Mathematically-Guaranteed Global Solutions to Structure-from-Motion

运动恢复结构（SfM）的核心问题是从投影的二维图像中恢复场景的三维结构。它的研究导致了影响我们社会的成功商业应用，例如自动驾驶汽车，机器人，增强/虚拟现实和视觉惯性导航。尽管SfM取得了令人印象深刻的进展，但仍有许多开放的计算和数学问题。这个项目的目标就是解决这些问题。这些问题不仅对计算机视觉研究很重要，而且也是计算数学和优化研究的基础。特别是，数学上保证的全球程序，避免不必要的mathematics和参数，预计将相关的其他应用问题。整个项目旨在为SfM管道创建理论上有保证的优化组件。目前的管道仍然使用增量和启发式程序，缺乏足够的保证来处理高度损坏的数据集，并且速度很慢。具体的子项目由严格的数学方法指导。特别是，数学论证提出了最佳选择和定义。它们也有助于SfM的许多实际考虑，例如减少参数的数量和提高对腐败的鲁棒性。这些论点有望发展成有趣的数学定理。研究员将继续指导研究生和本科生进行研究。调查员还将继续促进教育活动，为学生在行业中的成功职业做好准备。特别是安排暑期实习和组织工业问题研讨会。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The central problem of structure from motion (SfM) asks to recover the three-dimensional structure of a scene from projective two-dimensional images. Its study has led to successful commercial applications that impact our society, such as in self-driving cars, robotics, augmented/virtual reality and visual-inertial navigation. Despite the impressive progress in SfM, there are many open computational and mathematical problems. The goal of this project is to address these problems. Not only are these problems important to computer vision research, but they are also fundamental for computational mathematics and optimization research. In particular, mathematically guaranteed global procedures, which avoid unnecessary heuristics and parameters, are expected to be relevant to other applied problems. The overall project aims to create theoretically-guaranteed optimization components for the SfM pipeline. The current pipeline still uses incremental and heuristic procedures, lacks sufficient guarantees for handling highly corrupted datasets and is slow. The specific subprojects are guided by rigorous mathematical approaches. In particular, mathematical arguments suggest optimal choices and definitions. They are also helpful with many practical considerations of SfM, such as reducing the number of parameters and improving robustness to corruption. These arguments are expected to develop into interesting mathematical theorems. The investigator will continue guiding graduate and undergraduate students in research. The investigator will also continue facilitating educational activities that prepare students for successful careers in industry. In particular, arranging summer internships and organizing the industrial problem seminar.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.