Monocular Rectangle Reconstruction Based On Direct Linear Transformation

3D reconstruction is an important field in computer vision. Many approaches are based on multiple images of a given scene. Using only one single image is far more challenging. Monocular image reconstruction can still be achieved by using regular and symmetric structures, which often appear in human environment. In this work we derive two schemes to recover 3D rectangles based on their 2D projections. The first method improves a commonly known standard geometric derivation while the second one is a new algebraic solution based on direct linear transformation (DLT). In a second step, the obtained solutions of both methods serve as seeding points for an iterative linear least squares optimization technique. The robustness of the reconstruction to noise is shown. An insightful thought experiment investigates the ambiguity of the rectangle identification. The presented methods have various potential applications which cover a wide range of computer vision topics such as single image based reconstruction, image registration or camera path estimation.