题  目：Non-Convex Optimization for Rotation Search: Theory and Algorithms

报告人：彭良祖

单  位：Johns Hopkins University

时  间：9月23日10:00

地  点：腾讯116-933-726

摘要：Finding a transformation that best aligns two given point clouds is a fundamental task in geometric computer vision, and has been studied for decades under various settings. However, little to none existing algorithms can solve this problem in the greatest (and practical) generality, and compromises have been made among theoretical guarantees (e.g., global optimality), empirical accuracy, and scalability (e.g., how many points the algorithm can handle). Under the assumption that the two point clouds are related by an unknown 3D rotation, I first present a scalable and accurate method for solving this alignment problem, and furthermore endow the proposed algorithm with some convergence guarantees. Under the same rotation assumption I present several theoretical results concerning the correctness of certain semidefinite relaxations of the problem, for which accurate and scalable solvers have been under active research development. Along the way I discuss the limitations of the proposed methods, and at the end I conclude with several research directions.

报告人简介：Liangzu Peng is currently a PhD student at Johns Hopkins University, supervised by Rene Vidal, and has research interests in mathematics and algorithms of data science and their applications to problems that arise in machine learning, geometric computer vision, and robotics. He received his Master degree from ShanghaiTech University under the supervision of Manolis C. Tsakiris in 2021 and had doing his undergraduate study at Zhejiang University from 2013 to 2017.