In recent years, several international asteroid exploration missions have been successfully executed. The three-dimensional (3D) reconstruction technology based on image sequences is the core technical means to support task planning, navigation guidance, and scientific research. Current methods for asteroid shape reconstruction mainly include shape-from-silhouette (SfS), structure-from-motion (SfM), stereophotogrammetry (SPG), and stereophotoclinometry (SPC). Among them, SfM offers notable advantages in terms of versatility and automation, making it widely adopted in deep space scenarios. However, asteroid exploration often involves challenges such as long-range observations and complex illumination conditions, which can hinder the accuracy of the bundle adjustment step in SfM. Existing studies have shown that considering appropriate constraints, such as control point constraints, geometric feature constraints, and relative motion constraints, can effectively enhance the stability and accuracy of bundle adjustment. These studies perform well in the 3D reconstruction of Earth, Moon, and Mars, but there is currently no research on bundle adjustment constraints in asteroid exploration mission scenarios. In this paper, we propose a constraint-based structure-from-motion (C-SfM) method that considers the relative motion between the camera and the asteroid for images from hovering stations during the approach phase of asteroid exploration missions, to improve the accuracy and robustness of asteroid 3D modeling and camera pose estimation.

The proposed C-SfM method includes three main steps: image matching, incremental SfM reconstruction, and global constrained bundle adjustment. First, scale-invariant feature Transform (SIFT) is used to extract image features. A pairing strategy is defined based on the time sequence of images, and feature matching is performed using Hash-based indexing and random sample consensus (RANSAC) algorithm. Then, images are added one by one through incremental SfM. The perspective-n-point (PnP) algorithm estimates the camera poses, and bundle adjustment refines the initial 3D structure and camera parameters. Finally, to improve pose accuracy, two constraints based on hovering observations are added: a spatial circular trajectory constraint for camera positions and a rotational interval constraint between adjacent frames. A global bundle adjustment is then performed again to obtain more stable and accurate 3D reconstruction results.

The proposed algorithm is validated using simulated image datasets generated on the Blender platform under various observation conditions, including different observation distances, Sun phase angles, approach angles, image acquisition frequencies, and camera attitude stability (Fig. 3). Additionally, real in-orbit images of the asteroid Bennu from the OSIRIS-REx mission are used for further evaluation. The performance is assessed based on three metrics: reprojection error, camera position error, and camera pointing error. Results show that: 1) The proposed C-SfM method consistently outperforms the traditional SfM method in all evaluation metrics across all test datasets, demonstrating significant improvements in 3D reconstruction accuracy and pose estimation precision (Table 3, Figs. 4 and 5); 2) The method effectively corrects abnormal pose estimations caused by factors such as long observation distances, high sun phase angles, low approach angles, or insufficient image overlap, thereby improving the overall stability and accuracy of the reconstruction (Figs. 6, 7 and 8); 3) The method remains effective even with some degree of camera attitude instability (Table 4 and Fig. 9); 4) On the in-orbit data of Bennu, the proposed method achieves better performance, reducing reprojection error, camera position error, and pointing error by 6.5%, 33.7%, and 36.2% respectively, compared to the traditional SfM approach (Table 3). This confirms the method’s effectiveness and applicability in in-orbit observation scenarios.

This paper presents C-SfM method for images acquired during the hovering station of the approach of asteroid exploration missions. The proposed method leverages the relative motion between the spacecraft and the asteroid during this phase by introducing two prior constraints into the global bundle adjustment process: a spatial circular trajectory constraint on the camera positions and a rotational interval constraint between adjacent image frames. Experimental results on multiple simulated datasets and the real Bennu orbital dataset demonstrate the effectiveness and applicability of the method. Future work will explore incorporating external absolute measurements, such as laser altimetry, to further enhance the accuracy and practicality of SfM for asteroid 3D reconstruction and camera pose estimation.