The Sensitivity of Structure-From-Motion: A Comprehensive Theoretical and Experimental Study

卡洛·托马斯斯坦福大学运动结构的灵敏度：综合理论和实验研究这是一个为期三年的标准奖项。PI将对运动结构（SFM）的灵敏度进行一般的理论分析和实验评估。这项任务不仅需要发展计算机视觉技术，还需要发展统计参数估计技术。具体来说，将为非平方问题（测量值多于未知数）开发从测量值到未知数传播全密度的方法，并将标准协方差传播技术扩展到具有隐式公式的约束优化问题。将发展新的技术，将不适定问题分解为可解和不可解的部分。使用这些技术，将在不使用噪声发生器的情况下系统地分析SFM标准配方的灵敏度。此外，与以往的研究相比，非线性的影响将得到更全面的理解。通过新提出的校准方法，可以与实验结果进行比较，这将验证理论结论，并将导致对给定相机质量水平和给定性能要求的SFM计算的清晰描述。将SFM问题分解为可解和不可解组件，以及将性能空间划分为可行和不可行问题，将导致一种新的算法，该算法将成功的特殊情况算法以原则性和一般性的方式结合起来。

IIS-9820224Carlo TomasiStanford University$250,043 - 36 mosThe Sensitivity of Structure-from-Motion: A Comprehensive Theoretical and Experimental StudyThis 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.