P3.5P: Pose Estimation with Unknown Focal Length

Abstract

It is well known that the problem of camera pose estimation with unknown focal length has 7 degrees of freedom. Since each image point gives 2 constraints, solving this problem requires a minimum of 3.5 image points of 4 known 3D points, where 0.5 means either x or y coordinate of an image point. We refer to this minimal problem as P3.5P. However, the existing methods require 4 full image points to solve the camera pose and focal length. In this paper, we present a general solution to the true minimal P3.5P problem with up to 10 solutions. The remaining image coordinate is then used to filter the candidate solutions, which typically results in a single solution for good data or no solution for outliers. Experiments show the proposed method significantly improves the efficiency over the state of the art methods while maintaining a high accuracy.