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物体定位与图象矫正研究
其他题名A Study on Object Pose Estimation and Image Rectification
王波
学位类型工学博士
导师胡占义 ; 孙凤梅
2013-05-28
学位授予单位中国科学院大学
学位授予地点中国科学院自动化研究所
学位专业模式识别与智能系统
关键词摄像机姿态估计 Pnp问题 摄像机内参数标定 图象矫正 Camera Pose Estimation Perspective-n-point Problem Camera Intrinsic Parameter Calibration Image Rectification
摘要基于图像的物体定位是计算机视觉领域的一个重要内容,在诸如机器人导航和虚拟现实等领域有重要的应用价值。本文对基于点对应的物体定位方法进行了比较系统的研究,包括多解性,解的稳定性,求解途径和方法等。主要工作包括以下几方面: 1.针对多个点的PnP问题,证明了用于求解PnP问题时需要最小化的目标函数,形式上可以等价于一个由刚体和弹簧组成的弹性系统的势能。因此,求解PnP问题等价于求解使得系统达到能量最小的刚体位置的问题。本文使用模拟物理过程,使刚体在弹力和阻力的作用下逐渐运动到势能最小的位置,从而求得关于PnP 问题的稳定解。 2.一维标定是一类重要的摄像机标定方法。文献中关于一维标定的研究,或基于几何直观,或过分依赖计算技巧。 鉴于标定杆在运动前后处于同一个平面之内,同时由于标定杆运动前后所在的平面和像平面的单应矩阵从理论上说包含了所有的摄像机内外参数信息,所以,从原理上讲,从单应矩阵的角度应该同样可以得到关于内参数的等价约束。本文从标定杆运动前后所在平面和像平面的单应矩阵的角度出发,对一维标定进行了研究,得到了与文献中等价的对内参数的约束。 3.在使用圆为特征进行图象校正的问题中,如果已知圆和圆心的投影,则可以在相差一个正交变换下唯一确定圆所在的平面和图像平面的单应矩阵, 从而完成图象校正。本文针对使用圆和两条已知夹角的直线为特征,推导得出关于圆心投影的六次约束,即圆心的投影在一条六次曲线上。在两条直线垂直的情况下,约束退化为一个二次约束。并针对两条直线相互垂直的情况,具体讨论了在圆和两条直线位置关系在相交、相切、相离时,二次曲线的具体表现形式。 4.对P3P问题的多解性和稳定性之间的关系进行了研究。 研究表明P3P问题的多解性和稳定性是完全不同的两个概念。只有当光心位于危险圆柱上的时候,P3P问题存在多解,并且解是不稳定的。而其它情况下,多解都是稳定的。同时也对光心在三个垂面上时解的几何分布进行了研究,发现光心在趋于靠近危险圆柱时,共边解或共点解趋于重合的现象。
其他摘要Image based object pose estimation is an important topic in computer vision, and finds its applications in a variety of fields, such as vision based robot navigation, virtual reality etc. This thesis is focused on object pose estimation by point correspondences from space to image, such as new estimation approaches, and solution multiplicity and stability etc. The main results include: 1.We prove that the popular cost functions of the PnP problem in the literature can be reformulated as some kinds of equivalent potential energy of a dynamic mechanical system composed of a rigid body and springs, then the PnP problem solving is converted into finding the system’s configuration by iteratively minimizing the energy cost. A simulation of this physical progress with resistance and force of springs is carried out, and stable solutions are obtained. 2.One dimensional calibration is an important calibration approach. In the literature, either geometric intuition or some ingenuity is needed to derive the calibration constraints for 1-D calibration. Since the calibration stick’s position before and after the motion is coplanar, and the homography encapsulates all the information of the projection process from the space plane to the image plane, it must be possible, methodologically speaking, to derive the same calibration constraints via the planar homography. In this work, we present a new method to derive the similar calibration constraints via homogaphy, and our method appears general, and systematic. 3.It is shown that if the projections of a circle and its center are both known, the image rectification can be done up to either a rotation or a reflection. However in general, the projection of circle’ center is not the center of the projected ellipse, and additional information is needed to locate its projection. In this work, we investigate the possible constraint on the projection of the circle’s center by adding a coplanar pair of lines with known including angle. It is shown that the resulting constraint is generally a curve of 6-degree. However when the two lines are perpendicular, the constraint degenerates into a curve of 2-degree. In addition, for the perpendicular line pair, its geometric interpretation, and specific curve forms are provided depending on whether the lines intersect ( not) the circle, or tangent to the circle. 4.We systematically investigated the relationship of the solution’s multiplicity and stability for the PnP problem. W...
馆藏号XWLW1844
其他标识符200918014628049
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/6533
专题毕业生_博士学位论文
推荐引用方式
GB/T 7714
王波. 物体定位与图象矫正研究[D]. 中国科学院自动化研究所. 中国科学院大学,2013.
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