| 中文摘要 | 姿态估计问题，是计算机视觉中的经典问题之一。所谓姿态估计，就是要估计摄像机坐标系和世界坐标系之间的刚体变换关系，包含一个旋转和一个平移。本文主要研究了基于点对应或线对应的姿态估计问题，即PNP(Perspective-N-Point)和PNL(Perspective-N-Line)问题。对于PNP问题，我们主要考虑了N为3的情况，对它的多解现象做了一些探讨，而对于PNL问题，主要研究了一种新的估计算法。 本文的主要工作如下： 1. 给出了P3P问题存在多解的两个一般性条件。在P3P两种定义等价的前提下，推导出P3P问题有四个和三个解的一般性条件，即我们确定了某些平面，证明一旦光心落在这些区域，则相应的P3P问题一定有4个正解。另外，我们还证明了当光心落在危险圆柱面上时，相应的P3P问题一定有3个正解。这里“一般”的意思是说这个条件并不是孤立的或甚少发生的，而是很容易碰到的，这给实际应用带来相当大的风险。 2. 研究了P3P问题多解的概率问题。一般情况下, P3P问题可能出现1, 2, 3或4 个解。本文利用“蒙特卡罗方法”, 模拟出P3P问题分别出现1, 2, 3,4个解的概率为0.9993,0.0007, 0.0000,0.0000。 结果再次证实了如下的事实：即在大多数情况下，P3P问题有唯一解，这进一步说明了用P3P来定位的可行性。 3. 研究了基于PNL问题的估计算法。利用“对偶数”这一数学工具，可以得到与点变 换相类似的线之间的变换关系，从而可以利用线的整体信息进行定位，避免仅利用线上孤立的单个点的缺点。 |
| 英文摘要 | Pose determination is a classic issue in computer vision. The task is to determine the relative position and orientation between the camera and the scene frames from the known correspondences from space control entities to image ones, i.e., the translation and the rotation. In this thesis, the used entities are points or lines, and the corresponding pose determination problem is usually called the PNP(Perspective-N-Point) problem, or the PNL (Perspective-N-Line)problem. For the PNP problem, we only concentrated on the P3P problem due to its wide applicability as well as its pivotal role-played for the other PNP problem, in particular, the geometrical conditions of its multiple solutions are investigated. For the PNL problem, a new mathematical approach is explored. The main contributions of our work are summarized as follows: 1. Two general conditions of multiple solutions of the P3P problem are obtained. Under the equivalence between the distance-based definition and the transformation-based definition, we show that when the optical center lies on some planar regions, the corresponding P3P problem must have 4 positive solutions. In addition, we also proved that if the camera's optical center lies on the so-called “danger cylinder” and is enough far from the base-plane of control points, the corresponding P3P problem must have 3 positive solutions. Here by the word “general” is meant the condition is not an isolated or seldom occurred one, but some relatively highly risk one. 2. The occurrence probabilities of the number of solutions for the P3P Problem are studied. It is well known that under some special conditions, the P3P problem can have 1,2,3 and 4 solutions. In this paper, by the Monte Carlo approach of up to 1 million samples, we show that the probabilities of the P3P problem to have one, two, three, and four solutions are respectively 0.9993, 0.0007,0.0000,0.0000. The result confirms the well-known fact that in the most cases, the P3P has a unique solution. 3. A new method is introduced to solve the PNL Problem. Using the dual number as a tool, we present a new method for pose estimation from line correspondence, and introduce a similar formula with a general rigid transformation, thus, we set up a unified framework of coordinate transformations for lines and points. Then, according to the coplanarity of the corresponding image line and space line, a new group of constraints is introduced. Different from the existing methods based on lines, we do not use any point on either the space line or the image line, but the whole line data. |
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