RADIO PHYSICS AND RADIO ASTRONOMY

Subject and Purpose. Computer simulation methods are used for investigating the errors that arise in the course of retrieval, by means of an improved photoclinometry technique, of planetary surface reliefs from sets of their photo images. The work has been aimed at evaluating the level of errors in numerically calculated heights and slopes of the reliefs, as retrieved from images with a variety of signal-to-noise ratios, also including estimates for possibly minimal errors.

Methods and Methodology. The improved photoclinometry approach permits calculating the most probable relief realizations for parts of a planetary surface, proceeding from sets of their photographic images. Two optional ways for implementing the method are analyzed, namely application of an optimized Fourier transform-based filtering, or solution of Poisson’s equation within the finite-difference technique.

Results.Computer experiments have demonstrated that the reliefs retrievable from photo images with the use of the improved photoclinometry methods are always qualitatively similar to real ones. In the case of calculations within the finite-difference method the level of errors in height determination made 0.21s₀ to 0.27s₀, where s₀ stands for the root-mean-square deviation in the height of the relief being modeled. In the case of application of the Fourier analysis-based method the level of errors in the calculated heights varied between 0.86s₀ and 0.33s₀, while the signal-to-noise ratio for the initial images changed from 1.0 to 100. Within this version of the method the theoretical prediction for the lowest error in the calculated height varied from 0.83s₀ to 0.13s₀. The relief belonging to the middle portion of the area under study is always retrievable to a better accuracy, as compared with the sites adjacent to the image borders, no matter which of the two available techniques has been applied.

Conclusions.The improved photoclinometry method allows retrieving surface reliefs from sets of their images, with error levels for estimates of height equaling either 0.21s₀ to 0.27s₀ (in the case of application of the finite difference computational technique), or 0.33s₀ (if the Fourier analysis has been applied, with the signal-to-noise ratio SNR=50). It is recommended that relief retrieval were performed over sites of a larger surface area than might be strictly necessary for the purpose, since the error value estimated for the middle part of the site always turns out to be several times smaller than the error calculated over the entire area under study.

As a sign of concession to the authors’ categorical demand, added herein is their original, non-edited translation into English of the abstract of I.A. Dulova and N.V. Bondarenko, “AN IMPROVED PHOTOCLINOMETRY TECHNIQUE FOR SURFACE RELIEF RETRIEVAL FROM IMAGES: ERROR LEVELS FOR HEIGHT AND SLOPE ESTIMATES”.

Subject and Purpos. By means of computer simulation, errors aroused during relief retrieval from the images set with the improved photoclinometry method (IPCM) are investigated. The purpose of the work is to estimate the heights and surface slopes errors of the relief retrieved from images with different signal-to-noise ratio including estimations of the minimum possible errors.

Methods and Methodology. The improved photoclinometry method that allows the calculation of the most possible relief from the images set of the planet surface area is used. Two options for the method implementation were studied, namely the optimal Fourier-based filtration and the solving of the Poisson equation with the finite difference method.

Results.Computer experiments show that relief retrieved with IPCM from images is always qualitatively similar to the true one. The IPCM implementation with the finite difference method leads to heights errors of 0.21σ₀– 0.27σ₀ (σ₀ is root-mean-square deviations of the model relief heights). In the case of the IPCM implementation based on the Fourier analysis height errors vary from 0.86σ₀ to 0.33σ₀ when SNR (signal-to-noise ratio) of initial images vary from 1.0 to 100. In this case theoretically predicted minimal heights errors vary from 0.83σ₀ to 0.13σ₀. The relief in the middle part of the studied area is retrieved more accurately in comparison with sites near image boundaries when applying both options of the IPCM implementation

Conclusions. The use of the improved photoclinometry method allows retrieval of the surface topography from a set of images with height’s errors of 0.21σ₀ – 0.27σ₀ (IPCM implementation through the finite difference method) and 0.33σ₀ (IPCM implementation through the Fourier analysis, SNR = 50). It is good practice to retrieve the relief on a larger surface area than required for the study, since the heights error in the middle part of the site, always turns out to be several times smaller than the error calculated over the entire area under study.

Keywords: optimal filtering; planetary surface relief; error in height; photometry

Manuscript submitted  16.05.2023

Radio phys. radio astron. 2023, 28(4): 304-317

REFERENCES

1. 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, 19, pp. 20—24 (in Russian).

2. 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.

3. Nyquist, H., 1928. Thermal agitation of electric charge in conductors. Phys. Rev., 32, pp. 110—113. DOI: https://doi.org/10.1103/PhysRev.32.110

4. Huang, T.S., 1986. Advances in computer vision and image processing. USA: JAI Press.

5. Boncelet, C., and Bovik, A.C. ed., 2005. Image Noise Models. Handbook of image and video processing. USA: Academic Press, рр. 397—409. DOI: https://doi.org/10.1016/B978-012119792-6/50087-5

6. 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)90125-7

7. 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.1993.1143

8. 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)90204-9

9. 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.2007.12.006

10. Mouginis-Mark, P.J., and Wilson, L., 1981. MERC: a FORTRAN IV program for the production of topographic data for the planet Mercury. Comput. Geosci., 7(1), pp. 35—45. DOI: https://doi.org/10.1016/0098-3004(81)90038-8

11. Muinonen, K., Lumme, K. and Irvine, W. M., 1991. Slope variations on the surface of Phobos. Planet. Space Sci., 39(1—2), pp. 327—334. DOI: https://doi.org/10.1016/0032-0633(91)90153-2

12. 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/10.1029/95JE01854

13. 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.2006.03.002

14. 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., 160, pp. 120—135. DOI: https://doi.org/10.1016/j.pss.2018.05.020

15. 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., 193, 105090. DOI: https://doi.org/10.1016/j.pss.2020.105090

16. Velichko, S., Korokhin, V., Shkuratov, Y., Kaydash, V., Surkov, Y., and Videen, G., 2022. Photometric analysis of the Luna space-craft landing sites. Planet. Space Sci., 216, 105475. DOI: https://doi.org/10.1016/j.pss.2022.105475

17. 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., 43(6),. 1049—1061. DOI: https://doi.org/10.1111/j.1945-5100.2008.tb00692.x

18. 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., 163, pp. 487—510. DOI: https://doi.org/10.1007/s11214-011-9863-z

19. 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, 277, pp. 257—278. DOI: https://doi.org/10.1016/j.icarus.2016.05.002

20. Alexandrov, O., and Beyer, R.A., 2018. Multiview shape-from-shading for planetary images. Earth Space Sci., 5(10), pp. 652—666. DOI: https://doi.org/10.1029/2018EA000390

21. Wildey, R.L., 1990. Radarclinometry of the earth and Venus from Space-Shuttle and Venera-15 imagery. Earth Moon Planets, 48, pp. 197—231. DOI: https://doi.org/10.1007/BF00113857

22. Watters, T.R., and Robinson, M.S., 1997. Radar and photoclinometric studies of wrinkle ridges on Mars. J. Geophys. Res., 102(E5), pp. 10889—10903. DOI: https://doi.org/10.1029/97JE00411

23. Nguen Suan An’, and Kornienko, Y.V., 1998. Determination of the relief and radiooptical parameters of a surface area by means of a synthetic aperture radar. Telecommun. Radio Eng., 52(5), pp. 29—33. DOI: https://doi.org/10.1615/TelecomRadEng.v52.i5.40

24. Bondarenko, N.V., Dulova, I.A., and Kornienko, Y.V., 2018. High-resolution albedo and relief of the Lunar surface with the improved photoclinometry method for the topography reconstruction from a set of images. In: 49th Lunar and Planetary Science
Conference, LPI Contrib. No. 2083, id. 2459 [online]. [viewed 28 January 2023]. Available from: https://www.hou.usra.edu/meet-ings/lpsc2018/pdf/2459.pdf

25. Kornienko, Y.V. and Dulova, I.A., 2019. Optimal surface relief reconstruction from both the photometric and the altimetric data. Radiofiz. Electron., 24(4), pp. 46—52 (in Russian). DOI: https://doi.org/10.15407/rej2019.04.046

26. Kornienko, Y.V., Dulova, I.A., and Bondarenko, N.V., 2021. Involvement of altimetry information into the improved photoclinometry method for relief retrieval from a slope field. Radio Phys. Radio Astron., 26(2), pp. 173—188 (in Ukrainian). DOI: https://doi.org/10.15407/rpra26.02.173

27. Dulova, I.A., Kornienko, Yu.V. and Skuratovskiy, S.I., 2008. A clinometric technique for relief derivation from redundant or deficient input data. Telecommun. Radio Eng., 67(18), pp. 1605—1620. DOI: https://doi.org/10.1615/TelecomRadEng.v67.i18.10

28. Dulova, I.A., Skuratovsky, S.I., Bondarenko, N.V., and Kornienko, Yu.V., 2008. Reconstruction of the surface topography from single images with the photometric method. Sol. Sys. Res., 42(6), pp. 522—535. DOI: https://doi.org/10.1134/S0038094608060051

29. Bondarenko, N.V., Dulova, I.A. and Kornienko, Yu.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., 48(4), pp. 243—258. DOI: https://doi.org/10.1134/S0038094614040030

30. Bondarenko, N.V., Dulova, I.A., and Kornienko, Yu.V., 2020. Photometric functions and the improved photoclinometry method: mature Lunar mare surfaces. In: 51th Lunar and Planetary Science Conference. Abstract No. 1845 [online]. [viewed 28 January 2023]. Available from: https://www.hou.usra.edu/meetings/lpsc2020/eposter/1845.pdf

31. 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., 150(1—4), pp. 81—124. DOI: https://doi.org/10.1007/s11214-010-9634-2

32. Dulova, I.A. and Kornienko, Yu.V., 2001. Random error of surface relief reconstruction by radio brightness. Radio Phys. Radio Astron., 6(4), pp. 310—316 (in Russian). Available from: http://dspace.nbuv.gov.ua/handle/123456789/122282 [viewed 28 January 2023].

33. Bayes, T., 1763. An essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond., 53, pp. 360—418.

34. Smirnov, M.M., 1964. Second-order partial differential equations. Moscow, Russia: Nauka Publ. (in Russian).

35. Dulova, I.A., Kornienko, Yu.V., and Skuratovskiy, S.I., 2015. Images matching in case of surface relief reconstruction with the photoclinometric method. Radio Phys. Radio Astron., 20(1), pp. 30—36 (in Russian). DOI: https://doi.org/10.15407/rpra20.01.030

36. Samarskiy, A.A., Nikolayev, E.S. 1978. Methods for solving grid equations. Moscow, USSR: Nauka Publ. (in Russian).

37. Guo, P., 2021. The numerical solution of Poisson equation with Dirichlet boundary conditions. J. Appl. Math. Phys., 9(12), pp. 3007—3018. DOI: https://doi.org/10.4236/jamp.2021.912194

38. Liptser, R.S., and Shiryaev, A.N., 1974. Statistics of random processes (non-linear filtering and related issues). Moscow, Russia: Nauka Publ. (in Russian).

39. Landsberg, G.S., 1976. Optics. Moscow, Russia: Nauka Publ. (in Russian).

40. Korn, G., and Korn, T., 2000. Mathematical handbook for scientists and engineers. Dover Publ., Revised ed.