P3P问题解分布的临界曲面研究

项目名称： P3P问题解分布的临界曲面研究

项目编号： No.61503004

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 张彩霞

作者单位： 北方工业大学

项目金额： 20万元

中文摘要： P3P问题是基于单幅图像进行物体定位的重要方法，多解现象，即“是否有唯一解”及“解不唯一时可能解的个数”是P3P问题在具体应用中需解决的基本问题，但至今仍没有得到很好的解决。本项目通过确定“P3P问题解分布的临界曲面”的途径，探索研究P3P问题的多解现象。这里的“临界曲面”指由P3P问题的三个控制点确定的特殊曲面，它们可以将三维空间分割成不同的区域，当光心在同一区域时，所有对应的P3P问题的解的个数都相同；当光心穿越这些曲面时，解的个数必然变化。我们的近期工作表明，临界曲面至少包含危险圆柱面及其伴随曲面和6个超环面，本项目将对这些曲面是否构成临界曲面的完备集开展系统的研究，获得具有明确几何意义的多解条件和解的分布状况，建立起从代数到几何的桥梁。本项目从几何途径阐明P3P问题多解现象的本质，不仅对P3P问题多解现象的研究具有重要的理论价值，也对基于单幅图像的视觉定位应用具有一定的指导作用。

中文关键词： PnP问题；图像定位；实时定位；无人机定位；SLAM

英文摘要： P3P Problem, or the Perspective-Three-Point Problem, is a very important single-image based pose estimation method for any real applications, multi-solution phenomenon,i.e., whether the unique solution exists, and if not, how many solutions are possible must be addressed, is a key aspect of the P3P problem, and has not been well understood till now. This project is to investigate this multi-solution phenomenon by determining so-called “critical surface of solutions”. Here the critical surfaces are meant that the whole 3D space is partitioned into different regions by such surfaces that all the P3P problems whose optical centers lie in the same region must have the same number of solutions, and when the optical center passes through the surfaces, the number of the solutions of the corresponding P3P problem must change. Our recent work shows that the danger cylinder, its companying surface and the 6 toroids associated with the 3 control points must be part of the critical surfaces, but we cannot prove whether these surfaces constitute the complete set. This project will focus on the investigation on the complete set of critical surfaces, by which some geometrical interpretation of the multi-solution phenomenon could be provided, and hopefully it will also bridge the gap between the geometrical approach and the algebraic approach in the literature. The investigation is not only of theoretical interests and significance, it could also act as theoretical guidance for single-image based pose estimation practitioners.

英文关键词： Perspective 3 Point;Image based Pose Estimation;Real-time Positioning; UAV(Unmanned Aerial Vehicle) Positioning;Simultaneous Location And Mapping