多项式矩阵不等式规划法稳定标定径向畸变
Stable radial distortion calibration by polynomial matrix inequalities programming
摘要：
在镜头径向失真建模方面，多项式和有理函数是首选。然而，一些外推和数值问题可能会出现，而使用这些功能，还没有被文献所涵盖的。在本文中，我们确定了这些问题，并展示了如何处理它们，通过强制执行某些多项式的非负性。此外，我们展示了如何使用多项式矩阵不等式（PMI）和如何估计的径向失真参数的PMI约束，使用半定规划（SDP）的非负性模型。最后，我们提出了几种方法，如何将所提出的方法纳入整个摄像机校准过程。
英文摘要：
Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by the literature much so far. In this paper, we identify these problems and show how to deal with them by enforcing nonnegativity of certain polynomials. Further, we show how to model these nonnegativities using polynomial matrix inequalities (PMI) and how to estimate the radial distortion parameters subject to PMI constraints using semidefinite programming (SDP). Finally, we suggest several approaches on how to incorporate the proposed method into the overall camera calibration procedure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
