Reconstruction of planar scenes from multiple views using affine and projective shape manifolds

In this paper we describe a technique of fusing larger scenes from multiple views, using a landmark approach. For images of remote scenes, the fused image is reconstructed using sample mean shapes on affine shape manifolds. This manifold of configurations of points in general position is a real Grassmann manifold which can be equivariantly embedded in a space of matrices, and we consider the extrinsic means w.r.t. this embedding. On the other hand, for photographs taken from a close distance by a noncalibrated camera, the fused image is reconstructed using sample mean shapes on projective shape manifolds. This manifold of configurations of points under a given projective frame is a product of real projective planes and we consider extrinsic means w.r.t. to a standard embedding in a space of blocks of symmetric matrices. We illustrate these methods on two sets of images.