniki. 2023. № 3. S. 53–63. DOI: https://doi.org/10.18127/j20700784-202303-05 (in Russian).
9. Aboukhres S., Zerek A., Alfarah R. Digital Wiener filtering for signal and contour processing. 5th International conference on control engineering & information technology (CEIT-2017). Proceeding of engineering and technology – PET. V. 33. Р. 67-71.
10. Obrabotka mnogomernyh signalov. V 2-h knigah. Kn. 1. Linejnaja mnogomernaja diskretnaja obrabotka signalov. Metody analiza i sinteza. Pod red. A.V. Bogoslovskogo. M.: Radiotehnika. 2013. 168 s. (in Russian)/
11. Pantjuhin M.A., Bogoslovskij A.V., Zhigulina I.V. Dvumernaja diskretnaja fil'tracija testovyh izobrazhenij. Radio-tehnika. 2020. T. 84. № 3(5). S. 64–72. DOI: 10.18127/j00338486-202003(05)-07 (in Russian).
12. Bogoslovskij A.V., Afanas'ev A.S., Zhigulina I.V., Pantjuhin M.A. Okno prinjatija reshenija i kriterij ego ispol'zovanija pri dvumernoj diskretnoj fil'tracii. Radiotehnika. 2024. T. 88. № 11. S.78−87. DOI: 10.18127/j00338486-202411-11 (in Russian).