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

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 ≥ 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 × 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.1 Index TermsPose estimation, Perspective-n-Point, Absolute orientation. 's algorithm initialized with the output of our algorithm; EPnP+GN, our method followed by a Gauss-Newton optimization.

OpenMVG: Open Multiple View Geometry

“…OpenMVG provides various models and solvers, illustrated Fig.2: -Relative pose from pairs of image-image matching points, such as homography (4-point algorithm [6] for transform of planar scene or scene viewed under pure rotation), fundamental matrix (7/8-point algorithm [6], in case of ignorance of camera internal parameters), essential matrix (5-point [8], in case of known camera internal parameters). -Absolute pose from pairs of 3D-2D matching points by different algorithms, P3P (Perspective from 3 Points) [16], DLT (Direct Linear Transform) [6] (6 pairs), ePnP [15] (n pairs).…”

Leveraging Feature Uncertainty in the PnP Problem

“…This has recently been overcome by a series of O(n) formulations that can afford arbitrarily large point sets. The first of these techniques was the EPnP [18,23], that reduced the PnP to retrieving the position of four control points spanning any number n of 3D points. This reformulation of the problem, jointly with the use of linearization strategies, permitted dealing with hundreds of correspondences in real time.…”

“…We have compared our formulations against the most recent PnP approaches: the robust version of DLS [11], ASPnP [34], OPnP [33], RPnP [19], PPnP [8], EPnP + GN [18], SDP [30], EPPnP [5] and the LHM [21].…”

3D Object Recognition and Pose Estimation for Multiple Objects Using Multi-Prioritized RANSAC and Model Updating

“…Given the minimal subset, a pose estimation via EPnP [13] and an eventual non-linear minimization is performed in a sample-and-test framework to estimate the poseP that best fits the matches. In Table 1, each weight is evaluated in terms of the average number of iterations needed to find, for the first time, at least 75% of the inliers and it is averaged over 1000 runs per frame on a sample sequence.…”

“…Once the model is obtained offline, on-line recognition and pose estimation is performed by matching the image features against the model features and solving the Perspective-n-Point problem for the 2D-3D correspondences. Given a set of correct matches, pose estimation is a well-solved problem, and various solutions have been devised [13,6].…”