General Regular Polygon Method for Camera Calibration in Machine Vision

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.