Planetary topography measurement by descent stereophotogrammetry

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Highlights

  • Wide-angle descent stereo is an effective means of planetary topography measurement.

  • A novel imaging and stereo pipeline is simulated to quantify measurement accuracy.

  • Optimal stereo geometries are described for maximising measurement accuracy.

  • The technique could be applied to a wide range of planetary descent/ascent probes.

Abstract

Digital Terrain Models (DTMs) provide valuable insights into the nature of solar system surfaces, facilitating geological analysis, landing site selection and characterisation, and contextualising in situ measurements. For missions to solar system bodies for which orbiters and soft landed platforms are technologically or financially challenging to achieve, low mass descent or ascent probes (e.g. planetary penetrators) provide an alternative means by which to access the atmosphere and/or surface, and a platform from which to image the surface from a range of altitudes and perspectives. This paper presents a study into the concept of large-coverage descent stereophotogrammetry, whereby the stereo geometry of vertically offset wide-angle descent images is used to measure surface topography over a region of large extent. To do this, we simulate images of Mars' Gale Crater using a large coverage, high resolution DTM of the area, and derive topographic measurements by stereo matching pairs of simulated images. These topographic measurements are compared directly with the original DTM to characterise their accuracy, and dependence of elevation measurement accuracy on stereo geometry is thus investigated. For a stereo pair with a given altitude (corresponding to the altitude of its lower image), error in elevation measurement is found to have its minimum value for surface at a horizontal distance between 1 and 3 times the altitude. For a point on the surface with given horizontal distance from the imaging location, a stereo imaging altitude between 0.2 and 0.5 times this distance is found to achieve best elevation measurement accuracy. Surface appearance, and its change between two images of a stereo pair, is found to have a significant impact on stereo matching performance, limiting stereo baseline length to an optimum value range of 0.2–0.4 times the lower image's altitude, and resulting in the occurrence of occlusions and blind spots, particularly at oblique viewing angles.

Introduction

Images of planetary surfaces reveal many properties, and are a valuable tool for their investigation. But a single image gives a flattened representation of the surface, and the possible analysis can be elevated if knowledge of the surface topography is also available. Digital Terrain Models (DTMs), a common end product of topographic mapping, are an often-utilised and valuable product of spacecraft imagers. They store information on the 3D structure of a surface in a form that is both intuitive to inspect by eye and easy to represent in 3D visualisation software, and can be utilised for rigorous geological analysis and landing site characterisation. They are commonly produced from orbital imagery, allowing large-surface-coverage datasets (e.g. Tao et al. (2018)). Meanwhile, high-resolution DTMs with small spatial extent have been derived from rover images (e.g. Barnes et al. (2018)). A crucial step in the production of a DTM is the triangulation of three-dimensional (3D) positions on the surface.

For missions to solar system bodies for which orbiters and soft landed platforms are technologically or financially challenging to achieve, such as the moons of Jupiter and Saturn, low-mass descent platforms (e.g. penetrators/impactors) provide an alternative means by which to access the atmosphere and/or surface, and a platform from which to image (Gowen et al., 2011; Lorenz, 2011). Topographic measurement of the probe's landing site and surrounding area can provide valuable geological context to any in situ measurements, reveal local surface processes, and constrain landing site location (Liu et al., 2019). This paper focusses on the technique of utilising descent images to measure surface topography.

Descent imaging itself has been employed on a range of missions to solar system bodies. The majority of these missions went either to Mars or the Moon, and captured series of descent images containing tens to hundreds of images. Malin et al. (2001) describe the motivation for descent imaging, which derives largely from its ability to determine the location and geological characteristics of the landing or impact site. The nested, multi-scale nature of descent image sequences allows observations at a range of scales and accuracies to be tied together.

NASA's Mars Exploration Rovers (Crisp et al., 2003) were each equipped with a lander-mounted descent camera, which viewed directly downward with a square 45° field of view (FOV). Images were captured during descent with the prime objective of assisting automated on-board estimation of the crafts' horizontal velocities (Maki et al., 2003). The Mars Descent Imager (MARDI) of the Mars Science Laboratory followed the same theme, looking directly downward with its 90° FOV and capturing sequential images (several hundred) from the lander's heat shield release to its final touchdown, with pixel scales ranging from 1.5 ​m to 1.5 ​mm (Grotzinger et al., 2012; Malin et al., 2017). The primary purpose of its images was to determine the rover's landing site location and characteristics.

Whilst not the objective for the above mentioned cameras, topographic mapping has been a key outcome of several descent imaging campaigns. Both the Chang'e 3 (Li et al., 2015) and Chang'e 4 (Jia et al., 2018) missions placed rovers on the Moon's surface, and acquired descent images during the landing phases. Liu et al. (2015) applied feature matching and bundle adjustment to 180 Chang'e 3 descent images to produce sub-metre precision landing site DTMs extending as far as 1800 ​m from the landing site. Liu et al. (2019) used a similar approach with Chang'e 4 descent images, producing a landing site DTM and precisely constraining the landing site location.

Huygens descent probe images (Karkoschka et al., 2007) contrasted to those of the Martian and Lunar missions' downward looking cameras, in that their larger FOVs extended toward the horizon. Soderblom et al. (2007) performed stereophotogrammetry of multiple Huygens descent image pairs to derive topographic maps of two regions of Titan's surface, and the descent images were recently revisited to produce a new DTM of higher spatial accuracy (Daudon et al., 2020). Descent imaging has additionally been used to derive the topography of small bodies. For example, Mottola et al. (2015) performed stereophotogrammetry on two images from the Rosetta mission's Philae lander to produce a DTM of a small region of comet 67P/Churyumov-Gerasimenko's surface.

In spite of descent imaging being a common and important feature of planetary landers, and the applicability of its images to topography measurement having been demonstrated by several missions, a comprehensive study of the general technique of descent stereophotogrammetry has not previously been conducted. This paper aims to address this by providing a general quantitative assessment of the technique's achievable accuracies and coverage. Additionally, whilst most descent images are focussed on a limited region below the spacecraft, we address the concept of large-coverage descent stereophotogrammetry, whereby the stereo geometry of vertically offset wide-angle descent images is used to measure surface topography over a region of large extent.

To achieve large and multi-directional coverage, we envisage that each image's extent covers a full hemisphere, centred on the camera's nadir, such that it captures the entire visible surface (described further in section 2.2). The large field of view captures the surface with a range of ground sample distances (GSDs) and emission angles. This variation in imaging geometry will impact the efficacy of stereoscopic analysis, and this study focusses on characterising that dependency.

Section snippets

Method

The accuracy of surface topographic measurement is a function of many factors, and cannot be fully assessed without knowledge of the surface it represents. Often, the quality of a point cloud or DTM will therefore be investigated by comparing it to check points: measurements of the surface obtained by another means (Li, 1988). For topography measurements with high spatial resolution and large surface coverage, achieving a sufficiently large and distributed set of check points can be a barrier

Results

Fig. 11 shows a selection of elevation point clouds generated from simulated stereo pairs in this study. The descent nadir location is indicated by a yellow dot in the bottom right quadrant of each. Surface detail can be discerned in the diagrams, particularly where the points are so dense that they form contiguous surfaces. Point cloud spatial density decreases with distance from nadir, due to the camera's decreasing spatial resolution, but large areas of no data (white) also exist

Conclusions

It is of no surprise that imaging geometry has a strong impact on the outcomes of descent stereophotogrammetry presented in this paper, given that the connection between baseline and depth measurement error is well established for the more conventional cases of aerial and satellite imagery (e.g. Hallert (1960); Johnsson (1960)). The accuracy of descent stereophotogrammetry is a strong function of viewing angle, thus varying significantly over the surface of the observed body and resulting in

CRediT authorship contribution statement

G. Brydon: Conceptualization, Methodology, Software, Formal analysis, Writing – original draft, Writing – review & editing, Review & Editing. D.M. Persaud: Resources, Writing – original draft, Visualization. G.H. Jones: Conceptualization, Writing – original draft, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

GB is supported by a UK Science and Technology Facilities Council (STFC) PhD studentship.

GHJ is grateful to STFC for support through consolidated grant ST/S000240/1.

DMP is grateful to Y. Tao and J.-P. Muller for development of and guidance on using CASP-GO; A. D. R. Putri for guidance on using KM09-VICAR.

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