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 axis and viewed by orthogonal projection to a fixed view plane). We consider profiles of this surface (also known as apparent contours, occluding contours, and outlines), and we do not track marked points or curves nor assume that a correspondence problem has been solved. We show that, provided the angular speed is known, the location of the axis, and hence the surface, can be recovered from measurements on the profiles over an interval of time. If the angular speed is unknown, then there is a one-parameter family of solutions similar to the bas-relief ambiguity. The results are obtained by use of frontier points on the surface, which can also be viewed as points of epipolar tangency. Results of a numerical experiment showed that the performance was best with larger extents of rotation or when the axis was nearly perpendicular to the view direction.
© 1994 Optical Society of America
P. J. Giblin, F. E. Pollick, and J. E. Rycroft, "Recovery of an unknown axis of rotation from the profiles of a rotating surface," J. Opt. Soc. Am. A 11, 1976-1984 (1994)