NB: This page contains published material only.
For a better understanding of the lunar surface in geological terms, a digital elevation map (DEM) which yields information about its 3D structure is indispensable. The Clementine spacecraft launched in 1994 entirely mapped the lunar surface at a resolution on the ground of 0.25 degrees in longitude and latitude, i. e. better than 7.5 km, by means of laser altimetry. Although the obtained profiles nicely show large-scale features such as the huge South Pole Aitken Basin on the lunar far side, they do not reveal the 3D structure of the lunar surface on small, e. g. kilometre, scales. Small parts of the lunar surface (not necessarily the most interesting ones with respect to their geologic properties) have been mapped in 3D based on a stereoscopic analysis of image pairs acquired by the Clementine spacecraft and from the Apollo command modules orbiting the Moon. The resolution of the obtained surface profiles is 1 km on the ground, while the accuracy of the derived altitude values is usually not better than 100 m.
By far the oldest method for estimating altitudes (or better: altitude differences) on the lunar surface is the analysis of shadow lengths. It has already been used by 17th century lunar observers. The approach is simple, robust and accurate and does not require any assumptions about the surface properties. It yields, however, altitude differences only for a very sparse set of surface points, e. g. between the top of a mountain and the surrounding mare surface. A more recent well-known method for 3D surface reconstruction is shape from shading. It makes use of the fact that surface parts inclined towards the light source appear brighter than surface parts inclined away from it - apart from binocular vision, shading is one of the most important cues on which human vision is based. Generally spoken, the shape from shading approach aims at deriving the orientation of the surface at each image location by using a model of the reflectance properties of the surface and knowledge about the illumination conditions. Traditional applications of this technique in planetary science, mostly referred to as photoclinometry, have used line-based, integrative methods designed to reveal a set of profiles along one-dimensional lines rather than a 3D reconstruction of the complete surface. In contrast, techniques based on the minimization of a global error function have been developed in the field of computer vision. All shape from shading techniques, however, have in common that though they yield rather accurate estimates of small-scale altitude variations, the determined large-scale behaviour of the surface is easily subject to systematic errors due to imperfections in the imaging system or inappropriate modelling of reflectance properties. Furthermore, in many scenarios the shape from shading problem is ill-posed, i. e. there exists an infinite number of surface profiles that generate the observed image intensities under the given illumination conditions.
Here I will present results which were obtained with a novel method for 3D surface reconstruction based on the self-consistent fusion of shading and shadow features. To be able to obtain elevation data and to separate brightness changes due to variable albedo from those caused by topographic relief, it is advantageous to utilize at least two images of the surface region viewed under different illumination conditions. Prior to further evaluation, an image registration step is required, which means that one image is translated, rotated, and warped onto the other image such that pixels with identical coordinates in both images correspond to the same physical point on the surface. For further details on image registration techniques, refer e. g. to the MATLAB image processing toolbox. For details about the previously mentioned image-based 3D surface reconstruction techniques, see the following article and references therein:
C. Wöhler, K. Hafezi.
A general framework for three-dimensional
surface reconstruction by self-consistent fusion of shading and shadow
features.
Pattern Recognition, vol. 38, no. 7, pp. 965-983, 2005.
Unfortunately, the images taken by the lunar spacecraft that have been launched until present hardly contain several images of a certain surface region acquired under different illumination conditions. Generally, orbiting spacecraft map a planetary body such that the illumination conditions are largely constant for the acquired images in order to simplify their geological interpretation. This is the case for the Lunar Orbiter spacecraft which produced images under sunrise illumination at incidence angles of around 20 degrees, and also for the more recent Clementine spacecraft which took its images at local lunar noon. For the lunar DEMs presented here, I therefore used my own lunar CCD images obtained with the 125 mm and 200 mm Newton reflectors at a resolution of 0.3-0.45 arcseconds (corresponding to 500-800 m on the lunar surface) per pixel. The DEMs have a resolution on the surface of around 800 m per pixel. In contrast to stereo image analysis, the 3D reconstruction technique used here does not yield absolute elevations with respect to a reference geoid, but only relative elevations over the covered surface region. The accuracy of measured elevations (more exactly: elevation differences) is usually better than 100 m.
Examples of DEMs of lunar surface regions
Outer eastern crater rim of Wolf
Mare ridge south-west of Aristarchus
Lava flow at the border between Mare Serenitatis and Mare Imbrium
Region around lunar dome Herodotus
ω
Northern part of the tectonic fault Rupes Recta
Region between Hesiodus and Wolf,
Montes Recti, Reinhold B
DEM of the northern half of the crater Kepler
The DEM below has been obtained based on the analysis of a sequence of five images of the lunar crater Kepler acquired by the AMIE camera on board the Smart-1 spacecraft on January 13, 2006, from heights above the lunar surface between 1613 and 1702 km (cf. ESA press release of June 30, 2006). The crater diameter amounts to 32 km. During image acquisition the spacecraft flew over the crater and at the same time rotated around its axis, such that the crater remained in the field of view over a considerable period of time. The image sequence is also shown below. Image size is 512 x 512 pixels. The image is rotated such that north is to the top and west to the left. Based on a structure from motion approach, a 3D point cloud was extracted from the image sequence. The image scale amounts to 146 m per pixel, such that the absolute scaling constant could be readily determined for the structure from motion result. The 3D point cloud obtained by structure from motion was combined with the shape from shading technique, employing the Lunar-Lambert reflectance function. The DEM distinctly reveals the uneven crater floor of Kepler as well as the material that has slumped down the inner crater wall at several places, especially at the northern rim. The reconstructed surface obtained with the combined structure from motion and shape from shading approach reveals much finer detail than the structure from motion data alone. The typical depth difference between crater floor and rim amounts to about 2850 m. No ground truth is available for this crater since it is not covered by the existing lunar topographic maps. A fairly consistent crater depth of 2750 m is reported in the lunar atlas by Rükl (1999). This is an average value since most crater depths given in lunar atlases were determined by shadow length measurements based on telescopic or spacecraft observations.
P. d'Angelo, C. Wöhler.
Image-based 3D surface reconstruction
by combination of photometric, geometric, and real-aperture methods.
ISPRS Journal of Photogrammetry and Remote Sensing,
vol. 63, no. 3, pp. 297-321, 2008.
DEM of the northern part of the crater Kepler
A classification scheme for lunar domes
Many theories have been put forward to explain the origin of lunar shields and domes but there is now a general consensus in interpreting most of them as magmatic features, extrusive (volcanic) or intrusive (laccolith) in nature. The following article presents recent research concerning the detailed examination of a large set of lunar mare domes in terms of their spectrophometric properties, determined based on Clementine UVVIS imagery, their diameters, heights, and flank slopes, determined based on high-resolution ground-based CCD imagery evaluated with the previously described photoclinometry and shape from shading algorithms, and their rheologic parameters, i. e. lava viscosity, effusion rate, and duration of the effusion process, determined by geophysical modelling. The geophysical model essentially depends on the 3D properties inferred for the domes. The examined set of lunar mare domes displays a remarkable variety of 3D shapes. A novel classification scheme for lunar domes is proposed which divides them into several distinct groups, defined by the spectral appearances and 3D shapes of the domes but also strongly correlated with the rheologic parameters. Furthermore, the domes are examined with respect to their formation along crustal fractures, their rheologic properties, the dimensions of their feeder dikes, and the importance of magma evolution processes during dome formation. It can be concluded that different degrees of evolution of initially fluid basaltic magma are able to explain the broad range of lava viscosities inferred for the mare domes. These analyses illustrate the importance of the determination of reasonably accurate 3D properties when it is desired to gain insights into the geologic processes that governed the formation of lunar volcanic edifices.
C. Wöhler, R. Lena, P. Lazzarotti, J. Phillips, M. Wirths, Z. Pujic.
A combined spectrophotometric and morphometric study of the lunar mare dome fields near Cauchy, Arago, Hortensius, and Milichius.
Icarus, vol. 183, no. 2, pp. 237-264, 2006.
C. Wöhler, R. Lena, J. Phillips.
Formation of lunar mare
domes along crustal fractures: Rheologic conditions, dimensions of feeder
dikes, and the role of magma evolution.
Icarus, vol. 189, no. 2,
pp. 279-307, 2007.
3D reconstructions of lunar mare domes
Analysis of a complex lunar volcanic region
In the southern part of the crater Petavius a lunar dome is located, which was first described by C. A. Wood (Lunar Photo of the Day, September 27, 2004). This dome is partially covered by dark material of a lunar pyroclastic deposit. Hence, to obtain an accurate digital elevation map, the non-uniform albedo across the dome surface has to be taken into account. The following article describes the volcanic region in the south of Petavius, gives an overview about pyroclastic deposits on the Moon and their spectral properties, and describes a quotient-based two-image photoclinometry and shape from shading approach which simultaneously determines the 3D shape of the surface and its non-uniform albedo. This method is especially suited for the illumination geometry near the lunar equator.
R. Lena, C. Wöhler, M. T. Bregante, C. Fattinnanzi.
A combined morphometric and spectrophotometric
study of the complex lunar volcanic region in the south of Petavius.
Journal of the Royal Astronomical
Society of Canada, vol. 100, no. 1, pp. 14-25, 2006.
Lunar dome in the south of Petavius
The lunar dome complex Mons Rümker
The lunar volcanic complex Mons Rümker is situated in the northwestern part of Oceanus Procellarum. With a diameter of about 65 km, it is the largest known contiguous volcanic edifice on the Moon. The plateau is composed of a series of overlapping lava flows interrupted by local extrusions related to domes and to a ring surrounding the central portion. Scarps and ridges on the plateau are preferrably oriented in northeastern and northwestern direction, with the northeastern direction dominating. Several individual domes can be distinguished on the plateau surface, six of which are sufficiently well resolved in telescopic images for morphometric evaluation. A scarp separates the plateau from the surrounding mare plains. The DEM of Mons Rümker shows that the height of the plateau amounts to about 900 m in its western and northwestern part, 1100 m in its southern part, and 650 m in its eastern and northeastern part. The overall volume of erupted lava corresponds to about 1800 km3. The six examined individual domes on the Rümker plateau are typical mare domes morphometrically similar to the class B domes in the Hortensius/ Milichius/T. Mayer region. Rheologic modelling suggests that the domes were produced by low effusion rates, possibly during the terminal phases of the eruptions emplacing the plateau. Significant differences among the lava viscosities can be inferred for the domes, which cannot be attributed to compositional effects due to the spectral homogeneity of the volcanic plateau but which are more likely caused by different lava eruption temperatures and degrees of crystallisation.
The lunar dome complex Mons Rümker
C. Wöhler, R. Lena, K. C. Pau.
The lunar dome complex Mons
Rümker: Morphometry, rheology, and mode of emplacement.
Lunar and Planetary Science Conference XXXVIII, abstract #1091,
League City, Texas, 2007.
Lunar domes in Mare Undarum
A cluster of five large lunar domes is situated in Mare Undarum. Four domes termed Condorcet 1-4 are located between the craters Condorcet P and Dubiago, immediately east of Dubiago V and W. The fifth dome, termed Dubiago 3, is located about 35 km further south. The region under study is situated in a major trough concentric to the Crisium basin. The domes Condorcet 1-3 are aligned radially with respect to the Crisium basin. Similar dome configurations aligned radial to major impact basins are known from other lunar mare dome fields. All five domes have moderate diameters between 10 and 12 km. Condorcet 1-3 are similar to effusive domes of intermediate flank slope between 1° and 2° like those situated in the Hortensius/Milichius/T. Mayer region, while Condorcet 4 has an exceptionally steep flank slope of 2.8° and a large volume. With its low flank slope of 0.9°, the dome Dubiago 3 is morphometrically very similar to the intrusive dome immediately north of the well-known Valentine dome in western Mare Serenitatis, such that it is possibly of intrusive origin.
R. Lena, C. Wöhler, M. T. Bregante, P. Lazzarotti, S. Lammel.
Lunar domes in Mare Undarum: Spectral and morphometric properties, eruption conditions, and mode of emplacement.
Planetary and Space Science, vol. 56, pp. 553-569, 2008.
Further articles containing applications of the described techniques
to the 3D reconstruction of lunar domes can be found in my
list of publications.
The lunar domes for which the spectral and morphometric parameters have been
determined are listed in the Consolidated Lunar Dome Catalogue
(CLDC).
