Consistent pose uncertainty estimation for spherical cameras

In this work, we discuss and evaluate the reliability of first order uncertainty propagation results in context of spherical Structure from Motion, concluding that they are not valid without restrictions, but depend on the choice of the objective function. We furthermore show that the choice of the widely used geodesic error as objective function for a reprojection error optimization leads to disproportional pose uncertainty results of spherical cameras. This work identifies and outlines alternative objective functions to bypass those obstacles by deducing Jacobian matrices according to the chosen objective functions with subsequent conduction of first order uncertainty propagation. We evaluate the performance of the different objective functions in different optimization scenarios and show that best results for uncertainty propagation are obtained using the Euclidean distance to measure deviations of image points on the spherical image