Identification of television images in vision systems based on mathematical apparatus of cubic normalized B-splines

Introduction. The solution to the problem of television images identification under the creation of autonomous robots, vision systems, and noisy image analysis systems is considered. The question is, for example, on severe observing conditions hindering the registration process, and null aprior information on the type of background noise. The work objective is to develop and evaluate the efficiency of the method for image edge detection (two-dimensional signal) against the background of pulse noise using the mathematical apparatus of cubic B-splines. Materials and Methods. Involving intense background noise, spline-approximation of discrete values of signals and images is usually unproductive and leads to raw errors. In this case, the method of differentiating the image line against the noise background allows calculating the signal derivative with sufficient accuracy. Taking into account the information on the behavior of the first derivative, local maxima in the image line against the noise background are defined. The task of television image edge detection is solved by a new technique of spline-differentiation. For this, the image matrix is divided into lines and columns; the differentiation is performed; and then the edge extraction operators are calculated. Unlike the known approaches, the differentiation takes into account data on the intensity in the whole image line. This minimizes the noise effect. Image edges are defined using an intensity gradient. The resulting spline-differentiation algorithm is used for mathematical modeling. Research Results. The authors of the paper for the first time propose a high-precision method of digital differentiation of two-dimensional signals. This approach allows calculating values of the two-dimensional signal derivative and its gradient with sufficiently high accuracy. With that, there is no need to use standard numerical differentiation procedures which are incorrect in themselves. Lena test image distorted by pulse noises of “dead pixels” and “salt-pepper” is processed by the Sobel operator and the spline-differentiation method. Values of е_ско , SNR and SNRF are tabulated and analyzed. For the Lena test image, the gain in decibels was as follows: according to the MSD (mean-square deviation) - 1.6 ÷ 2.7; relative to peak signal/ SNR noise ratio - 8 ÷ 9.4; relative to peak signal/ MSD noise of SNRF background - 11 ÷ 12. Discussion and Conclusions. Under the conditions of rapid development of microtechnology, the problems solved with the help of vision systems take a new way of application. This proves the relevance of research in the field of increasing the efficiency and stability of methods and algorithms for digital processing of two-dimensional signals. The experiments show that the presented technique has considerably higher noise immunity than algorithms based on standard differentiation procedures.

двумерный сигнал, изображение, выделение контуров, сглаживающий кубический В-сплайн, импульсный шум, two-dimensional signal, image, edge detection, smoothing cubic B-spline, pulse noise

1. Pratt, W. Tsifrovaya obrabotka izobrazheniy. [Digital image processing.] Moscow: Mir, 1982, 312 p. (in Russian).

2. Gonzalez, R., Woods, R. Tsifrovaya obrabotka izobrazheniy. [Digital image processing.] Moscow: Tekhnosfera, 2005, 1104 p. (in Russian).

3. Ahlberg, J., Nilson, E., Walsh, J. Teoriya splaynov i ee prilozheniya. [The theory of splines and their applications.] Moscow: Mir, 1972, 316 p. (in Russian).

4. Zavyalov, Y.S., Kvasov, B.I., Miroshnichenko, V.L. Metody splayn-funktsiy. [Spline-function methods.] Moscow: Nauka, 1980, 350 p. (in Russian).

5. Bezuglov, D.A., Krutov, V.A., Shvachko, O.V. Metod differentsirovaniya signalov s ispol'zovaniem splaynapproksimatsii. [The method of differentiation of signals using spline-approximation.] Fundamental Research, 2017, no.4, part 1, pp. 24 – 28 (in Russian).

6. Bezuglov, D.A., Krutov, V.A., Shvachko, O.V. Splayn-approksimatsiya v zadache differentsirovaniya signalov i izobrazheniy. [Spline approximation in the problem of differentiation of signals and images.] Modern High Technologies, 2017, no. 4, pp. 17–22 (in Russian).

7. Bezuglov, D.A., Kuzin, A.P., Voronin, V.V. Сontour detection based on wavelet differentiation. Mobile Multimedia/Image Processing, Security, and Applications, 2016: Proceedings of SPIE — The International Society for Optical Engineering, 2016, pp. 986–900.

8. Bezuglov, D.A., Bezuglov, Y.D., Shvidchenko, S.A. Method of discrete wavelet analysis of edges on the random background. 22nd International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision: poster papers proceedings. Plzen, 2014, pp. 15–19.

9. Voronin, V.V., et al. Inpainting strategies for reconstruction of missing data in images and videos: Techniques, algorithms and quality assessment. Intelligent Information Technologies for Industry: Proceedings of the First International Scientific Conference. Sochi, 2016, vol. 2, pp. 163–174.

10. Bezuglov, D.A., Pomortsev, P.M., Sklyarov, A.V. Obrabotka rezul'tatov izmereniy na baze approksimatsii plotnosti raspredeleniya sglazhivayushchimi kubicheskimi B- splaynami. [Processing of measurement results based on approximation of distribution density by smoothing cubic B-splines.] Measurement Technique, 2000, no. 9, pp. 32 (in Russian).

11. Bezuglov, D.A., Sklyarov, A.V. Algoritm vosstanovleniya volnovogo fronta na baze dvumernykh sglazhivayushchikh kubicheskikh normalizovannykh B-splaynov. [Algorithm for reconstructing the wave front on the basis of twodimensional smoothing cubic normalized B-splines.] Atmospheric and Oceanic Optics, 2000, vol. 13, no. 8, pp. 770 (in Russian).

12. Bezuglov, D.A., et al. Algoritmy otsenivaniya negaussovskikh protsessov na osnove matematicheskogo apparata sglazhivayushchikh B-splaynov. [Algorithms for estimating non-Gaussian processes on the basis of mathematical apparatus of smoothing B-splines.] Izvestiya vuzov. Severo-Kavkazskiy region. Natural Sciences. 2005, no. S4, pp. 99–106 (in Russian).

13. Bezuglov, D.A., et al. Suboptimal'nyy algoritm otsenivaniya na osnove apparata sglazhivayushchikh B-splaynov. [A suboptimal estimation algorithm based on smoothing B-splines.] Measurement Technique, 2006, no. 10, pp. 14–17 (in Russian).

14. Bezuglov, D.A., Shvidchenko, S.A. Informatsionnaya tekhnologiya veyvlet-differentsirovaniya rezul'tatov izmereniy na fone shuma. [Information technology of wavelet differentiation measurements results on the background noise.] Herald of Computer and Information Technologies, 2011, no. 6 (84), pp. 42–45 (in Russian).

15. Bezuglov, D., et al. Vydelenie konturov izobrazheniy v informatsionnykh i upravlyayushchikh sistemakh s ispol'zovaniem metoda veyvlet-preobrazovaniya. [Isolation of the contour image in information system and control system by using method of wavelet transform.] NonlinearWorld, 2012, no. 11, pp. 846–852 (in Russian).

16. Bezuglov, D.A., Rytikov, S.Y., Shvidchenko, S.A. Metod veyvlet-differentsirovaniya v zadache vydeleniya konturov. [Method of wavelet differentiation in the problem of allocation of contours.] Telecommunications and Radio Engineering, 2012, no. 6, pp. 52–57 (in Russian).

17. Bezuglov, D.A., et al. Informatsionnaya tekhnologiya identifikatsii izobrazheniy. [Information technology of identification picture.] Fundamental Research, 2015, no. 2, part 16, pp. 3466–3470 (in Russian).

18. Bezuglov, D.A., Kuzin, A.P. Informatsionnaya tekhnologiya vydeleniya konturov izobrazheniy na fone shuma. [Information technology of image edge detection in the noise condition.] Modern Problems of Science and Education, 2015, no. 2, part 2, pp. 190 (in Russian).