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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 8523604, 14 pages
Research Article

Projective Invariants from Multiple Images: A Direct and Linear Method

School of Computer Science and Engineering, Northeastern University, Shenyang 110819, China

Received 3 October 2015; Accepted 3 March 2016

Academic Editor: Antonino Laudani

Copyright © 2016 Yuanbin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The projective reconstruction of 3D structures from 2D images is a central problem in computer vision. Existing methods for this problem are usually nonlinear or indirect. In the previous direct methods, we usually have to solve a system of nonlinear equations. They are very complicated and hard to implement. The previous linear indirect methods are usually imprecise. This paper presents a linear and direct method to derive projective structures of 3D points from their 2D images. Algorithms to compute projective invariants from two images, three images, and four images are given. The method is clear, simple, and easy to implement. For the first time in the literature, we present explicit linear formulas to solve this problem. Mathematica codes are provided to demonstrate the correctness of the formulas.