This paper presents a general solution to the determination of the pose of a perspective camera with unknown focal length from images of four 3D reference points. Our problem is a generalization of the P3P and P4P problems previously developed for fully calibrated cameras. Given four 2D-to-3D correspondences, we estimate camera position, orientation and recover the camera focal length. We formulate the problem and provide a minimal solution from four points by solving a system of algebraic equations. We compare the Hidden variable resultant and Gröbner basis techniques for solving the algebraic equations of our problem. By evaluating them on synthetic and on real-data, we show that the Gröbner basis technique provides stable results.

In this paper a robust method to track a head in 3D using a static monocular camera is presented. Head pose is recovered by formulating the problem as a camera pose estimation problem. Several 3D feature points are acquired from the head prior to tracking and used as a model. Both artificial and natural occurring features can be used. Pose is estimated by solving a robust version of ”Perspective n Point ” problem (PnP). The proposed algorithm can handle self occlusions, outliers and recover from tracking failures. Results were validated by simulations and were compared to pose obtained using an accurate magnetic field 3D measuring device. Our system is not limited to tracking human heads and can be used to track animal heads as well. To demonstrate the applicability of our method, three types of heads were tracked (human, barn owl, chameleon) in a series of biological experiments. 1.

Classifying the Perspective-Three-Point problem (abbreviated by P3P in the sequel) consists in determining the number of possible positions of a camera with respect to the apparent position of three points. In the case where the three points form an isosceles triangle, we give a full classification of the P3P. This leads to consider a polynomial system of polynomial equations and inequalities with 4 parameters which is generically zero-dimensional. In the present situation, the parameters represent the apparent position of the three points so that solving the problem means determining all the possible numbers of real solutions with respect to the parameters’ values and give a sample point for each of these possible numbers. One way for solving such systems consists first in computing a discriminant variety. Then, one has to

We propose a new robust estimator for camera pose estimation based on a recently developed nonlinear mean shift algorithm. This allows us to treat pose estimation as a clustering problem in the presence of outliers. We compare our method to RANSAC, which is the standard robust estimator for computer vision problems. We also show that under fairly general assumptions our method is provably better than RANSAC. Synthetic and real examples to support our claims are provided. 1.

Abstract. Camera pose estimation is the problem of determining the position and orientation of an internally calibrated camera from known 3D reference points and their images. We introduce a new polynomial equation system for 4-point pose estimation and apply our symbolicnumeric method to solve it stably and efficiently. In particular, our algorithm can also recognize the points near critical configurations and deal with these near critical cases carefully. Numerical experiments are given to show the performance of the hybrid algorithm. 1

Structure-From-Motion (SFM) methods, using stereo data, are among the best performing algorithms for motion estimation from video imagery, or visual odometry. Critical to the success of SFM methods is the quality of the initial pose estimation algorithm from feature correspondences. In this work, we evaluate the performance of pose estimation algorithms commonly used in SFM visual odometry. We consider two classes of techniques to develop the initial pose estimate: Absolute Orientation (AO) methods, and Perspective-n-Point (PnP) methods. To date, there has not been a comparative study of their performance on robot visual odometry tasks. We undertake such a study to measure the accuracy, repeatability, and robustness of these techniques for vehicles moving in indoor environments and in outdoor suburban roadways. Our results show that PnP methods outperform AO methods, with P3P being the best performing algorithm. This is particularly true when stereo triangulation uncertainty is high due to a wide Field of View lens and small stereo-rig baseline.

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Abstract. Structure-From-Motion (SFM) methods, using stereo data, are among the best performing algorithms for motion estimation from video imagery, or visual odometry. Critical to the success of SFM methods is the quality of the initial pose estimation algorithm from feature correspondences. In this work, we evaluate the performance of pose estimation algorithms commonly used in SFM visual odometry. We consider two classes of techniques to develop the initial pose estimate: Absolute Orientation (AO) methods, and Perspective-n-Point (PnP) methods. To date, there has not been a comparative study of their performance on robot visual odometry tasks. We undertake such a study to measure the accuracy, repeatability, and robustness of these techniques for vehicles moving in indoor environments and in outdoor suburban roadways. Our results show that PnP methods outperform AO methods, with P3P being the best performing algorithm. This is particularly true when stereo triangulation uncertainty is high due to a wide Field of View lens and