CONSTRUCTING A 3D SCALE-SPACE FROM IMPLICIT SURFACES FOR VISION-BASED SPACECRAFT RELATIVE NAVIGATION

The observation and description of partially observed objects is an important aspect of spacecraft relative navigation. Approaching an object reveals keypoints on the object's surface at decreasing scale, while scale-space theory diffuses surface signals at increasing scale. This paper applies a scale-space approach to identifying surface features. While scale-space is well-studied for 2D images, the corresponding procedure for 3D surfaces is immature. Construction of a 3D scale-space is accomplished by solving the diffusion equation on an implicit surface using a backward Euler scheme. This implicit surface approach reduces the effects of irregular meshed surfaces and complicated definitions of the discrete Laplace-Beltrami operator. Two methods for scale estimation are presented that are inherent to the diffusion equation and independent of the surface. A method of keypoint localization is discussed and compared to that of image feature localization. Examples demonstrate that features of various scale are distributed across the surface models of Itokawa and Mars Global Surveyor which may be used for spacecraft relative navigation.