基于同心圆标志的空间平面夹角测量

Measurement of Space Plane Angle Based on Concentric Circle Mark

为实时准确地测量两平面之间的夹角值,根据射影变换原理,提出一种基于同心圆标志的空间平面夹角测量的方法。首先拟合出获取的图像中同心圆标志对应的曲线方程;再依据交比不变及调和比原理,先计算多个消隐点,拟合出同心圆所在平面的消隐线方程,以此确定两平面法线的消隐点;最后,结合已知的相机内部参数解算出两法线间的夹角值,对其取补即可得到两平面间的夹角值。仿真结果说明该方法真实可行。真实图像实验表明,该方法测量的绝对误差小于1°,相对误差不超过1%。该方法仅需已知相机内部参数,对同心圆标志尺寸及拍照位置无特殊要求,具有较高的灵活性,能为夹角测量提供便捷高效的技术方案。

This study proposes a method for the accurate and real-time measurement of the angle between two planes based on the concentric circle mark and the principle of projective transformation.First,the curve equation corresponding to the concentric circle mark in the obtained image is fitted.Second,several vanishing points are calculated according to the invariant cross and harmonic ratios.The vanishing line equation of the plane,where the concentric circles are located,is fitted to determine the vanishing points of the two plane normals.Third,the angle between the two normals is calculated by combining known camera internal parameters.The angle between the two planes is the supplementary angle.The simulation results show that the method is feasible.The actual image experiments show that the absolute error is less than 1°,while the relative error is less than 1%.This method requires only the internal parameters of the camera and has no special requirements for the size of the concentric circle mark and shoot angle.Moreover,the method has high flexibility and can provide a convenient and efficient scheme for the space angle measurement.