Parameterized Image Varieties and Estimation with Bilinear Constraints

This paper addresses the problem of reliably estimating the coeÆcients of the parameterized image variety (PIV) [3] associated with the set of weak perspective images of a rigid scene, with applications in image-based rendering. Exploiting the fact that the constraints de ning the PIV are linear in its coeÆcients and bilinear in the image data, the estimation procedure is cast in the errors-in-variables framework and solved using the method proposed in [9] for this type of problems. The proposed approach has been implemented, and experiments with real data are shown to yield much better prediction power than the original method based on singular value decomposition. Extensions to the more diÆcult case of paraperspective projection are brie y discussed.