Reconstruction from Uncalibrated Affine Silhouettes

In this paper we address the problem of model building in environments we do not control. An example problem is the reconstruction of aircraft geometry from images obtained from the ground. We show that using six or more unconstrained scaled orthographic silhouette views it is possible to recover the geometry of the aircraft and the motion between the camera views using only the two outer epipolar tangency constraints in each image. The silhouette outline is comprised of a subset of the set of apparent contours [2] which are the projections of the contour generators which divide the visible part from the occluded part of the object surface. The contour generators are functions of both the surface geometry and viewpoint. Contour generators corresponding to two distinct viewpoints of the same surface are, in general, different space curves. These space curves intersect at frontier points, which provide a pair of point correspondences between the two viewpoints [1, 3]. The epipolar lines are parallel for an affine camera model so only the relative rotation between the viewpoints is required to determine the angle of the epipolar lines. The two epipolar tangent points at which the epipolar lines at this angle first touch the silhouette outline are the projections of the two outer frontier points. These point correspondences provide an epipolar tangency constraint on the camera motion between the viewpoint pair.