We propose a new method to recover 3D structures of artificial
objects from scene pictures using orthogonality and parallelism.
A new transformation group, “semi-metric space,” is defined to describe
the scenes of artificial objects consisting of orthogonal and parallel line
features. A metric invariant called conic dual to the circular points has
a simple diagonal form in the semi-metric space. Furthermore, under
some assumptions, the metric reconstruction is possible using some affine
properties. The algorithms are verified with real images captured with a
camera in a commercial mobile phone.