A.A. Potapov - Dr. Sci. (Phys.-Math.), Professor, Member of Russian A.M. Prokhorov Academy of Engineering. E-mail: potapov@cplire.ru

A task of detecting objects including stealthy ones at fuzzy images which are obtained from unmanned aerial vehicles (UAV) has been considered. As before the investigation is conducted within the framework of fractal-scaling thresholding including an adaptive threshold. At the same time issues of processing the images from UAV basing on the integer Lebesgue measure have been also considered. Currently the inadequacy of conventional physical models is clearly felt. Effectiveness of radio physical researches can be significantly enhanced by taking into account fractality of wave phenomena which develop at every stage of radiation, scattering and propagation of waves in different media. Revolutionary steps which consist in transfer of integer measure signals obtained by a system to the fractional measure space and following calling of scaling ratios allow to bring absolutely new ideas and methods into conventional areas of classical radio physics and radio electronics and to get results rather unexpected for practice which are however physically valid. The fractal radio systems conception, sampling topology, global fractal-scaling approach and the fractal paradigm underlies the scientific direction established by the author in Russia and over the world for the first time. The author has been investigating these issues for exactly 35 years. In the author\'s works the determinant conception of processing of low-contrast images was from the beginning involved unlike foreign works. The basis of the fractal detecting theory is results of fractal researches of essentiality of processes occurring during using the fractional measure theory and physical scaling theory in the radiolocation. In our opinion the obtained researches of the new experimental data in aggregate with the previous data give us enough information for proving of the fundamentals of theory and methods which were put forward by the author as long ago as the end of XX century. Application of fractals, scaling effects and fractional operators may mean the future of radio electronics because all the previous and current radio electronics is based solely (and only!) on the theory of integer-valued functions and does not take into account the fractional measure in information theory. Introduction of the fractal conception into radio physics, radio location, radio engineering and functional radio electronics is not only proved but is required.

 

1. Bespilotnye letatelnye apparaty: sprav. posobie (VUNC VVS «VVA») / Pod obshh. red. S.A. Popova. Voronezh: IPC «Nauchnaja kniga». 2015.
2. Bystrov R.P., Potapov A.A., Nemcov A.V. Bespilotnye letatelnye apparaty vedushhikh gosudarstv mira. M.: 3 CNII MO RF. 2016.
3. Potapov A.A. Fraktaly v radiofizike i radiolokacii: Topologija vyborki. Izd. 2-e, pererab. i dop. M.: Universitetskaja kniga. 2005.
4. Potapov A.A. Fraktaly i khaos kak osnova novykh proryvnykh tekhnologijj v sovremennykh radiosistemakh. (Dopolnenie k kn.: Kronover R. Fraktaly i khaos v dinamicheskikh sistemakh / Per. s angl.; Pod red. T.EH. Krenkelja). M.: Tekhnosfera. 2006. S. 374−479.
5. Potapov A.A., Guljaev JU.V., Nikitov S.A., Pakhomov A.A., German V.A. Novejjshie metody obrabotki izobrazhenijj / Pod red. A.A. Potapova. M.: FIZMATLIT. 2008. (monografija - po grantu RFFI № 07 - 07 - 07005).
6. Potapov A.A., German V.A. Detection of Artificial Objects with Fractal Signatures // Pattern Recognition and Image Analysis. 1998. V. 8. № 2. P. 226−229.
7. Potapov A.A. Ckejjling, integralnye operatory i fraktaly v obrabotke malokontrastnykh nechetkikh izobrazhenijj // Zbornik radova Konferencije MIT - Matematicke i informacione tehnologije (Vrnjackoj Banji od 5. do 9. septembra i u Becicima od 10. do 14. septembra 2013. godine). Kosovska Mitrovica: Prirodno-matematicki fakultet Ulverziteta u Pristini (Serbia). 2014. P. 530−538.
8. Podosenov S.A., Potapov A.A., Foukzon Dzh., Menkova E.R. Negolonomnye, fraktalnye i svjazannye struktury v reljativistskikh sploshnykh sredakh, ehlektrodinamike, kvantovojj mekhanike i kosmologii: V 3-kh tomakh / Pod red. A.A. Potapova. M.: LENAND. 2015.
9. Potapov A.A. Fraktalno-skejjlingovye ili masshtabno - invariantnye principy radiolokacii i ikh primenenie v radiolokatorakh s sintezirovannojj aperturojj // Sb. trudov III Vseros. Nauch. tekhnich. konf. «Perspektivy razvitija RLS dalnego obnaruzhenija, integrirovannykh sistem i kompleksov informacionnogo obespechenija VKO i kompleksov upravlenija i obrabotki informacii: «RTI Sistemy VKO - 2015» (Moskva, OAO «RTI im. akademika A.L. Minca», 28 maja 2015 g.)». M.: Izd-vo MGTU im. N.EH. Baumana. 2015. S. 573−90.
10. Potapov A.A. U istokov fraktalno-skejjlingovojj ili masshtabno-invariantnojj radiolokacii (1980−2015) // Radiotekhnika. 2015. № 8. S. 95−108.
11. Potapov Alexander A. Fractal Radar: Towards 1980−2015 // Proc. of CHAOS 2015 Int. Conf. (26−29 May 2015. France). Paris: Henri Poincaré Institute. 2015. P. 559−573.
12. Guljaev JU.V., Potapov A.A. Sozdanie i razvitie v IREH RAN teksturnykh i fraktalnykh metodov obnaruzhenija, obrabotki i raspoznavanija slabykh signalov i izobrazhenijj nepodvizhnykh i dvizhushhikhsja celejj na fone intensivnykh pomekh dlja sovremennykh zadach statisticheskojj radiofiziki, radiolokacii, navigacii i distancionnogo zondirovanija // Materialy 18-jj Mezhdunar. nauch.-tekhn. konf. «Problemy peredachi i obrabotki informacii v setjakh i sistemakh telekommunikacijj» (Rjazan, 26−28 oktjabrja 2015 g.). M.: Izd-vo «Gorjachaja linija - Telekom». 2015. S. 3−9.
13. Potapov A.A. Chaos Theory, Fractals and Scaling in the Radar: A Look from 2015. - Glava 12 v knige: Skiadas S. (ed.) The Foundations of Chaos Revisited: From Poincaré to Recent Advancements. - Switzerland, Basel: Springer. 2016. P. 195−218.