LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD
Subject and Purpose. In this work, the planet surface area relief is calculated using the Improved Photoclinometry Method (IPCM) and starting from a set of source images. Height deviations from the true relief altitudes are studied by computer simulation at small spatial scales (smaller than a quart...
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Видавничий дім «Академперіодика»
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Radio physics and radio astronomy |
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optimal filtering height calculation error planetary surface relief photometry |
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optimal filtering height calculation error planetary surface relief photometry Dulova, I. A. Bondarenko, N. V. LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD |
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optimal filtering height calculation error planetary surface relief photometry оптимальна фільтрація похибка обчислення висоти рельєф поверхні планети фотометрія |
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Article |
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Dulova, I. A. Bondarenko, N. V. |
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Dulova, I. A. Bondarenko, N. V. |
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Dulova, I. A. |
| title |
LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD |
| title_short |
LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD |
| title_full |
LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD |
| title_fullStr |
LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD |
| title_full_unstemmed |
LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD |
| title_sort |
local height calculation errors in the planet surface relief retrieved from images by the improved photoclinometry method |
| title_alt |
ЛОКАЛЬНІ ПОХИБКИ ОБЧИСЛЕННЯ ВИСОТ РЕЛЬЄФУ ПОВЕРХНІ ПЛАНЕТИ, ВІДНОВЛЕНОГО ЗА ЗОБРАЖЕННЯМИ МЕТОДОМ УДОСКОНАЛЕНОЇ ФОТОКЛИНОМЕТРІЇ |
| description |
Subject and Purpose. In this work, the planet surface area relief is calculated using the Improved Photoclinometry Method (IPCM) and starting from a set of source images. Height deviations from the true relief altitudes are studied by computer simulation at small spatial scales (smaller than a quarter of the area’s size). We seek to estimate these "local" errors in surface heights and slopes using source images with different signal-to-noise ratios (SNRs).Methods and Methodology. The improved photoclinometry method calculates the most probable relief of a planet surface area from its images. Two optional techniques implement this method. The IPCM-F technique employs the optimum Fourier- transform-based fi ltering in the spatial frequency domain. The IPCM-T uses the finite diff erence method to solve the Poisson equation.Results. Computer experiments on retrieving the surface topography from the source images have shown that the higher the signal-to-noise ratio (SNR) of the initial image, the smaller the size of small-scale features that are reliably reproduced in shape. In the calculations by the IPCM-T technique, the smallest reliably reproduced features are four times the initial image resolution G at SNR ≥ 50 and five times at SNR = 10. With the IPCM-F, the relief features are reliably reproduced starting from spatial scales 9G (SNR ≥ 50) and 17G (SNR ≥ 10). With the IPCM-T, the worst local height error characterizing the smallest reliably reproduced surface features is 0.35σ0 (SNR = 1) and 0.17σ0 (SNR = 50), where σ0is the root-mean-square deviation of the modeled relief height. For both IPCM implementations, larger topographic objects are characterized by local height errors 0.01σ0 to 0.08σ0 (SNR = 50).Conclusions. It has been shown that the surface topography retrieval by the improved photoclinometry method from a set of images with SNR ≥ 50 reliably reproduces shapes of size features ≥ 4G (IPCM-T) and ≥ 9G (IPCM-F). For 8G to 64G size features, the retrieved height local errors are 0.004σ0 to 0.07σ0 (IPCM–T) and 0.01σ0 to 0.08σ0 (IPCM–F). To study smaller, 4G to 8G size features, the topography relief should be reconstructed using the IPCM-F upon the finite diff erence method.Keywords: optimal filtering, height calculation error, planetary surface relief, photometryManuscript submitted 13.09.2024Radio phys. radio astron. 2025, 30(1): 024-040REFERENCES1. Ford, P.G., and Pettengill, G.H., 1992. Venus topography and kilometer-scale slopes. J. Geophys. Res., 97(E8), pp. 13103—13114. DOI: https://doi.org/10.1029/92JE010852. Smith, D.E., Zuber, M.T., Frey, H.V., Garvin, J.B., Head, J.W., Muhleman, D.O., Pettengill, G.H., Phillips, R.J., Solomon, S.C., Zwally, H.J., Banerdt, W.B., Duxbury, T.C., Golombek, M.P., Lemoine, F.G., Neumann, G.A., Rowlands, D.D., Aharonson, O., Ford, P.G., Ivanov, A.B., and Johnson, C.L., 2001. Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars. J. Geophys. Res. 106(E10), pp. 23689—23722. DOI: https://doi.org/10.1029/2000JE0013643. 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., Duxbury, T.H., Aharonson, O., Lucey, P.G., Robinson, M.S., Barnouin, O.S., Cavanaugh, J.F., Sun, X., Liiva, P., Mao, Dan-dan, Smith, J.C., and Bartels, A.E., 2010. Initial observations from the Lunar Orbiter Laser Altimeter (LOLA). Geophys. Res. Lett., 37(18), id. L18204. DOI: https://doi.org/10.1029/2010GL0437514. Araki, H., Tazawa, S., Noda, H., Ishihara, Y., Goossens, S., Sasaki, S., Kawano, N., Kamiya, I., Otake, H., Oberst, J., and Shum, C., 2009. Lunar global shape and polar topography derived from Kaguya-LALT Laser Altimetry. Science, 323(5916), pp. 897—900. DOI: https://doi.org/10.1126/science.11641465. Scholten, F., Oberst, J., Matz, K.D., Roatsch, T., Wählisch, M., Speyerer, E.J., and Robinson, M.S., 2012. GLD100: The near-global lunar 100 m raster DTM from LROC WAC stereo image data. J. Geophys. Res.: Planet, 117(E12). DOI: https://doi.org/10.1029/2011JE0039266. Henriksen, M.R., Manheim, M.R., Burns, K.N., Seymour, P., Speyerer, E.J., Deran, A., Boyd, A.K., Howington-Kraus, E., Rosiek, M.R., Archinal, B.A., and Robinson, M.S., 2017. Extracting accurate and precise topography from LROC narrow angle camera stereo observations. Icarus, 283, pp. 122—137. DOI: https://doi.org/10.1016/j.icarus.2016.05.0127. 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. 11, pp. 283—289.8. Howard, A.D., Blasius, K.R., and Cutts, J.A., 1982. Photoclinometric determination of the topography of the Martian north polar cap. Icarus, 50(2—3), pp. 245—258. DOI: https://doi.org/10.1016/0019-1035(82)90125-79. Barnes, J.W., Brown, R.H., Soderblom, L., Sotin, C., Le Mouèlic, S., Rodriguez, S., Jaumann, R., Beyer, R.A., Buratti, B.J., Pitman, K., Baines, K.H., Clark, R., and Nicholson, P., 2008. Spectroscopy, morphometry, and photoclinometry of Titan’s dunefields from Cassini/VIMS. Icarus, 195(1), pp. 400—414. DOI:https://doi.org/10.1016/j.icarus.2007.12.00610. Squyres, S.W., 1981. The topography of Ganymede’s grooved terrain. Icarus, 46(2), pp. 156—168. DOI: https://doi.org/10.1016/0019-1035(81)90204-911. Goldspiel, J.M., Squyres, S.W., and Jankowski, D.G., 1993. Topography of small Martian valleys. Icarus, 105(2), pp. 479—500. DOI: https://doi.org/10.1006/icar.1993.114312. Nyquist, H., 1928. Thermal agitation of electric charge in conductors. Phys. Rev., 32, pp. 110—113. DOI: https://doi.org/10.1103/PhysRev.32.11013. Huang, T.S., 1986. Advances in computer vision and image processing. USA: JAI Press.14. Efford, N.D., 1991. Sources of error in the photoclinometric determination of planetary topography: A reappraisal. Earth Moon Planets, 54, pp. 19—58. DOI: https://doi.org/10.1007/BF0005504615. Lohse, V., Heipke, C., and Kirk, R.L., 2006. Derivation of planetary topography using multi-image shape-from shading. Planet. Space Sci. 54(7), pp. 661—674. DOI: https://doi.org/10.1016/j.pss.2006.03.00216. Schenk, P.M., and Moore, J.M., 1995. Volcanic constructs on Ganymede and Enceladus: Topographic evidence from stereo images and photoclinometry. J. Geophys. Res., 100(E9), pp. 19009—19022. DOI: https://doi.org/10.1029/95JE0185417. 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DOI: https://doi.org/10.1016/0019-1035(71)90121-741. Jehl, A., Pinet, P., Baratoux, D., Daydou, Y., Chevrel, S., Heuripeau, F., Manaud, N., Cord, A., Rosemberg, C., Neukum, G., Gwinner, K., Scholten, F., Hoffman, H., Roatsch, T., and HRSC Team, 2008. Gusev photometric variability as seen from orbit by HRSC/Mars-express. Icarus, 197(2), pp. 403—428. DOI: https://doi.org/10.1016/j.icarus.2008.05.02242. McEwen, A.S., 1991. Photometric Functions for Photoclinometry and Other Applications. Icarus, 92(2), pp. 298—311. DOI: https://doi.org/10.1016/0019-1035(91)90053-V43. Shkuratov, Yu., Kaydash, V., Korokhin, V., Velikodsky, Yu., Opanasenko, N., and Videen, G., 2011. Optical measurements of the Moon as a tool to study its surface. Planet. Space Sci. 59(13), pp. 1326—1371. DOI: https://doi.org/10.1016/j.pss.2011.06.01144. Hapke, B., 1981. Bidirectional reflectance spectroscopy. 1. Theory. J. Geophys. Res., 86, pp. 3039—3054. DOI: https://doi.org/10.1029/JB086iB04p0303945. Born, M., and Wolf, E., 1959. Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. 1st ed. London, New York, Paris: Pergamon Press, OCLC 48969150646. Wiener, N., 1948. Cybernetics: or control and communication in the animal and the machine. Cambridge, Massachusetts, USA: MIT Press. Publication date: 2019. DOI: https://doi.org/10.7551/mitpress/11810.001.000147. Korn, G., and Korn, T., 2000. Mathematical handbook for scientists and engineers. Dover Publ., Revised ed.48. Kotelnikov, V.A., 2006. On the transmission capacity of the "ether" and wire in electric communications, 1933. Adv. in Phys. Sci. 49, pp. 744—748 (reprint of the article). |
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Видавничий дім «Академперіодика» |
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oai:ri.kharkov.ua:article-14612025-03-23T08:41:46Z LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD ЛОКАЛЬНІ ПОХИБКИ ОБЧИСЛЕННЯ ВИСОТ РЕЛЬЄФУ ПОВЕРХНІ ПЛАНЕТИ, ВІДНОВЛЕНОГО ЗА ЗОБРАЖЕННЯМИ МЕТОДОМ УДОСКОНАЛЕНОЇ ФОТОКЛИНОМЕТРІЇ Dulova, I. A. Bondarenko, N. V. optimal filtering; height calculation error; planetary surface relief; photometry оптимальна фільтрація; похибка обчислення висоти; рельєф поверхні планети; фотометрія Subject and Purpose. In this work, the planet surface area relief is calculated using the Improved Photoclinometry Method (IPCM) and starting from a set of source images. Height deviations from the true relief altitudes are studied by computer simulation at small spatial scales (smaller than a quarter of the area’s size). We seek to estimate these "local" errors in surface heights and slopes using source images with different signal-to-noise ratios (SNRs).Methods and Methodology. The improved photoclinometry method calculates the most probable relief of a planet surface area from its images. Two optional techniques implement this method. The IPCM-F technique employs the optimum Fourier- transform-based fi ltering in the spatial frequency domain. The IPCM-T uses the finite diff erence method to solve the Poisson equation.Results. Computer experiments on retrieving the surface topography from the source images have shown that the higher the signal-to-noise ratio (SNR) of the initial image, the smaller the size of small-scale features that are reliably reproduced in shape. In the calculations by the IPCM-T technique, the smallest reliably reproduced features are four times the initial image resolution G at SNR ≥ 50 and five times at SNR = 10. With the IPCM-F, the relief features are reliably reproduced starting from spatial scales 9G (SNR ≥ 50) and 17G (SNR ≥ 10). With the IPCM-T, the worst local height error characterizing the smallest reliably reproduced surface features is 0.35σ0 (SNR = 1) and 0.17σ0 (SNR = 50), where σ0is the root-mean-square deviation of the modeled relief height. For both IPCM implementations, larger topographic objects are characterized by local height errors 0.01σ0 to 0.08σ0 (SNR = 50).Conclusions. It has been shown that the surface topography retrieval by the improved photoclinometry method from a set of images with SNR ≥ 50 reliably reproduces shapes of size features ≥ 4G (IPCM-T) and ≥ 9G (IPCM-F). For 8G to 64G size features, the retrieved height local errors are 0.004σ0 to 0.07σ0 (IPCM–T) and 0.01σ0 to 0.08σ0 (IPCM–F). To study smaller, 4G to 8G size features, the topography relief should be reconstructed using the IPCM-F upon the finite diff erence method.Keywords: optimal filtering, height calculation error, planetary surface relief, photometryManuscript submitted 13.09.2024Radio phys. radio astron. 2025, 30(1): 024-040REFERENCES1. Ford, P.G., and Pettengill, G.H., 1992. Venus topography and kilometer-scale slopes. J. Geophys. Res., 97(E8), pp. 13103—13114. DOI: https://doi.org/10.1029/92JE010852. Smith, D.E., Zuber, M.T., Frey, H.V., Garvin, J.B., Head, J.W., Muhleman, D.O., Pettengill, G.H., Phillips, R.J., Solomon, S.C., Zwally, H.J., Banerdt, W.B., Duxbury, T.C., Golombek, M.P., Lemoine, F.G., Neumann, G.A., Rowlands, D.D., Aharonson, O., Ford, P.G., Ivanov, A.B., and Johnson, C.L., 2001. Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars. J. Geophys. Res. 106(E10), pp. 23689—23722. DOI: https://doi.org/10.1029/2000JE0013643. 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., Duxbury, T.H., Aharonson, O., Lucey, P.G., Robinson, M.S., Barnouin, O.S., Cavanaugh, J.F., Sun, X., Liiva, P., Mao, Dan-dan, Smith, J.C., and Bartels, A.E., 2010. Initial observations from the Lunar Orbiter Laser Altimeter (LOLA). Geophys. Res. Lett., 37(18), id. L18204. DOI: https://doi.org/10.1029/2010GL0437514. Araki, H., Tazawa, S., Noda, H., Ishihara, Y., Goossens, S., Sasaki, S., Kawano, N., Kamiya, I., Otake, H., Oberst, J., and Shum, C., 2009. Lunar global shape and polar topography derived from Kaguya-LALT Laser Altimetry. Science, 323(5916), pp. 897—900. DOI: https://doi.org/10.1126/science.11641465. Scholten, F., Oberst, J., Matz, K.D., Roatsch, T., Wählisch, M., Speyerer, E.J., and Robinson, M.S., 2012. GLD100: The near-global lunar 100 m raster DTM from LROC WAC stereo image data. J. Geophys. Res.: Planet, 117(E12). DOI: https://doi.org/10.1029/2011JE0039266. Henriksen, M.R., Manheim, M.R., Burns, K.N., Seymour, P., Speyerer, E.J., Deran, A., Boyd, A.K., Howington-Kraus, E., Rosiek, M.R., Archinal, B.A., and Robinson, M.S., 2017. Extracting accurate and precise topography from LROC narrow angle camera stereo observations. Icarus, 283, pp. 122—137. DOI: https://doi.org/10.1016/j.icarus.2016.05.0127. 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. 11, pp. 283—289.8. Howard, A.D., Blasius, K.R., and Cutts, J.A., 1982. Photoclinometric determination of the topography of the Martian north polar cap. Icarus, 50(2—3), pp. 245—258. DOI: https://doi.org/10.1016/0019-1035(82)90125-79. Barnes, J.W., Brown, R.H., Soderblom, L., Sotin, C., Le Mouèlic, S., Rodriguez, S., Jaumann, R., Beyer, R.A., Buratti, B.J., Pitman, K., Baines, K.H., Clark, R., and Nicholson, P., 2008. 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Dover Publ., Revised ed.48. Kotelnikov, V.A., 2006. On the transmission capacity of the "ether" and wire in electric communications, 1933. Adv. in Phys. Sci. 49, pp. 744—748 (reprint of the article). Предмет і мета роботи. Відхилення висот рельєфу ділянки поверхні планети, обчисленого методом удосконаленої фотоклинометрії (МУФК) за набором зображень, від їх справжніх значень на малих просторових масштабах (менших за чверть розміру всієї ділянки) вивчаються шляхом комп’ютерного моделювання. Метою роботи є визначення таких «локальних» похибок обчислення висот та нахилів поверхні з використанням зображень із різними відношеннями сигнал/шум (ВСШ).Методи та методологія. Метод удосконаленої фотоклинометрії застосовується для обчислення найімовірнішого рельєфу ділянки поверхні планети за її зображеннями. Вивчаються два підходи, які можна застосувати для реалізації методу: МУФК–Ф, що використовує оптимальну фільтрацію в області просторових частот за допомогою перетворення Фур’є, та МУФК–Т, у якому метод скінченних різниць застосовується для розв’язання рівняння Пуассона.Результати. Тестові експерименти з відновлення топографії поверхні за зображеннями методом удосконаленої фотоклинометрії показали, що розмір дрібномасштабних деталей рельєфу, які зберігають свою форму, буде тим більшим, що меншим є ВСШ початкових зображень. У разі реалізації обчислень методом МУФК–Т розмір найменших надійно відтворюваних за формою деталей перевищує у 4 рази (ВСШ ≥ 50) та у 5 разів (ВСШ=10) роздільну здатність початкових зображень G. У разі використання МУФК–Ф форми рельєфу зберігаються тільки починаючи з просторових масштабів 9G (ВСШ ≥ 50) та 17G (ВСШ = 10). За МУФК–Т найбільша локальна похибка була характерною для найдрібніших об’єктів поверхні: 0.35σ0 (ВСШ = 1) та 0.17σ0 (ВСШ = 50), де σ0 — середньоквадратичне відхилення висот моделі рельєфу.Висновки. Обчислення рельєфу поверхні методом удосконаленої фотоклинометрії за набором зображень із ВСШ ≥ 50 дозволяє надійно відтворити форму об’єктів, розмір яких ≥4G та ≥ 9G, з використанням МУФК–Т та МУФК–Ф відповідно. Для об’єктів, що мають розмір 8G...64G, локальна похибка обчислення висот досягала значень 0.004 σ0 ...0.07σ0 (МУФКТ) та 0.01σ0...0.08σ0 (МУФК–Ф). З метою вивчення найдрібніших об’єктів поверхні розміром 4G...8G рельєф потрібно відновлювати методом скінченних різниць.Ключові слова: оптимальна фільтрація, похибка обчислення висоти, рельєф поверхні планети, фотометріяСтаття надійшла до редакції 13.09.2024Radio phys. radio astron. 2025, 30(1): 024-040БІБЛІОГРАФІЧНИЙ СПИСОК1. Ford P.G., and Pettengill G.H. Venus topography and kilometer-scale slopes. J. Geophys. Res. 1992. 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Adv. in Phys. Sci. 2006. Vol. 49. P. 744—748 (reprint of the article). Видавничий дім «Академперіодика» 2025-03-18 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1461 10.15407/rpra30.01.024 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 30, No 1 (2025); 24 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 30, No 1 (2025); 24 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 30, No 1 (2025); 24 2415-7007 1027-9636 10.15407/rpra30.01 uk http://rpra-journal.org.ua/index.php/ra/article/view/1461/pdf Copyright (c) 2025 RADIO PHYSICS AND RADIO ASTRONOMY |