RECOVERY OF AN UNKNOWN AXIS OF ROTATION FROM THE PROFILES OF A ROTATING SURFACE

We consider a surface (semitransparent or opaque) in space, viewed by orthogonal projection to a view plane that is rotating uniformly about an unknown axis (equivalently, a surface rotating about an unknown ax is and viewed by orthogonal projection to a fixed view plane). We cons ider profiles of this surface (also known as apparent contours, occlud ing contours, and outlines), and we do not track marked points or curv es nor assume that a correspondence problem has been solved. We show t hat, provided the angular speed is known, the location of the axis, an d hence the surface, can be recovered from measurements on the profile s over an interval of time. If the angular speed is unknown, then ther e is a one-parameter family of solutions similar to the bas-relief amb iguity. The results are obtained by use of frontier points on the surf ace, which can also be viewed as points of epipolar tangency. Results of a numerical experiment showed that the performance was best with la rger extents of rotation or when the axis was nearly perpendicular to the view direction.