A novel 3D planar object reconstruction from multiple uncalibrated images using the plane-induced homographies

A computer vision method is proposed to determine all the visible 3D planar surfaces in a scene from uncalibrated images and locate them in a single 3D projective space. Most of the existing methods for reconstructing planar objects use point correspondences to estimate the fundamental matrix and derive the compatible projection equations, before they apply the standard triangulation technique to find the 3D points and fit the planes to the 3D points. This type of approaches is generally slow and less accurate because the 3D points are estimated separately, making them vulnerable to image error. We present a plane based reconstruction method to estimate the 3D projective structure using the planar homographies estimated from the plane features in the images. First, we estimate the homography for each visible plane, and then we use the homographies of two primary planes to compute an epipole. We proceed to represent the epipolar geometry for each image pair using the estimated homography and epipole, together with a specified reference plane coefficient vector. Next, we show that the 3D plane coefficient vector of any plane visible in each image pair can be determined with respect to the reference plane coefficient vector once its planar homography is found. Finally, the reconstruction results obtained in individual projective spaces are integrated within a common projective space. To this end, we use the homography and plane equation information of two planes and the epipole associated to derive the coordinate transformation matrix between two involved projective spaces. To evaluate the performance of our method, we apply our method to the synthetic images and real images. All the results indicate the method works successfully. 2004 Published by Elsevier B.V.