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 @math -continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyse the behaviour of split interpolation on @math and on @math , and a joint interpolation on @math , 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 @math and on @math is preferable over @math 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.
When re-projecting a landmark in a frame there is an additional complication in the rolling shutter case. As one image coordinate (typically the image row) corresponds to observation time, the reprojection of a landmark at time @math will not necessarily end up at the row corresponding to that time. Early methods handled this by setting the reprojection time to the landmark observation time . This was improved upon by @cite_4 who also linearize the reprojection time error and convert it to a spatial error covariance. @cite_7 instead use the Newton method to iteratively find a reprojection time with a consistent row coordinate, and this approach is also followed by @cite_2 . Yet another approach is to add a projection time parameter for each landmark observation, as well as a cost term for the projection time deviation . In the experiments, we refer to this approach as lifting , which is the common term for elimination of alternating optimization by adding variables and constraints . No previous publication has compared these choices, instead each paper makes a hard commitment to one of the methods. In @cite_0 some of the choices are discussed, but a comparison is left for future work.
@cite_0 @cite_4 @cite_7 @cite_2
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This paper shows how to carry out batch continuous-time trajectory estimation for bodies translating and rotating in three-dimensional (3D) space, using a very efficient form of Gaussian-process (GP) regression. The method is fast, singularity-free, uses a physically motivated prior (the mean is constant body-centric velocity), and permits trajectory queries at arbitrary times through GP interpolation. Landmark estimation can be folded in to allow for simultaneous trajectory estimation and mapping (STEAM), a variant of SLAM. Rolling Shutter (RS) cameras are used across a wide range of consumer electronic devices-from smart-phones to high-end cameras. It is well known, that if a RS camera is used with a moving camera or scene, significant image distortions are introduced. The quality or even success of structure from motion on rolling shutter images requires the usual intrinsic parameters such as focal length and distortion coefficients as well as accurate modelling of the shutter timing. The current state-of-the-art technique for calibrating the shutter timings requires specialised hardware. We present a new method that only requires video of a known calibration pattern. Experimental results on over 60 real datasets show that our method is more accurate than the current state of the art. This paper describes a general continuous-time framework for visual-inertial simultaneous localization and mapping and calibration. We show how to use a spline parameterization that closely matches the torque-minimal motion of the sensor. Compared to traditional discrete-time solutions, the continuous-time formulation is particularly useful for solving problems with high-frame rate sensors and multiple unsynchronized devices. We demonstrate the applicability of the method for multi-sensor visual-inertial SLAM and calibration by accurately establishing the relative pose and internal parameters of multiple unsynchronized devices. We also show the advantages of the approach through evaluation and uniform treatment of both global and rolling shutter cameras within visual and visual-inertial SLAM systems. This paper discusses the recursive Bayesian formulation of the simultaneous localization and mapping (SLAM) problem in which probability distributions or estimates of absolute or relative locations of landmarks and vehicle pose are obtained. The paper focuses on three key areas: computational complexity; data association; and environment representation