A Linear Method for the PnP Problem

摘要

The classical PnP problem (3n5) is inherently non-linear and generally of multiple solutions and sensitive to errors associated with image points. In the classical PnP problem, only a single image is involved. Inspired by the problems in robot navigation, the PnP problem is extended to the two-image case where the camera undergoes a pure translation between the two images. The obtained main results are: given two images of n known control points captured by a translating camera, (1) When n=3, the camera抯 pose and two scaling parameters of the two image axes can be linearly determined; (2) When n4, the camera抯 pose and all its 5 intrinsic parameters can be linearly determined. In other words, the PnP problem with an uncalibrated camera can be linearly solved in this case. The results presented in this paper appears instructive from both theoretical and practical points of view.