The support function, curvature functions and 3-D attitude determination

Attitude is the 3-D rotation between the coordinate system of a known object and that of a sensed portion of its surface. Combinations of the support function of a known object with curvature measurements from a visible surface transform attitude determination into optimization problems that can be solved using standard numerical methods. Previous work using the extended Gaussian image (EGI) defined for convex polyhedra is extended to the domain of smooth, strictly convex objects where the EGI becomes equivalent to the second curvature function. Three-dimensional shape matching using the first curvature function is new. Emphasis is placed on theoretical foundations, algorithm development, and experimental proof-of-concept using real objects and surface data obtained from an existing photometric stereo system