摘要
提出基于三角形及其九点圆的摄像机标定方法.利用了三角形九点圆中其九个点的特殊性,并且利用透视投影变换保二次曲线不变性,得到其像点在像平面共椭圆,从而可以通过九点的映射关系将透视投影变换的非线性问题线性化.图像分割和角点提取的误差会直接影响标定的精度,在此三角形及其九点圆中的点特别是算法中的关键点三角形顶点和垂心都是三条直线的交点,减小图像分割与提取时造成的误差.DLT方法的不精确就源于图像分割和角点提取的误差,方法克服了DLT方法的不足.张的方法无法保证单应性矩阵的正交性,因此为了保证正交性和提高精度需要优化.与传统方法相比操作简单,应用九点圆定理,仿射变换的引入将透视投影非线性问题线性化,避免了参数之间的非线性方程求解,降低了参数求解的复杂性,因此其定标过程快捷,准确.模板的构造,减少了图像分割和交点提取误差,算法实现保证旋转矩阵的正交性.综合上述分析,理论上表明方法的有效性.同时实验表明,标定方法操作简单,不需要计算机视觉的专业知识,快速,精度高,鲁棒性好.
This paper presents a camera calibration method based on a triangle and its nine point circle （NPC）. By using the characteristic of a triangle＇ s NPC and the invariance of quadratic function in perspective projection transformation, the images of the nine concyclic points kept lying on a common ellipse on image plane, thus a perspective projection transformation, which in general is a nonlinear problem, is linearised. In the algorithm, the points on this triangle and its NPC, especially those key points, i.e. the vertices and the orthocenter of the triangle, are the intersections of three straight lines, hence reducing the error due to image segmentation and extraction which will determines the accuracy of calibration. The DLT （direct linear transformation） method has a major inaccuracy due to the image segmentation and corner detection error. In contrast, the present method can mitigate this problem. Zhang＇s method cannot assure that the orthogonality of the homography. In order to ensure the orthogonality and to improve the accuracy, an optimization is required. Compared with traditional methods, the present method is simpler in use. By using the NPC theorem and introducing affine transformation nonlinear perspective projection is linearised hence nonlin- ear parameter equation solving is avoided. The complexity of the parameter seeking process is reduced. The calibration process is quicker and more accurate. The template structure reduces the error in image segmentation and extraction of the intersections. The algorithm ensures that the rotation matrix is orthogonal. From above it can be seen that theoretically the method is effective. Oil the other hand experiments show that this calibration method is simple, fast, precise, and robustness. There is no need of computer vision expertise in order to use it.
出处
《数学的实践与认识》
CSCD
北大核心
2012年第11期91-98,共8页
Mathematics in Practice and Theory
基金
国家自然科学基金(61075035)
关键词
九点圆定理
摄像机标定
摄像机自标定
机器人视觉
nine-point circle theorem
camera calibration
a camera self calibration
robot vision
