Using projective invariant properties for efficient 3D reconstruction

Abstract

3D reconstruction over long sequences has been to the main problem of computer vision. Projective reconstruction is known to be an important process for 3D reconstruction in Euclidean space. In this paper, we present a new projective reconstruction algorithm using invariant properties of the line segments in projective space: collinearity, order of contact, and intersection. Points on each line segment in the image are reconstructed in projective space, and we calculate the best-fit 3D line from them by Least-Median-Squares (LMedS). Our method regards the points unsatisfying collinearity as outliers, which are caused by false feature detection and tracking. In addition, both order of contact and intersection in projective space are considered. By using the points that are the orthogonal projection of outliers onto the 3D line, we iteratively obtain more precise projective matrix than the previous method. The experimental results showed that the proposed algorithm can estimate camera parameters and reconstruct 3D model exactly.