The quasi-perspective model: Geometric properties and 3D reconstruction

The paper investigates geometric properties of quasi-perspective projection model in one and two-view geometry. The main results are as follows. (i) Quasi-perspective projection matrix has nine degrees of freedom (DOF), and the parallelism along X and Y directions in world system are preserved in images. (ii) Quasi-fundamental matrix can be simplified to a special form with only six DOFs. The fundamental matrix is invariant to any non-singular projective transformation. (iii) Plane induced homography under quasi-perspective model can be simplified to a special form defined by six DOFs. The quasi-homography may be recovered from two pairs of corresponding points with known fundamental matrix. (iv) Any two reconstructions in quasi-perspective space are defined up to a non-singular quasi-perspective transformation. The results are validated experimentally on both synthetic and real images.