This is a three year standard award. The PI will carry out a general theoretical analysis and experimental evaluation of the sensitivity of structure-from-motion (SFM). This task requires the development of techniques that extend the state of the art not only of computer vision but also of statistical parameter estimation. Specifically, methods for propagating full densities from measurements to unknowns will be developed for nonsquare problems (more measurements than unknowns), and standard covariance propagation techniques will be extended to constrained optimization problems with implicit formulations. New techniques will be developed for the decomposition of ill-posed problems into solvable and unsolvable components. Using these techniques, the sensitivity of standard formulations of SFM will be analyzed systematically, and without the use of noise generators. In addition, the effects of nonlinearities will be understood more completely than in previous studies. Comparison with experimental results, made possible by newly proposed calibration methods, will validate the theoretical conclusions and will lead to a clear delineation of which SFM computations are possible with a given level of camera quality and for a given performance requirement. The decomposition of SFM problems into solvable and unsolvable components, as well as the partition of performance space into feasible and infeasible problems, will lead to a new algorithm that combines successful special-case algorithms in a principled and general way.
