I. A. Dulova, N. V. Bondarenko


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.

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

Manuscript submitted  16.05.2023

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


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:

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:

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:

7. Goldspiel, J.M., Squyres, S.W., and Jankowski, D.G., 1993. Topography of small Martian valleys. Icarus, 105(2), pp. 479—500. DOI:

8. Squyres, S.W., 1981. The topography of Ganymede’s grooved terrain. Icarus, 46(2), pp. 156—168. DOI:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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:

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: [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:

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:

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.


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

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