Self-Calibrating Isometric Non-Rigid Structure-from-Motion

We present self-calibrating isometric non-rigid structure- from-motion (SCIso-NRSfM), the first method to reconstruct a non-rigid object from at least three monocular images with constant but unknown focal length. The majority of NRSfM methods using the perspective cam- era simply assume that the calibration is known. SCIso-NRSfM leverages the recent powerful differential approaches to NRSfM, based on formu- lating local polynomial constraints, where local means correspondence- wise. In NRSfM, the local shape may be solved from these constraints. In SCIso-NRSfM, the difficulty is to also solve for the focal length as a global variable. We propose to eliminate the shape using resultants, obtaining univariate polynomials for the focal length only, whose sum of squares can then be globally minimized. SCIso-NRSfM thus solves for the focal length by integrating the constraints for all correspondences and the whole image set. Once this is done, the local shape is easily re- covered. Our experiments show that its performance is very close to the state-of-the-art methods that use a calibrated camera.