围绕机器视觉摄像机标定问题，该文将通常几种基于特定正多边形模型的标定方法拓展为一般正多边形模型的摄像机标定方法. 首先分析一般正多边形的平面几何性质，结合射影几何中的交比和调和共轭的性质计算正多边形各条边和正多边形内切圆心与切点连线方向的消失点. 利用消失点与光心的连线方向和形成消失点空间直线方向相同的性质建立线性方程组，从而求解摄像机内参数. 最后通过几个特定正多边形（正三角形、正四边形、正五边形、正六边形）模版的摄像机标定验证一般正多边形标定方法的正确性. 实验中还发现几种特定正多边形的摄像机标定精度不同，正五边形的标定精度最高，正四边形最低.

Abstract: We expand certain special regular polygon models for camera calibration in machine vision to a general regular polygon model, and propose the general regular polygon calibration method. For general regular polygons, geometrical characteristics on the polygon plane are analyzed. We determine two types of vanishing point according to the cross ratio and the harmonic-conjugate rules in projective geometry. One type is formed by every edge vector of the polygon, and the other formed from the center of the inscribed circle to the tangent points. The camera’s intrinsic parameters can then be calculated. Calculation can be done in this way because the direction from the vanishing point to the optic center is the same as that of the vector making the vanishing point. Finally, the general regular polygon calibration method is validated by camera calibration experiments with four specific regular polygons: regular triangle, square, regular pentagon, and regular hexagon. Experimental results also show that, among the four specific regular polygons, calibration accuracy of the regular pentagon model is the highest, while that of the square model is the lowest.