Rigorous Bounds for Two-Frame Structure from Motion

We present an analysis of the problem of recovering motion, particularly rotation, from two image frames. We derive an exact bound on the magnitude of the error in recovering the rotation. With the single weak requirement that the average translational image displacements are smaller than the eld of view, we demonstrate rigorously that the error in recovering the rotation is small. A lower bound on the rotation error can be derived which, for reasonable values of the eld of view, is very close to the upper bound. Thus the upper bound is in fact a good estimate of the rotation error. We demonstrate the validity of these theoretical claims on synthetic and real images. These results form part of our correctness proof for a recently developed algorithm for recovering structure and motion from a multiple{image sequence. In addition, we argue and demonstrate experimentally that in the complementary domain, when the translation is large, the whole motion can be recovered robustly if also perspective eeects are important. Thus it appears that rotation can be robustly recovered over a large domain. multiframe structure from motion. Abstract We present an analysis of the problem of recovering motion, particularly rotation, from two image frames. We derive an exact bound on the magnitude of the error in recovering the rotation. With the single weak requirement that the average translational image displacements are smaller than the eld of view, we demonstrate rigorously that the error in recovering the rotation is small. A lower bound on the rotation error can be derived which, for reasonable values of the eld of view, is very close to the upper bound. Thus the upper bound is in fact a good estimate of the rotation error. We demonstrate the validity of these theoretical claims on synthetic and real images. These results form part of our correctness proof for a recently developed algorithm for recovering structure and motion from a multiple{image sequence. In addition, we argue and demonstrate experimentally that in the complementary domain, when the translation is large, the whole motion can be recovered robustly if also perspective eeects are important. Thus it appears that rotation can be robustly recovered over a large domain.