EPnP: An Accurate O(n) Solution to the PnP Problem

  • Authors:

  • Vincent Lepetit;Francesc Moreno-Noguer;Pascal Fua

  • Affiliations:

  • Computer Vision Laboratory, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland CH-1015;Computer Vision Laboratory, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland CH-1015;Computer Vision Laboratory, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland CH-1015

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 2009

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Abstract

We propose a non-iterative solution to the PnP problem--the estimation of the pose of a calibrated camera from n 3D-to-2D point correspondences--whose computational complexity grows linearly with n. This is in contrast to state-of-the-art methods that are O(n 5) or even O(n 8), without being more accurate. Our method is applicable for all n驴4 and handles properly both planar and non-planar configurations. Our central idea is to express the n 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done in O(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12脳12 matrix and solving a small constant number of quadratic equations to pick the right weights. Furthermore, if maximal precision is required, the output of the closed-form solution can be used to initialize a Gauss-Newton scheme, which improves accuracy with negligible amount of additional time. The advantages of our method are demonstrated by thorough testing on both synthetic and real-data.