Optimal surface relief reconstruction from both the photometric and the altimetric data

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 value

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An Improved Photoclinometry Technique for Surface Relief Retrieval From Images: Error Levels for Height and Slope Estimates

Dulova,

Bondarenko

2023

Radio phys. radio astron.

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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.

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Optimal surface relief reconstruction from both the photometric and the altimetric data

Cited by 3 publications

References 2 publications

Simulation of Onboard Helicopter Radar Signals for Surface Elevation Measurements

Simulation of Onboard Helicopter Radar Signals for Surface Elevation Measurements

Involvement of Altimetry Information Into the Improved Photoclinometry Method for Relief Retrieval From a Slope Field

An Improved Photoclinometry Technique for Surface Relief Retrieval From Images: Error Levels for Height and Slope Estimates

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