An Analytical Method of Determining the Plane Based on Dual Ellipse Equations

Since the spot is elliptical when the cylindrical laser comes to the spatial plane, it proves that the laser spots in the CCD images, which are acquired by binocular stereo vision, are also elliptical. Through image edge extraction in image processing, it can obtain space equations of imaging ellipse edge by least square ellipse fitting, which can be transformed into the standard ellipse equations through translation and rotation. Selecting one point of the right imaging ellipse and the left and right camera coordinate system origins, by which a plane is constructed to make simultaneous solution with left imaging ellipse curves so as to obtain the corresponding matching points. From the selective point of right imaging ellipse and right camera coordinate system origin it can make one spatial straight line and from the corresponding analytical point of left imaging ellipse and left camera coordinate system origin it can make another spatial straight line, from which it will obtain the point of intersection which is the point on the spatial plane. With the change of the selective point of right imaging ellipse in a circle, a number of points on the spatial plane can be acquired to determine the spatial plane. The numerical results show that the method is effective and feasible.