An Efficient Solution to the Homography-Based Relative Pose Problem With a Common Reference Direction

Abstract

In this paper, we propose a novel approach to two-view minimal-case relative pose problems based on homography with a common reference direction. We explore the rank-1 constraint on the difference between the Euclidean homography matrix and the corresponding rotation, and propose an efficient two-step solution for solving both the calibrated and partially calibrated (unknown focal length) problems. We derive new 3.5-point, 3.5-point, 4-point solvers for two cameras such that the two focal lengths are unknown but equal, one of them is unknown, and both are unknown and possibly different, respectively. We present detailed analyses and comparisons with existing 6-and 7-point solvers, including results with smart phone images

Homography-Based Egomotion Estimation Using Gravity and SIFT Features

“…This means that each SIFT correspondence gives four constraints on the homography matrix G (three linear ones from (9) and (11) and one quadratic one from (12)) and each ORB correspondence gives just three linear constraints ((9) and (11)). Our objective is to estimate the camera motion by estimating a homography from a combination of SIFT/ORB and point correspondences.…”

“…Our objective is to estimate the camera motion by estimating a homography from a combination of SIFT/ORB and point correspondences. Note, that constraints (11) and (12) were derived for a general homography. In our case, the y-axes of the cameras are aligned with the gravity direction.…”

“…This changes not only the point coordinates, but also affects the orientation and scale of the features. Thus, the constraints (11) and (12) cannot be directly applied when estimating the Euclidean homography matrix H y via Eq. (3).…”

“…Such a prior is, for example, the assumption that the camera moves on a plane -e.g., it is mounted to a vehicle -and, therefore, only a single rotation and two translation parameters have to be estimated [4,5]. Recently, largely motivated by the availability of camera-IMU systems, smart phones and tablets, which have accelerometers to measure the gravity direction, point-plus-direction solvers have shown a number of benefits [6][7][8][9][10][11][12][13][14]. Using this measurement, the y-axes of the cameras can be aligned with the gravity direction, reducing the relative orientation of two cameras from three to a single degree of freedom (DOF).…”

Minimal Solutions for Relative Pose With a Single Affine Correspondence

“…This common direction can be determined from an IMU (which provides the known pitch and roll angles of the camera), but as well from vanishing points extracted across the two views. When the common direction of rotation is known, a variety of algorithms have been proposed to estimate the relative pose utilizing this information [14,29,40,33,16,10].…”