Mathematically-Guaranteed Global Solutions to Structure-from-Motion

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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.