3D Reconstruction Based on Invariant Properties of 2D Lines in Projective Space

Abstract

Projective reconstruction is known to be an important step for 3D reconstruction in Euclidean space. In this paper, we present a new projective reconstruction algorithm based on invariant properties of the line segments in projective space: collinearity, order of contact, intersection. Points on each line segment in the image are reconstructed in projective space, and we determine 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.