Shape reconstruction and rotation axis estimation of small bodies using a voxel-divided shape-from-silhouette method

In the space between long-distance photometric observations and close-range visual feature observations, images that present only silhouette information of small bodies are valuable for estimating the physical characteristics and establishing a body-fixed coordinate frame. The voxel-based shape-from-silhouette (SFS) method has been proven to be able to estimate the shape and rotation axis of small bodies. However, the large number of voxels and iterations causes the SFS method to be inefficient and time-consuming, and it cannot meet the requirements for the autonomy and timeliness of on-orbit missions. In addition, existing studies on the silhouette-based rotation axis estimation lack the exploration of adaptability to multiple small body observation conditions. In this study, we developed a fast and effective integrated inversion method for both shape and rotation axis, which is suitable for images where small bodies occupy only tens to hundreds of pixels. First, we developed an octree-based voxel-divided SFS (VD-SFS) algorithm to enable the establishment of the silhouette voxel model hierarchically and efficiently. Then, by defining the rotation model of the small body and applying the VD-SFS algorithm, the rotation axis orientation can be estimated according to the silhouette similarity between the silhouette model and the actual images. Finally, simulation data under different observation conditions verify that the proposed method can significantly enhance the modeling efficiency, reducing both modeling time and memory consumption by several times compared to traditional methods. Additionally, the method proves effective in estimating the rotation axis of the small body, and remains robust even when images have a high sun phase angle. Using data from the approach phases of the Rosetta and OSIRIS-REx missions, the rotation axis error was estimated at under 2° for 67P and around 5° for Bennu, demonstrating that the proposed method can be effectively applied to on-orbit missions.