An efficient solution to the five-point relative pose problem

Abstract

An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well-known 8 and 7-point methods and a 6-point scheme. The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay. The real-time system uses solely visual input and has been demonstrated at major conferences.

Monocular Height Estimation Method with 3 Degree-Of-Freedom Compensation of Road Unevennesses

“…In order to estimate the camera displacement ∆Cam N in each frame, we adopted a simple VO with rotation estimation by Nister's 5-point algorithm [17] and translation by the FSM using features in a ground region close to the camera (details in the Appendix section), similarly to [12]. The parameters (FOV u , FOV v , W, V, H, etc) necessary for the experiments were adopted according to the provided by the KITTI.…”

Map Building Fusing Acoustic and Visual Information using Autonomous Underwater Vehicles

“…The former case uses image matches made over small displacements to provide an independent estimate of local robot motion, while the latter case treats images as containing information that will allow the robot to recognize its position at a later point in time. A pair of cameras calibrated together can yield metric 6-DOF relative pose estimates, called stereo visual odometry, a technique widely used in terrestrial robotics [Howard, 2008] [Olson et al, 2003, and underwater in [Beall et al, 2010], for example. Underwater, we have found that a DVL generally provides more reliable odometry information over short distances than does a pair of cameras, without any calibration requirements [Kunz and Singh, 2010].…”

“…The K matrix allows us to use normalized image coordinates, and gives rise to the essential matrix, which specializes the epipolar geometry to the normalized case. The essential matrix can be estimated from five matched pixels, and it can be decomposed into a 3-D rotation and a translation vector [Nistér, 2004]. This means that even without incorporating any prior estimate of the camera motion from AUV odometry, a pair of image matches in principle can inform five of the six degrees of freedom of the camera motion between two points in time -only the scale of the motion is not recoverable.…”

Robust monocular visual odometry for road vehicles using uncertain perspective projection

“…In this calibrated setting, visual odometry is achieved by estimating the essential matrix that relates the homogeneous image coordinates of the same world point in the two viewpoints up to a scale factor [4]. A computationally efficient solution for this was published in the 1990s by Philip [5] and improved upon by Nistér [6]. In Nistérs solution, a RANSAC algorithm evaluates sets of five correspondence points to find the best estimate for the essential matrix.…”