Reconstruction of 3D Plane using Min-Max Approach

In this paper, a new approach for the reconstruction of a 3D plane by solving the geometry of two perspective projections of the plane is presented. It is assumed that the position and the orientation of one camera are known with respect to the other one. The correspondence between the object space and image planes is established using the collinearity equation. The projection of the original plane into two image planes results in two set of discrete points from which the min-max points of horizontal and vertical axes are obtained. A set of four 2D points for each plane, is obtained from these corresponding points. Then four points in 3D space are obtain from the corresponding sets of 2D points using the collinearity equations and the correspondence (extrinsic and intrinsic parameter) between the respective pair of projections. The equation of the plane obtained from these four points is the equation of reconstructed plane in 3D space. This work, deals with the digitized and normalized image planes for both general and perfect stereo cases and considering various noisy cases in the reconstruction process. The angle and distance between the reconstructed and the original plane in 3D space have been used as the criterion for the measurement of the error. The results of this study are useful for the design of a stereo-based imaging system and for the best reconstruction with minimum error. Results for planes are presented using simulation studies. Simulation studies have been conducted to observe the effect of noise on errors in the process of reconstruction.