INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD
Purpose: The paper discusses the possibility for increasing the planet’s surface relief retrieving accuracy with the improved photoclinometry method through the reference of the desired relief to the altimetry data. The general approach to solving the problem is proposed. The use of altimeters havin...
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Kornienko, Yu. V. Dulova, I. A. Bondarenko, N. V. INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD |
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planet surface relief photometry altimetry optimal filtering statistical estimation of random value рельєф поверхні планети фотометрія альтиметр оптимальна фільтрація статистична оцінка випадкової величини |
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Article |
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Kornienko, Yu. V. Dulova, I. A. Bondarenko, N. V. |
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Kornienko, Yu. V. Dulova, I. A. Bondarenko, N. V. |
| author_sort |
Kornienko, Yu. V. |
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INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD |
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INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD |
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INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD |
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INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD |
| title_full_unstemmed |
INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD |
| title_sort |
involvement of altimetry information into the improved photoclinometry method for relief retrieval from a slope field |
| title_alt |
INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD УРАХУВАННЯ АЛЬТИМЕТРИЧНОЇ ІНФОРМАЦІЇ ПРИ ВИЗНАЧЕННІ РЕЛЬЄФУ ПОВЕРХНІ ПЛАНЕТИ МЕТОДОМ УДОСКОНАЛЕНОЇ ФОТОКЛИНОМЕТРІЇ ЗА ПОЛЕМ НАХИЛІВ |
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Purpose: The paper discusses the possibility for increasing the planet’s surface relief retrieving accuracy with the improved photoclinometry method through the reference of the desired relief to the altimetry data. The general approach to solving the problem is proposed. The use of altimeters having both wide and narrow beam patterns are discussed, but the narrow beam pattern altimeter data is studied more in detail. The spatial resolution of the retrieved relief calculated with the improved photoclinometry method conforms to the one of the source images. Altimetry allows absolute reference to the surface heights and improves the accuracy of the relief determination.Design/metodology/approach: The work is based on the improved photoclinometry method for the planet’s surface relief retrieving from images. This method is mathematically rigorous and uses the Bayesian statistical approach, that allows calculation of the most probable relief according to available observations.Findings: An approach to determining the optimal statistical estimate of the surface heights from images in the frames of the improved photoclinometry method is proposed and an expression for the optimal filter which converts source images along with the wide beam pattern altimetry data into the most probable relief of the planet surface area is presented. The reference technique for the narrow beam pattern altimeter data is formulated. The efficiency of the method has been verified with the computer simulation. The relief of the surface area in Mare Imbrium on the Moon was retrieved using three images and laser altimeter data taken by the “Lunar Reconnaissance Orbiter” spacecraft.Conclusions: Accounting for the narrow beam pattern altimeter data increases the accuracy of the relief determination. Using the narrow beam pattern altimeter data turns out to be more preferable over the involving wide beam pattern altimeter data. Computer simulation has shown that accounting for the narrow beam pattern altimeter data significantly increases the accuracy of the calculated heights as against using images exclusively and helps to speed up the calculation procedure.Key words: planet surface relief; photometry; altimetry; optimal filtering; statistical estimation of random valueManuscript submitted 26.11.2020Radio phys. radio astron. 2021, 26(2): 173-188REFERENCES1. PETTENGILL, G. H., ELIASON, E., FORD, P. G., LORIOT, G. B., MASURSKY, H. and MCGILL, G. E., 1980. Pioneer Venus Radar Results: Altimetry and Surface Properties. J. Geophys. Res. Space Phys. vol. 85, is. A13, pp. 8261–8270. DOI: https://doi.org/10.1029/JA085iA13p082612. SMITH, D. E., ZUBER, M. T., NEUMANN, G. A. and LEMOINE, F. G., 1997. Topography of the Moon from the Clementine Lidar. J. Geophys. Res. Planet. vol. 102, is. E1, pp. 1591–1611. DOI: https://doi.org/10.1029/96JE029403. THOMAS, N., HUSSMANN, H., SPOHN, T., LARA, L. M., CHRISTENSEN, U., AFFOLTER, M., BANDY, T., BECK, T., CHAKRABORTY, S., GEISSBUEHLER, U., GERBER, M., GHOSE, K., GOUMAN, J., HOSSEINIARAN,I S., KUSKE, K., PETEUT, A., PIAZZA, D., RIEDER, M., SERVONET, A., ALTHAUS, C., BEHNKE, T., GWINNER, K., HÜTTIG, C., KALLENBACH, R., LICHOPOJ, A., LINGENAUBER, K., LÖTZKE, H.-G., LÜDICKE, F., MICHAELIS, H., OBERST, J., SCHRÖDTER, R., STARK, A., STEINBRÜGGE, G., DEL TOGNO, S., WICKHUSEN, K., CASTRO, J. M., HERRANZ, M., RODRIGO, J., PERPLIES, H., WEIGEL, T., SCHULZE-WALEWSKI, S., BLUM, S., CASCIELLO, A., RUGI-GROND, E., COPPOOLSE, W., RECH, M., WEIDLICH, K., LEIKERT, T., HENKELMANN, R., TREFZGER, B. and METZ, B., 2021. The BepiColombo Laser Altimeter. Space Sci. Rev. vol. 217, is. 1, id. 25. DOI: https://doi.org/10.1007/s11214-021-00794-y4. SMITH, D. E., ZUBER, M. T., NEUMANN, G. A., MAZARICO, E., LEMOINE, F. G., HEAD, J. W., LUCEY, P. G., AHARONSON, O., ROBINSON, M. S., SUN, X., TORRENCE, M. H., BARKER, M. K., OBERST, J., DUXBURY, T. C., MAO, D., BARNOUIN, O. S., JHA, K., ROWLANDS, D. D., GOOSSENS, S., BAKER, D., BAUER, S., GLÄSER, P., LEMELIN, M., ROSENBURG, M., SORI, M, M., WHITTEN, J and MCCLANAHAN, T., 2017. Summary of the results from the lunar orbiter laser altimeter after seven years in lunar orbit. Icarus. vol. 283, pp. 70–91. DOI: https://doi.org/10.1016/j.icarus.2016.06.0065. PARUSIMOV, V. G. and KORNIENKO, Y. V., 1973. On determination of the most probable relief of a surface region by its optical image. Astrometriya i astrofizika. no. 19, pp. 20‑24. (in Russian).6. KORNIENKO, Y. V., DULOVA, I. A. and NGUYEN XUAN ANH, 1994. Wiener Approach to the Determination of Optical Characteristics of a Planetary Surface from Photometric Observations. Kinematika i fizika nebesnyh tel. vol. 10, no. 5, pp. 69‑76. (in Russian).7. KORNIENKO, Y. V. and NGUYEN XUAN ANH, 1996. Determination of relief and radiooptical parameters of a surface area through the use of a synthetic aperture radar. Radiofizika i elektronika. no. 1, pp. 129‑133. (in Russian).8. DULOVA, I. A., SKURATOVSKY, S. I., BONDARENKO, N. V. and KORNIENKO, Y. V., 2008. Reconstruction of the Surface Topography from Single Images with the Photometric Method. Sol. Syst. Res.. vol. 42, is. 6, pp. 522‑535. DOI: https://doi.org/10.1134/S00380946080600519. BONDARENKO, N. V., DULOVA, I. A. and KORNIENKO, Y. V., 2014. Topography of polygonal structures at the Phoenix landing site on mars through the relief retrieval from the HiRISE images with the improved photoclinometry method. Sol. Syst. Res. vol. 48, is. 4. pp. 243–258. DOI: https://doi.org/10.1134/S003809461404003010. VAN DIGGELEN, J., 1951. A photometric investigation of the slopes and the heights of the ranges of hills in the Maria of the Moon. Bull. Astron. Inst. Netherlands. vol. 11, pp. 283–289.11. AKIMOV, L. A. and KORNIENKO, Y. V., 1994. Light Scattering by the Lunar Surface. Kinematika i fizika nebesnyh tel. vol. 10, no. 2, pp. 14–21. (in Russian).12. KOCHIN, N. E., 1965. Vector calculus and beginnings of tensor calculus. Moscow, Russia: Nauka Publ. (in Russian).13. WILDEY, R. L., 1990. Radarclinometry of the earth and Venus from Space-Shuttle and Venera-15 imagery. Earth Moon Planet. vol. 48, pp. 197–231. DOI: https://doi.org/10.1007/BF0011385714. WATTERS, T. R. and ROBINSON, M. S., 1997. Radar and photoclinometric studies of wrinkle ridges on Mars. J. Geophys. Res. vol. 102, is. E5. pp. 10889–10903. DOI: https://doi.org/10.1029/97JE0041115. KIRK, R L., BARRETT, J. M. and SODERBLOM, L. A., 2003. Photoclinometry made simple? ISPRS Working Group IV/9 “Advances in planetary mapping”. Workshop. Houston, TX.16. LOHSE, V., HEIPKE, C. and KIRK, R. L. 2006. Derivation of planetary topography using multi-image shape-from-shading. Planet. Space Sci. vol. 54, is. 7, pp. 661–674. DOI: https://doi.org/10.1016/j.pss.2006.03.00217. GRUMPE, A. M. and WÖHLER, C., 2011. DEM construction and calibration of hyperspectral image data using pairs of radiance images. In: 2011 7th International Symposium on Image and Signal Processing and Analysis. pp. 609–614.18. GASKELL, R. W., BARNOUIN-JHA, O. S., SCHEERES, D. J., KONOPLIV, A. S., MUKAI, T., ABE, S., SAITO, J., ISHIGURO, M., KUBOTA, T., HASHIMOTO, T., KAWAGUCHI, J., YOSHIKAWA, M., SHIRAKAWA, K., KOMINATO, T., HIRATA, N. and DEMURA, H., 2008. Characterizing and navigating small bodies with imaging data. Meteorit. Planet. Sci. vol. 43, is. 6, pp. 1049–1061. DOI: https://doi.org/10.1111/j.1945-5100.2008.tb00692.x19. RAYMOND, C. A., JAUMANN, R., NATHUES, A., SIERKS, H., ROATSCH, T., PREUSKER, F., SCHOLTEN, F., GASKELL, R. W., JORDA, L., KELLER, H.-U., ZUBER, M. T., SMITH, D. E., MASTRODEMOS, N. and MOTTOLA, S., 2011. The Dawn Topography Investigation. Space Sci. Rev. vol. 163, pp. 487–510. DOI: https://doi.org/10.1007/s11214-011-9863-z20. GROUSSIN, O., JORDA, L., AUGER, A.-T., KÜHRT, E., GASKELL, R., CAPANNA, C., SCHOLTEN, F., PREUSKER, F., LAMY, P., HVIID, S., KNOLLENBERG, J., KELLER, U., HUETTIG, C., SIERKS, H., BARBIERI, C., RODRIGO, R., KOSCHNY, D., RICKMAN, H., A’HEARN, M. F., AGARWAL, J., BARUCCI, M. A., BERTAUX, J.-L., BERTINI, I., BOUDREAULT, S., CREMONESE, G., DA DEPPO, V., DAVIDSSON, B., DEBEI, S., DE CECCO, M., EL-MAARRY, M. R., FORNASIER, S., FULLE, M., GUTIÉRREZ, P. J., GÜTTLER, C., IP, W.-H, KRAMM, J.-R., KÜPPERS, M., LAZZARIN, M., LARA, L. M., LOPEZ MORENO, J. J., MARCHI, S., MARZARI, F., MASSIRONI, M., MICHALIK, H., NALETTO, G., OKLAY, N., POMMEROL, A., PAJOLA, M., THOMAS, N., TOTH, I., TUBIANA, C. and VINCENT, J.-B., 2015. Gravitational slopes, geomorphology, and material strengths of the nucleus of comet 67P/Churyumov-Gerasimenko from OSIRIS observations. Astron. Astrophys. vol. 583, id. A32. DOI: https://doi.org/10.1051/0004-6361/20152637921. JORDA, L., GASKELL, R., CAPANNA, C., HVIID, S., LAMY, P., ĎURECH,J., FAURY, G., GROUSSIN, O., GUTIÉRREZ, P., JACKMAN, C., KEIHM, S. J., KELLER, H. U., KNOLLENBERG, J., KÜHRT, E., MARCHI, S., MOTTOLA, S., PALMER, E., SCHLOERB, F. P., SIERKS, H., VINCENT, J.-B., A’HEARN, M. F., BARBIERI, C., RODRIGO, R., KOSCHNY, D., RICKMAN, H., BARUCCI, M. A., BERTAUX, J. L., BERTINI, I., CREMONESE, G., DA DEPPO, V., DAVIDSSON, B., DEBEI, S., DE CECCO, M., FORNASIER, S., FULLE, M., GÜTTLER, C., IP, W.-H., KRAMM, J. R., KÜPPERS, M., LARA, L. M., LAZZARIN, M., LOPEZ MORENO, J. J., MARZARI, F., NALETTO, G., OKLAY, N., THOMAS, N., TUBIANA, C. and WENZEL, K.-P., 2016. The global shape, density and rotation of Comet 67P/Churyumov-Gerasimenko from preperihelion Rosetta/OSIRIS observations. Icarus. vol. 277, pp. 257–278. DOI: https://doi.org/10.1016/j.icarus.2016.05.00222. VELIKODSKY, Y. I., KOROKHIN, V. V., SHKURATOV, Y. G., KAYDASH, V. G. and VIDEEN, G., 2016. Opposition effect of the Moon from LROC WAC data. Icarus. vol. 275, pp. 1–15. DOI: https://doi.org/10.1016/j.icarus.2016.04.00523. KOROKHIN, V., VELIKODSKY, Y., SHKURATOV, Y., KAYDASH, V., MALL, U., and VIDEEN, G., 2018. Using LROC WAC data for lunar surface photoclinometry. Planet. Space Sci. vol. 160, pp. 120–135. DOI: https://doi.org/10.1016/j.pss.2018.05.02024. VELICHKO, S., KOROKHIN, V., VELIKODSKY, Y, KAYDASH, V., SHKURATOV, Y. and VIDEEN, G., 2020. Removal of topographic effects from LROC NAC images as applied to the inner flank of the crater Hertzsprung S. Planet. Space Sci. vol. 193, id. 105090. DOI: https://doi.org/10.1016/j.pss.2020.10509025. DULOVA, I. A., BONDARENKO, N. V. and KORNIENKO, Y. V., 2010. Involvement of altimetric information into planet surface relief reconstruction from a set of images. In: The 8th International Kharkov Symposium of Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves and Workshop of Terahertz Technologies (MSMW’08 and TERATECH’08) Proceedings. Kharkov, Ukraine. vol. 2, pp. 766–768. DOI: https://doi.org/10.1109/MSMW.2010.554610726. BAYES, T., 1763. An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond. vol. 53, pp. 360–418.27. LAPLACE, P. S., 1891. Memoire sur la probabilité des causes par les événements. Oeuvres Complètes. vol. 8. Paris: Gauthier-villars, pp. 27–65.28. GAUSS, J. C. F., 1957. The theory of motion of celestial bodies revolving around the Sun along conical sections (1809). In: S. G. SUDAROV, ed. Selected geodesic works. Vol. 1. Moscow, Russia: Izdatelstvo geodezicheskoi literatury. (in Russian).29. LEGENDRE, A. M., 1820. Nouvelles methodes pour la determination des orbites des cometes. Second supplement. Paris. pp. 79–80.30. WALD, A. 1967. Statistical decision Functions. In: Positional games. Moscow, Russia: Nauka Publ., pp. 300–522. (in Russian).31. DE GROOT, M. H., 1970. Optimal statistical decisions. New York: McGRAW-Hill company.32. KORNIENKO, Y. V., 2005. Statistical Approach for Filtering and Image Informativity. Radiofizika i Elektronika. vol. 10, special issue, pp. 652-676. (in Russian).33. KORNIENKO, Y. V. and DULOVA, I. A., 2019. Optimal surface relief reconstruction from both the photometric and the altimetric data. Radiophys. Electron. vol. 24, no. 4, pp. 46–52. (in Russian). DOI: https://doi.org/10.15407/rej2019.04.04634. KORNIENKO, Y. V., 2008. Image Processing at the IRE NAS of Ukraine. Radiofizika i elektronika. vol. 3, special issue, pp. 423–45. (in Russian).35. SER WMS SYSTEM, 2020. SER WMS System [online]. [viewed 15 November 2020]. Available from: http://wms.lroc.asu.edu36. ROBINSON, M. S.; BRYLOW, S. M.; TSCHIMMEL, M., HUMM, D., LAWRENCE, S. J., THOMAS, P. C., DENEVI, B. W., BOWMAN-CISNEROS, E., ZERR, J., RAVINE, M. A., CAPLINGER, M. A., GHAEMI, F. T., SCHAFFNER, J. A., MALIN, M. C., MAHANTI, P., BARTELS, A., ANDERSON, J., TRAN, T. N., ELIASON, E. M., MCEWEN, A. S., TURTLE, E., JOLLIFF, B. L. and HIESINGER, H., 2010. Lunar Reconnaissance Orbiter Camera (LROC) Instrument Overview. Space Sci. Rev. vol. 150, is.1-4, pp. 81–124. DOI: https://doi.org/10.1007/s11214-010-9634-237. SMITH, D. E., ZUBER, M. T., NEUMANN, G. A., LEMOINE, F. G., MAZARICO, E., TORRENCE, M. H., MCGARRY, J. F., ROWLANDS, D. D., HEAD, J. W. III, DUXBURY, T. H., AHARONSON, O., LUCEY, P. G., ROBINSON, M. S., BARNOUIN, O. S., CAVANAUGH, J. F., SUN, X., LIIVA, P., MAO, D.-D., SMITH, J. C. and BARTELS, A. E., 2010. Initial observations from the Lunar Orbiter Laser Altimeter (LOLA). Geophys. Res. Lett. vol. 37, is 18, id. L18204. DOI: https://doi.org/10.1029/2010GL043751 |
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Видавничий дім «Академперіодика» |
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2021 |
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http://rpra-journal.org.ua/index.php/ra/article/view/1356 |
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rpra-journalorgua-article-13562021-06-30T10:22:33Z INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD INVOLVEMENT OF ALTIMETRY INFORMATION INTO THE IMPROVED PHOTOCLINOMETRY METHOD FOR RELIEF RETRIEVAL FROM A SLOPE FIELD УРАХУВАННЯ АЛЬТИМЕТРИЧНОЇ ІНФОРМАЦІЇ ПРИ ВИЗНАЧЕННІ РЕЛЬЄФУ ПОВЕРХНІ ПЛАНЕТИ МЕТОДОМ УДОСКОНАЛЕНОЇ ФОТОКЛИНОМЕТРІЇ ЗА ПОЛЕМ НАХИЛІВ Kornienko, Yu. V. Dulova, I. A. Bondarenko, N. V. planet surface relief; photometry; altimetry; optimal filtering; statistical estimation of random value рельєф поверхні планети; фотометрія; альтиметр; оптимальна фільтрація; статистична оцінка випадкової величини Purpose: The paper discusses the possibility for increasing the planet’s surface relief retrieving accuracy with the improved photoclinometry method through the reference of the desired relief to the altimetry data. The general approach to solving the problem is proposed. The use of altimeters having both wide and narrow beam patterns are discussed, but the narrow beam pattern altimeter data is studied more in detail. The spatial resolution of the retrieved relief calculated with the improved photoclinometry method conforms to the one of the source images. Altimetry allows absolute reference to the surface heights and improves the accuracy of the relief determination.Design/metodology/approach: The work is based on the improved photoclinometry method for the planet’s surface relief retrieving from images. This method is mathematically rigorous and uses the Bayesian statistical approach, that allows calculation of the most probable relief according to available observations.Findings: An approach to determining the optimal statistical estimate of the surface heights from images in the frames of the improved photoclinometry method is proposed and an expression for the optimal filter which converts source images along with the wide beam pattern altimetry data into the most probable relief of the planet surface area is presented. The reference technique for the narrow beam pattern altimeter data is formulated. The efficiency of the method has been verified with the computer simulation. The relief of the surface area in Mare Imbrium on the Moon was retrieved using three images and laser altimeter data taken by the “Lunar Reconnaissance Orbiter” spacecraft.Conclusions: Accounting for the narrow beam pattern altimeter data increases the accuracy of the relief determination. Using the narrow beam pattern altimeter data turns out to be more preferable over the involving wide beam pattern altimeter data. Computer simulation has shown that accounting for the narrow beam pattern altimeter data significantly increases the accuracy of the calculated heights as against using images exclusively and helps to speed up the calculation procedure.Key words: planet surface relief; photometry; altimetry; optimal filtering; statistical estimation of random valueManuscript submitted 26.11.2020Radio phys. radio astron. 2021, 26(2): 173-188REFERENCES1. PETTENGILL, G. H., ELIASON, E., FORD, P. G., LORIOT, G. B., MASURSKY, H. and MCGILL, G. E., 1980. Pioneer Venus Radar Results: Altimetry and Surface Properties. J. Geophys. Res. Space Phys. vol. 85, is. A13, pp. 8261–8270. DOI: https://doi.org/10.1029/JA085iA13p082612. SMITH, D. E., ZUBER, M. T., NEUMANN, G. A. and LEMOINE, F. G., 1997. Topography of the Moon from the Clementine Lidar. J. Geophys. Res. Planet. vol. 102, is. E1, pp. 1591–1611. DOI: https://doi.org/10.1029/96JE029403. THOMAS, N., HUSSMANN, H., SPOHN, T., LARA, L. M., CHRISTENSEN, U., AFFOLTER, M., BANDY, T., BECK, T., CHAKRABORTY, S., GEISSBUEHLER, U., GERBER, M., GHOSE, K., GOUMAN, J., HOSSEINIARAN,I S., KUSKE, K., PETEUT, A., PIAZZA, D., RIEDER, M., SERVONET, A., ALTHAUS, C., BEHNKE, T., GWINNER, K., HÜTTIG, C., KALLENBACH, R., LICHOPOJ, A., LINGENAUBER, K., LÖTZKE, H.-G., LÜDICKE, F., MICHAELIS, H., OBERST, J., SCHRÖDTER, R., STARK, A., STEINBRÜGGE, G., DEL TOGNO, S., WICKHUSEN, K., CASTRO, J. M., HERRANZ, M., RODRIGO, J., PERPLIES, H., WEIGEL, T., SCHULZE-WALEWSKI, S., BLUM, S., CASCIELLO, A., RUGI-GROND, E., COPPOOLSE, W., RECH, M., WEIDLICH, K., LEIKERT, T., HENKELMANN, R., TREFZGER, B. and METZ, B., 2021. The BepiColombo Laser Altimeter. Space Sci. Rev. vol. 217, is. 1, id. 25. DOI: https://doi.org/10.1007/s11214-021-00794-y4. SMITH, D. E., ZUBER, M. T., NEUMANN, G. A., MAZARICO, E., LEMOINE, F. G., HEAD, J. W., LUCEY, P. 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DOI: https://doi.org/10.1029/2010GL043751 Purpose: The paper discusses the possibility for increasing the planet’s surface relief retrieving accuracy with the improved photoclinometry method through the reference of the desired relief to the altimetry data. The general approach to solving the problem is proposed. The use of altimeters having both wide and narrow beam patterns are discussed, but the narrow beam pattern altimeter data is studied more in detail. The spatial resolution of the retrieved relief calculated with the improved photoclinometry method conforms to the one of the source images. Altimetry allows absolute reference to the surface heights and improves the accuracy of the relief determination.Design/metodology/approach: The work is based on the improved photoclinometry method for the planet’s surface relief retrieving from images. This method is mathematically rigorous and uses the Bayesian statistical approach, that allows calculation of the most probable relief according to available observations.Findings: An approach to determining the optimal statistical estimate of the surface heights from images in the frames of the improved photoclinometry method is proposed and an expression for the optimal filter which converts source images along with the wide beam pattern altimetry data into the most probable relief of the planet surface area is presented. The reference technique for the narrow beam pattern altimeter data is formulated. The efficiency of the method has been verified with the computer simulation. The relief of the surface area in Mare Imbrium on the Moon was retrieved using three images and laser altimeter data taken by the “Lunar Reconnaissance Orbiter” spacecraft.Conclusions: Accounting for the narrow beam pattern altimeter data increases the accuracy of the relief determination. Using the narrow beam pattern altimeter data turns out to be more preferable over the involving wide beam pattern altimeter data. Computer simulation has shown that accounting for the narrow beam pattern altimeter data significantly increases the accuracy of the calculated heights as against using images exclusively and helps to speed up the calculation procedure.Key words: planet surface relief; photometry; altimetry; optimal filtering; statistical estimation of random valueManuscript submitted 26.11.2020Radio phys. radio astron. 2021, 26(2): 173-188REFERENCES1. PETTENGILL, G. H., ELIASON, E., FORD, P. G., LORIOT, G. B., MASURSKY, H. and MCGILL, G. E., 1980. Pioneer Venus Radar Results: Altimetry and Surface Properties. J. Geophys. Res. Space Phys. vol. 85, is. A13, pp. 8261–8270. DOI: https://doi.org/10.1029/JA085iA13p082612. SMITH, D. E., ZUBER, M. T., NEUMANN, G. A. and LEMOINE, F. G., 1997. Topography of the Moon from the Clementine Lidar. J. Geophys. Res. Planet. vol. 102, is. E1, pp. 1591–1611. DOI: https://doi.org/10.1029/96JE029403. THOMAS, N., HUSSMANN, H., SPOHN, T., LARA, L. M., CHRISTENSEN, U., AFFOLTER, M., BANDY, T., BECK, T., CHAKRABORTY, S., GEISSBUEHLER, U., GERBER, M., GHOSE, K., GOUMAN, J., HOSSEINIARAN,I S., KUSKE, K., PETEUT, A., PIAZZA, D., RIEDER, M., SERVONET, A., ALTHAUS, C., BEHNKE, T., GWINNER, K., HÜTTIG, C., KALLENBACH, R., LICHOPOJ, A., LINGENAUBER, K., LÖTZKE, H.-G., LÜDICKE, F., MICHAELIS, H., OBERST, J., SCHRÖDTER, R., STARK, A., STEINBRÜGGE, G., DEL TOGNO, S., WICKHUSEN, K., CASTRO, J. M., HERRANZ, M., RODRIGO, J., PERPLIES, H., WEIGEL, T., SCHULZE-WALEWSKI, S., BLUM, S., CASCIELLO, A., RUGI-GROND, E., COPPOOLSE, W., RECH, M., WEIDLICH, K., LEIKERT, T., HENKELMANN, R., TREFZGER, B. and METZ, B., 2021. The BepiColombo Laser Altimeter. Space Sci. Rev. vol. 217, is. 1, id. 25. DOI: https://doi.org/10.1007/s11214-021-00794-y4. SMITH, D. E., ZUBER, M. T., NEUMANN, G. A., MAZARICO, E., LEMOINE, F. G., HEAD, J. W., LUCEY, P. 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Determination of relief and radiooptical parameters of a surface area through the use of a synthetic aperture radar. Radiofizika i elektronika. no. 1, pp. 129‑133. (in Russian).8. DULOVA, I. A., SKURATOVSKY, S. I., BONDARENKO, N. V. and KORNIENKO, Y. V., 2008. Reconstruction of the Surface Topography from Single Images with the Photometric Method. Sol. Syst. Res.. vol. 42, is. 6, pp. 522‑535. DOI: https://doi.org/10.1134/S00380946080600519. BONDARENKO, N. V., DULOVA, I. A. and KORNIENKO, Y. V., 2014. Topography of polygonal structures at the Phoenix landing site on mars through the relief retrieval from the HiRISE images with the improved photoclinometry method. Sol. Syst. Res. vol. 48, is. 4. pp. 243–258. DOI: https://doi.org/10.1134/S003809461404003010. VAN DIGGELEN, J., 1951. A photometric investigation of the slopes and the heights of the ranges of hills in the Maria of the Moon. Bull. Astron. Inst. Netherlands. vol. 11, pp. 283–289.11. AKIMOV, L. A. and KORNIENKO, Y. V., 1994. 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DOI: https://doi.org/10.1029/2010GL043751 Предмет і мета роботи: Досліджується можливість підвищення точності визначення рельєфу поверхні планети за допомогою методу вдосконаленої фотоклинометрії шляхом прив’язки шуканого рельєфу до альтиметричних даних. Запропоновано загальний підхід до розв’язання проблеми. Обговорюється використання альтиметрів, що мають як широку, так і вузьку діаграму спрямованості, однак більш детально розглядається урахування даних альтиметра з вузькою діаграмою спрямованості. Просторова роздільна здатність обчисленого рельєфу при використанні методу вдосконаленої фотоклинометрії відповідає просторовій роздільній здатності використовуваних зображень. Альтиметр дозволяє виконати абсолютну прив’язку висот поверхні та підвищує точність визначення рельєфу.Методи і методологія: Робота базується на використанні методу вдосконаленої фотоклинометрії для визначення рельєфу ділянки поверхні планети за зображеннями. Цей метод є математично строгим і спирається на байєсівський статистичний підхід, що дозволяє визначити найбільш імовірний рельєф за наявними даними спостережень.Результати: Запропоновано підхід до визначення оптимальної статистичної оцінки висот поверхні за зображеннями в рамках методу вдосконаленої фотоклинометрії та отримано вираз для оптимального фільтра, що переводить вихідні зображення і дані альтиметра з широкою діаграмою спрямованості в найбільш імовірний рельєф ділянки поверхні планети. Сформульовано метод прив’язки даних альтиметра з вузькою діаграмою спрямованості. Виконано перевірку працездатності цього методу за допомогою комп’ютерного моделювання. Виконано відновлення рельєфу ділянки поверхні Місяця в Морі Дощів за трьома зображеннями й даними лазерного альтиметра, отриманими космічним апаратом “Lunar Reconnaissance Orbiter”.Висновки: Урахування даних альтиметра, що має вузьку діаграму спрямованості, підвищує точність визначення рельєфу. Використанню даних, отриманих альтиметром з вузькою діаграмою спрямованості, слід надати перевагу порівняно з даними альтиметра з широкою діаграмою спрямованості. Показано, що урахування даних альтиметра з вузькою діаграмою спрямованості істотно підвищує точність визначення висот порівняно з випадком використання виключно зображень та допомагає прискорити процедуру обчислень.Ключові слова: рельєф поверхні планети; фотометрія; альтиметр; оптимальна фільтрація; статистична оцінка випадкової величиниСтаття надійшла до редакції 26.11.2020Radio phys. radio astron. 2021, 26(2): 173-188СПИСОК ЛІТЕРАТУРИ1. Pettengill G. H., Eliason E., Ford P. G., Loriot G. B., Masursky H., and McGill G. E. Pioneer Venus Radar Results: Altimetry and Surface Properties. J. Geophys. Res. Space Phys. 1980. Vol. 85, Is. A13. P. 8261–8270. DOI: 10.1029/JA085iA13p082612. Smith D. E., Zuber M. T., Neumann G. A., and Lemoine F. G. Topography of the Moon from the Clementine Lidar. J. Geophys. Res. Planet. 1997. 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DOI: 10.1029/2010GL043751 Видавничий дім «Академперіодика» 2021-06-22 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1356 10.15407/rpra26.02.173 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 26, No 2 (2021); 173 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 26, No 2 (2021); 173 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 26, No 2 (2021); 173 2415-7007 1027-9636 10.15407/rpra26.02 uk http://rpra-journal.org.ua/index.php/ra/article/view/1356/pdf Copyright (c) 2021 RADIO PHYSICS AND RADIO ASTRONOMY |