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 C2-continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyze the behavior of split spline interpolation on SO(3) and on R3, and a joint spline 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 in the Spline Fusion framework show that a split spline on R3andSO(3) is preferable over an SE(3) spline 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, whereas their computational load varies by a factor of two.

Scene reconstruction, i.e. the process of creating a 3D representation (mesh) of some real world scene, has recently become easier with the advent of cheap RGB-D sensors (e.g. the Microsoft Kinect).

Many such sensors use rolling shutter cameras, which produce geometrically distorted images when they are 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.

For scene reconstruction we use the Kinect Fusion algorithm to produce meshes. We create meshes from both raw and rectified depth scans, and these are then compared to a ground truth mesh. The types of motion we investigate are: pan, tilt and wobble (shaking) motions.

As our method relies on gyroscope readings, the amount of computations required is negligible compared to the cost of running Kinect Fusion.

This chapter is an extension of a paper at the IEEE Workshop on Robot Vision [10]. Compared to that paper, we have improved the rectification to also correct for lens distortion, and use a coarse-to-fine search to find the time shift more quicky.We have extended our experiments to also investigate the effects of lens distortion, and to use more accurate ground truth. The experiments demonstrate that correction of rolling shutter effects yields a larger improvement of the 3D model than correction for lens distortion.

We investigate spline-based continuous-time pose trajectory estimation using non-linear explicit motion priors. Current regularization priors either linearize the orientation, rely on the implicit regularization obtained from the used spline basis function, or use sampling based regularization schemes. The latter is a special case of a Riemann sum approximation, and we demonstrate when and why this can fail, and propose a way to avoid these issues. In addition we provide a number of novel practically useful theoretical contributions, including requirements on knot spacing for orientation splines, new basis functions for constant velocity extrapolation, and a generalization of the popular P-Spline penalty to orientation. We analyze the properties of the proposed approach using synthetic data. We validate our system using the standard task of visual-inertial calibration, and apply it to stereo visual odometry where we demonstrate real-time performance on KITTI.

In this paper we introduce an efficient method to unwrap multi-frequency phase estimates for time-of-flight ranging. The algorithm generates multiple depth hypotheses and uses a spatial kernel density estimate (KDE) to rank them. The confidence produced by the KDE is also an effective means to detect outliers. We also introduce a new closed-form expression for phase noise prediction, that better fits real data. The method is applied to depth decoding for the Kinect v2 sensor, and compared to the Microsoft Kinect SDK and to the open source driver libfreenect2. The intended Kinect v2 use case is scenes with less than 8m range, and for such cases we observe consistent improvements, while maintaining real-time performance. When extending the depth range to the maximal value of 18.75 m, we get about 52% more valid measurements than libfreenect2. The effect is that the sensor can now be used in large depth scenes, where it was previously not a good choice.

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.

Using images to reconstruct the world in three dimensions is a classical computer vision task. Some examples of applications where this is useful are autonomous mapping and navigation, urban planning, and special effects in movies. One common approach to 3D reconstruction is ”structure from motion” where a scene is imaged multiple times from different positions, e.g. by moving the camera. However, in a twist of irony, many structure from motion methods work best when the camera is stationary while the image is captured. This is because the motion of the camera can cause distortions in the image that lead to worse image measurements, and thus a worse reconstruction. One such distortion common to all cameras is motion blur, while another is connected to the use of an electronic rolling shutter. Instead of capturing all pixels of the image at once, a camera with a rolling shutter captures the image row by row. If the camera is moving while the image is captured the rolling shutter causes non-rigid distortions in the image that, unless handled, can severely impact the reconstruction quality.

This thesis studies methods to robustly perform 3D reconstruction in the case of a moving camera. To do so, the proposed methods make use of an inertial measurement unit (IMU). The IMU measures the angular velocities and linear accelerations of the camera, and these can be used to estimate the trajectory of the camera over time. Knowledge of the camera motion can then be used to correct for the distortions caused by the rolling shutter. Another benefit of an IMU is that it can provide measurements also in situations when a camera can not, e.g. because of excessive motion blur, or absence of scene structure.

To use a camera together with an IMU, the camera-IMU system must be jointly calibrated. The relationship between their respective coordinate frames need to be established, and their timings need to be synchronized. This thesis shows how to automatically perform this calibration and synchronization, without requiring e.g. calibration objects or special motion patterns.

In standard structure from motion, the camera trajectory is modeled as discrete poses, with one pose per image. Switching instead to a formulation with a continuous-time camera trajectory provides a natural way to handle rolling shutter distortions, and also to incorporate inertial measurements. To model the continuous-time trajectory, many authors have used splines. The ability for a spline-based trajectory to model the real motion depends on the density of its spline knots. Choosing a too smooth spline results in approximation errors. This thesis proposes a method to estimate the spline approximation error, and use it to better balance camera and IMU measurements, when used in a sensor fusion framework. Also proposed is a way to automatically decide how dense the spline needs to be to achieve a good reconstruction.

Another approach to reconstruct a 3D scene is to use a camera that directly measures depth. Some depth cameras, like the well-known Microsoft Kinect, are susceptible to the same rolling shutter effects as normal cameras. This thesis quantifies the effect of the rolling shutter distortion on 3D reconstruction, depending on the amount of motion. It is also shown that a better 3D model is obtained if the depth images are corrected using inertial measurements.