In this paper we derive and test a probability-based weighting that can balance residuals of different types in spline fitting. In contrast to previous formulations, the proposed spline error weighting scheme also incorporates a prediction of the approximation error of the spline fit. We demonstrate the effectiveness of the prediction in a synthetic experiment, and apply it to visual-inertial fusion on rolling shutter cameras. This results in a method that can estimate 3D structure with metric scale on generic first-person videos. We also propose a quality measure for spline fitting, that can be used to automatically select the knot spacing. Experiments verify that the obtained trajectory quality corresponds well with the requested quality. Finally, by linearly scaling the weights, we show that the proposed spline error weighting minimizes the estimation errors on real sequences, in terms of scale and end-point errors.

This paper revisits the problem of continuous-time structure from motion, and introduces a number of extensions that improve convergence and efficiency. The formulation with a C 2 -continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyse the behaviour of split interpolation on SO(3) and on R 3 , and a joint interpolation on SE (3), and show that the latter implicitly couples the direction of translation and rotation. Such an assumption can make good sense for a camera mounted on a robot arm, but not for hand-held or body-mounted cameras. Our experiments show that split interpolation on R 3 and SO(3) is preferable over SE (3) interpolation in all tested cases. Finally, we investigate the problem of landmark reprojection on rolling shutter cameras, and show that the tested reprojection methods give similar quality, while their computational load varies by a factor of 2. Figure 1. Rendered model estimated on the RC-Car dataset, using split interpolation. Top: model rendered using Meshlab. Bottom: Sample frames from dataset.

Abstract-We propose a technique for joint calibration of a wide-angle rolling shutter camera (e.g. a GoPro) and an externally mounted gyroscope. The calibrated parameters are time scaling and offset, relative pose between gyroscope and camera, and gyroscope bias. The parameters are found using non-linear least squares minimisation using the symmetric transfer error as cost function.The primary contribution is methods for robust initialisation of the relative pose and time offset, which are essential for convergence. We also introduce a robust error norm to handle outliers. This results in a technique that works with general video content and does not require any specific setup or calibration patterns.We apply our method to stabilisation of videos recorded by a rolling shutter camera, with a rigidly attached gyroscope. After recording, the gyroscope and camera are jointly calibrated using the recorded video itself. The recorded video can then be stabilised using the calibrated parameters.We evaluate the technique on video sequences with varying difficulty and motion frequency content. The experiments demonstrate that our method can be used to produce high quality stabilised videos even under difficult conditions, and that the proposed initialisation is shown to end up within the basin of attraction. We also show that a residual based on the symmetric transfer error is more accurate than residuals based on the recently proposed epipolar plane normal coplanarity constraint, and that the use of robust errors is a critical component to obtain an accurate calibration.

Many RGB-D sensors, e.g. the Microsoft Kinect, use rolling shutter cameras. Such cameras produce geometrically distorted images when the sensor is moving. To mitigate these rolling shutter distortions we propose a method that uses an attached gyroscope to rectify the depth scans. We also present a simple scheme to calibrate the relative pose and time synchronization between the gyro and a rolling shutter RGB-D sensor.We examine the effectiveness of our rectification scheme by coupling it with the the Kinect Fusion algorithm. By comparing Kinect Fusion models obtained from raw sensor scans and from rectified scans, we demonstrate improvement for three classes of sensor motion: panning motions causes slant distortions, and tilt motions cause vertically elongated or compressed objects. For wobble we also observe a loss of detail, compared to the reconstruction using rectified depth scans.As our method relies on gyroscope readings, the amount of computations required is negligible compared to the cost of running Kinect Fusion.