This paper addresses the problem of reliably estimating the coefficients of the parameterized image variety (PIV) associated with the set of weak perspective images of a rigid scene, with applications in image-based rendering. Exploiting the fact that the constraints defining the PIV are linear in its coefficients and bilinear in the image data, the estimation procedure is cast in the errors-in-variables framework and solved using the method proposed by Y. Leedan and P. Meer (1998) 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 difficult case of paraperspective projection are briefly discussed.

A complete analysis of the statistical issues related to the estimation of a bilinear form, one of the fundamental problems in computer vision, is presented. It is shown why already at moderate noise levels most available techniques fail to provide a satisfactory solution. A new estimation procedure is proposed in which the nonlinear nature of the errors is taken into account and the implementation is based on the generalized singular value decomposition for superior numerical behavior. As an example, the ellipse fitting problem is discussed, and the performance of the new algorithm is compared with the current state-of-the-art.