In real world, there are many artificial objects. We propose a new method to
reconstruct the 3D structure of the artificial objects from the scene pictures using orthogonality
and parallelism. The new transformation group “semi-metric space” is defined and using that
we describe the artificial scenes effectively. Through the analysis of the plane and parallax, the
relative distance between a line and the reference plane is estimated, and it gives us a partial
3D structure from a single image. The algorithms are verified with real image captured with
camera in commercial mobile phone.