A Novel Solution to the P4P Problem for an Uncalibrated Camera

We present a novel solution for the absolute camera pose and the camera calibration (effective focal length and aspect ratio) based on perspective four point (P4P) problem. By converting perspective transformation to affine transformation and using invariance to 3D affine transformation, we explore the relationship between the dual image of the absolute conic (DIAC) and the world coordinate of camera optical center and show how the coplanar and noncoplanar cases are cast into the problems of solving a quadratic polynomial equation and an eighth degree polynomial equation in a single variable respectively using only linear algebra. In particular, geometric configurations for infinite solutions of the coplanar case are explored. We also confirm the conclusion that the upper bound of eight real solutions for noncoplanar case is attainable by an example. The performance and usefulness of our novel solution are demonstrated by thorough testing on both synthetic and real data.