Shape Recovery from Stationary Surface Contours by Controlled Observer Motion

The projected deformation of stationary contours and markings on object surfaces is analyzed in this paper. It is shown that given a marked point on a stationary contour, an active observer can move deterministically to the osculating plane for that point by observing and controlling the deformation of the projected contour. Reaching the osculating plane enables the observer to recover the object surface shape along the contour as well as the Frenet frame of the contour. Complete local surface recovery requires either two intersecting surface contours and the knowledge of one principle direction, or more than two intersecting contours. To reach the osculating plane, two strategies involving both pure translation and a combination of translation and rotation are analyzed. Once the Frenet frame for the marked point on the contour is recovered, the same information for all points on the contour can be recovered by staying on osculating planes while moving along the contour. It is also shown that occluding contours and stationary contours deform in a qualitatively different way and the problem of discriminating between these two types of contours can be resolved before the recovery of local surface shape.