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

IIS-9820224 Carlo Tomasi斯坦福大学$250，043 - 36 mos运动结构的灵敏度： 一个全面的理论和实验研究这是一个为期三年的标准奖。PI将对结构自运动（SFM）的灵敏度进行一般理论分析和实验评估。 这项任务需要开发的技术，扩展的最先进的不仅是计算机视觉，而且统计参数估计。 具体来说，传播全密度从测量到未知数的方法将开发非方问题（更多的测量比未知数），和标准的协方差传播技术将扩展到约束优化问题与隐式配方。 将开发新的技术，用于将不适定问题分解为可解和不可解的部分。 使用这些技术，SFM的标准配方的灵敏度将被系统地分析，而不使用噪声发生器。 此外，非线性的影响将比以前的研究更全面地理解。 通过新提出的校准方法与实验结果的比较，将验证理论结论，并将导致一个明确的划定，其中SFM计算是可能的与给定的相机质量水平和给定的性能要求。 将SFM问题分解为可解和不可解的部分，以及将性能空间划分为可行和不可行的问题，将导致一种新的算法，该算法以原则和一般的方式结合了成功的特殊情况算法。

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.