Multi-View Shape from Shading for High-Resolution DEM and Albedo Reconstruction of the Lunar Surface

Multi-View Shape from Shading for High-Resolution DEM and Albedo Reconstruction of the Lunar Surface. M. Tenthoff1, S. Doliwa1, and C. Wöhler1, 1Image Analysis Group, TU Dortmund University ([email protected]) Introduction: The increasing number of Moon landings and rover missions on the lunar surface heightens the need for accurate Digital Elevation Models (DEMS). The most common methods to generate DEMs from satellite data are photogrammetry (Stereo), laser altimetry, and shading-based approaches (e.g., Shape from Shading). Stereo and laser altimetry provide global coverage with high vertical accuracy (e.g., SLDEM512 [1]). However, artifacts caused by faulty block matches and pixel locking [2] result in a resolution several times coarser than the resolution of the input data. SfS (Shape from Shading) provides highly accurate slope estimates and a resolution close to the pixel extents of the initial image. The complex nature of the SfS algorithm requires parameter fine-tuning. The method is, therefore, best suited for local mapping efforts, e.g., analysis of potential landing sites. While singleview approaches have led to good results for the Moon [3,4], Mars [5], and Mercury [6], it can be challenging to separate the influence of the topography from the albedo. If sufficient image data are available, multi-view SfS can be used to achieve better results [4, 7]. We recently adapted our SfS framework to use multiple MDIS [8] images of Mercury to reconstruct surface features exhibiting substantial albedo variations. In this work, we apply the process to LROC [9] NAC images. Methods: The basic concept of every SfS implementation is to use the shading information in a radiance image to estimate the surface shape (slope and/or height) [10]. The implementations differ in the choice of the reflectance model and additional regularization terms. Further, most SfS algorithms use a low-frequency initial DEM to increase the absolute vertical accuracy. Reflectance Model. Shape from Shading utilizes a reflectance model to render an image of the current surface estimation and compare it to the input image (under the same illumination and viewing conditions). This deviation is termed the intensity error and is minimized by the SfS algorithm to find the best matching representation of the surface. Strictly empirical models like the Lunar-Lambert law are often chosen for SfS due to their simplicity. However, we employ the more physically sound Hapke reflectance model [11]. The Hapke model is more complex but better approximates the light scattering behavior of regolith-covered airless planetary bodies. Furthermore, the Hapke model allows us to retrieve and optimize the single-scattering albedo simultaneously with the surface height. The intensity error is extended to include multiple images (each with its own geometry). This also helps to constrain the albedo estimation. Regularization terms. Shape from Shading is an ill-posed problem because two gradient components and one albedo value must be estimated from one or multiple measured grayscale values. We use three regularization terms: the integrability error [10], the deviation of absolute heights from the initial DEM, and the deviation of the estimated gradient from the gradient of the initial DEM [3]. The latter two terms are computed for filtered versions of the estimated and initial DEMs to ensure a comparison at a lower frequency. This approach suppresses high-frequency artifacts in the initial Stereo DEM and allows the SfS algorithm to reconstruct details not present in the initial DEM. We refrain from utilising the frequently used smoothness constraint because it tends to oversmooth the results. Results: Figure 1 shows two images of a bright young crater taken under different illumination conditions. The images exhibit some strong local albedo variations. The resulting SfS DEMs are shown in Figure 2. The single-view approach already produces excellent results, including the boulders inside the crater. However, some typical artefacts are noticeable. Most evident is the irregular appearance of the crater rim. The crater walls perpendicular to the illumination direction are unrealistically raised. Furthermore, some of the brighter and darker rays appear as topography in the DEM. In contrast, the multi-view SfS DEM is a more plausible representation of the central crater and the surrounding terrain. Figure 3 illustrates how multi-view SfS can remove the ambiguity introduced by strong albedo variations. Aknowledgement: This work was partially funded by the European Space Agency (Selected via OSIP, contract number: 4000146080/24/D/BL) References: [1] Barker M. K. et al. (2016) Icarus, 273, 346–355. [2] Gehrig S. and Franke U. (2016) Stereovision for ADAS, Springer, 495-524. [3] Grumpe A. and Wöhler C. (2014) ISPRS J. Photogramme. Remote Sens., 94, 37-45. [4] Grumpe A. et al. (2014) Adv. Space Res., 53, 1735-1767 [5] Hess et al. (2022), J. Imaging, 8(6), 158. [6] Tenthoff et al. (2020), Remote Sensing, 12, 3989. [7] Alexandrov O. and Beyer R.A. (2018) Earth Space Sci., 5, 652–666. [8] Hawkins S.E. et al. (2007), Space Sci. Rev. 131, 247–338. [9] Robinson M. S. et al. (2010). Space Sci Rev 150, 81–124. [10] Horn B. K. P. (1990), Int. J. Comput. Vis., 5, 37–75. [11] Hapke B. (2012) Theory of Reflectance and Emittance Spectroscopy, 2nd ed.; Cambridge University Press Figure 1: Parts of LROC NAC images M1167070402L and M1205935572L showing a small bright crater in Mare Serenitatis. Figure 2: Color-coded SfS DEMs. Left: Only image 2 is used for SfS. The topography of the crater perpendicular to the direction of illumination is exaggerated. Right: Both images are used for multi-view SfS. The crater rim looks more natural. Figure 3: Zoomed in SfS DEMs showing the area marked in the red box in Figure 2. The red circle shows the different reconstructions of a small dark crater. Using only one image, the crater is erroneously reconstructed as a small hill. Using two images the crater is reconstructed correctly.