Silhouette-Based 3D Shape Reconstruction of a Small Body from a Spacecraft

In this paper, we present a novel Shape from Silhouette (SfS) algorithm to estimate the physical and dynamical properties of a small body-such as an asteroid or comet-from periodic images taken from a distant approaching spacecraft. Standard mapping techniques such as Stereo-Photo-Clinometry (SPC) and Stereo-Photo-Grammetry (SPG) are designed for close-proximity observations in which the body is 1000s of pixels in area, and there are enough surface features on the object. In contrast, our algorithms are suited for distant observations (i.e. during first approach) in which the body is only 10s-100s of pixels in area and does not present any useful visual features. First, using the Fast-Fourier-Transform of the light curve of the small body, we estimate its rotation rate. Then, using our novel silhouette-based 3D shape reconstruction technique, we estimate the shape and size of the small body and its pole of rotation. In this paper, we assume that the small body is performing pure rotation (no tumbling) about its principal axis, that the Sun is directly behind the spacecraft, and that the distance from the spacecraft to the small body is known. These algorithms have been tested using both simulated data from Comet 67P, Asteroids Eros and Itokawa; and real data from the Rosetta mission.