An Experimental Study of Projective Structure

This paper studies the usefulness of the projective approach to structure from motion (SFM). We conduct an essentially algorithm{independent experimental comparison of projective versus Euclidean reconstruction. Our results show that Euclidean reconstruction is essentially as accurate as pro-jective reconstruction, even with signiicant calibration error and for the pure projective structure. Thus calibration error is not a compelling motivation for the projective framework. But projective optimization is more reliable than its Euclidean equivalent: we nd that it has fewer problems with local minima. We describe several techniques that enhance the convergence of our Levenberg{Marquardt optimization algorithm. Most importantly, we nd that it is crucial to exploit the compactness of projective space|even in the pure Euclidean framework. We also analyze the problem of determining a stable basis set of 5 points for projective reconstruction. Abstract This paper studies the usefulness of the projective approach to structure from motion (SFM). We conduct an essentially algorithm{independent experimental comparison of projective versus Euclidean reconstruction. Our results show that Euclidean reconstruction is essentially as accurate as pro-jective reconstruction, even with signiicant calibration error and for the pure projective structure. Thus calibration error is not a compelling motivation for the projective framework. But projective optimization is more reliable than its Euclidean equivalent: we nd that it has fewer problems with local minima. We describe several techniques that enhance the convergence of our Levenberg{Marquardt optimization algorithm. Most importantly, we nd that it is crucial to exploit the compactness of projective space|even in the pure Euclidean framework. We also analyze the problem of determining a stable basis set of 5 points for projective reconstruction.