The rolling shutter camera has received great attention due to its low cost imaging capability, however, the estimation of relative pose between rolling shutter cameras still remains a difficult problem owing to its line-by-line image capturing characteristics. To alleviate this problem, we exploit gyroscope measurements, angular velocity, along with image measurement to compute the relative pose between rolling shutter cameras. The gyroscope measurements provide the information about instantaneous motion that causes the rolling shutter distortion. Having gyroscope measurements in one hand, we simplify the relative pose estimation problem and find a minimal solution for the problem based on the Grobner basis polynomial solver. The proposed method requires only five points to compute relative pose between rolling shutter cameras, whereas previous methods require 20 or 44 corresponding points for linear and uniform rolling shutter geometry models, respectively. Experimental results on synthetic and real data verify the superiority of the proposed method over existing relative pose estimation methods.
@cite_22: It this paper we present a novel minimal case solution to the calibrated relative pose problemusing 3 point correspondences for the case of two known orientation angles. This case is relevant when a camera is coupled with an inertial measurement unit (IMU) and it recently gained importance with the omnipresence of Smartphones (iPhone, Nokia N900) that are equippedwith accelerometers tomeasure the gravity normal. Similar to the 5-point (6-point), 7-point, and 8-point algorithm for computing the essential matrix in the unconstrained case, we derive a 3-point, 4-point and, 5-point algorithm for the special case of two known orientation angles. We investigate degenerate conditions and show that the new 3-point algorithm can cope with planes and even collinear points. We will show a detailed analysis and comparison on synthetic data and present results on cell phone images. As an additional application we demonstrate the algorithm on relative pose estimation for a micro aerial vehicle's (MAV) camera-IMU system.
@cite_36: 
@cite_1: We present a solution to the rolling shutter (RS) absolute camera pose problem with known vertical direction. Our new solver, R5Pup, is an extension of the general minimal solution R6P, which uses a double linearized RS camera model initialized by the standard perspective P3P. Here, thanks to using known vertical directions, we avoid double linearization and can get the camera absolute pose directly from the RS model without the initialization by a standard P3P. Moreover, we need only five 2D-to-3D matches while R6P needed six such matches. We demonstrate in simulated and real experiments that our new R5Pup is robust, fast and a very practical method for absolute camera pose computation for modern cameras on mobile devices. We compare our R5Pup to the state of the art RS and perspective methods and demonstrate that it outperforms them when vertical direction is known in the range of accuracy available on modern mobile devices. We also demonstrate that when using R5Pup solver in structure from motion (SfM) pipelines, it is better to transform already reconstructed scenes into the standard position, rather than using hard constraints on the verticality of up vectors.
@cite_6: In this paper, we present our minimal 4-point and linear 8-point algorithms to estimate the relative pose of a multi-camera system with known vertical directions, i.e. known absolute roll and pitch angles. We solve the minimal 4-point algorithm with the hidden variable resultant method and show that it leads to an 8-degree univariate polynomial that gives up to 8 real solutions. We identify a degenerated case from the linear 8-point algorithm when it is solved with the standard Singular Value Decomposition (SVD) method and adopt a simple alternative solution which is easy to implement. We show that our proposed algorithms can be efficiently used within RANSAC for robust estimation. We evaluate the accuracy of our proposed algorithms by comparisons with various existing algorithms for the multi-camera system on simulations and show the feasibility of our proposed algorithms with results from multiple real-world datasets.
@cite_24: We propose an algorithm to estimate the relative camera pose using four feature correspondences and one relative rotation angle measurement. The algorithm can be used for relative pose estimation of a rigid body equipped with a camera and a relative rotation angle sensor which can be either an odometer, an IMU or a GPS INS system. This algorithm exploits the fact that the relative rotation angles of both the camera and relative rotation angle sensor are the same as the camera and sensor are rigidly mounted to a rigid body. Therefore, knowledge of the extrinsic calibration between the camera and sensor is not required. We carry out a quantitative comparison of our algorithm with the well-known 5-point and 1-point algorithms, and show that our algorithm exhibits the highest level of accuracy.
@cite_23: Vision-aided inertial navigation techniques are described. In one example, a vision-aided inertial navigation system (VINS) comprises an image source to produce image data at a first set of time instances along a trajectory within a three-dimensional (3D) environment, wherein the image data captures features within the 3D environment at each of the first time instances. An inertial measurement unit (IMU) to produce IMU data for the VINS along the trajectory at a second set of time instances that is misaligned with the first set of time instances, wherein the IMU data indicates a motion of the VINS along the trajectory. A processing unit comprising an estimator that processes the IMU data and the image data to compute state estimates for 3D poses of the IMU at each of the first set of time instances and 3D poses of the image source at each of the second set of time instances along the trajectory. The estimator computes each of the poses for the image source as a linear interpolation from a subset of the poses for the IMU along the trajectory.
@cite_15: In this paper we provide new simple closed-form solutions to two minimal absolute pose problems for the case of known vertical direction. In the first problem we estimate absolute pose of a calibrated camera from two 2D-3D correspondences and a given vertical direction. In the second problem we assume camera with unknown focal length and radial distortion and estimate its pose together with the focal length and the radial distortion from three 2D-3D correspondences and a given vertical direction. The vertical direction can be obtained either by direct physical measurement by, e.g., gyroscopes and inertial measurement units or from vanishing points constructed in images. Both our problems result in solving one polynomial equation of degree two in one variable and one, respectively two, systems of linear equations and can be efficiently solved in a closed-form. By evaluating our algorithms on synthetic and real data we demonstrate that both our solutions are fast, efficient and numerically stabled.
@cite_20: Video acquired by handheld CMOS cameras may suffer from rolling shutter artifacts. Rolling shutter artifacts, which are due to the rows in the image sensor array being exposed sequentially from top to bottom, increase with the speed of the relative motion between the scene and camera. To rectify these artifacts, one needs to recover the projection parameters for each row. In this paper, we propose a probabilistic method to estimate 3-D camera rotation by using video and inertial measurements on the handheld platform, such as a smart phone. Our contributions are (1) an efficient sensor fusion algorithm using an extended Kalman filter, and (2) a quality assessment method using vanishing point detection. Experiments indicate that the proposed sensor fusion algorithm produces a more accurate orientation estimate and better rectifies rolling shutter artifacts.
On the other hand, the methods to utilize an inertial measurement unit (IMU) to deal with the rolling shutter distortion in visual odometry (VO) and SLAM have been also studied. Jia and Evans @cite_20 proposed a method to estimate the camera orientation using gyroscope measurements and to correct the rolling shutter distortion of the image. Guo al @cite_23 applied a rolling shutter camera projection model to the visual-inertial odometry framework that uses IMUs and cameras to estimate egomotion. They estimated the readout time of the rolling shutter camera as well as the time delay between the IMU and the camera. Albl al @cite_1 proposed a method to improve the speed and accuracy of the method in @cite_36 using the gravity measurements obtained from the IMU. In addition, IMUs are also used to solve conventional relative or absolute pose estimation problems for global shutter cameras. It has been studied to estimate relative pose with the partially known orientation angle between two cameras @cite_22 @cite_24 , or with known vertical direction @cite_15 @cite_6 .