In this paper we consider critical motion sequences (CMSs) of rolling-shutter (RS) SfM. Employing an RS camera model with linearized pure rotation, we show that the RS distortion can be approximately expressed by two internal parameters of an "imaginary" camera plus one-parameter nonlinear transformation similar to lens distortion. We then reformulate the problem as self-calibration of the imaginary camera, in which its skew and aspect ratio are unknown and varying in the image sequence. In the formulation, we derive a general representation of CMSs. We also show that our method can explain the CMS that was recently reported in the literature, and then present a new remedy to deal with the degeneracy. Our theoretical results agree well with experimental results; it explains degeneracies observed when we employ naive bundle adjustment, and how they are resolved by our method.
@cite_26: Low cost CMOS cameras can have an acquisition mode called rolling shutter which sequentially exposes the scan-lines. When a single object moves with respect to the camera, this creates image distortions. Assuming 2D-3D correspondences known, previous work showed that the object pose and kinematics can be estimated from a single rolling shutter image. This was achieved using a suboptimal initialization followed by local iterative optimization. We propose a polynomial projection model for rolling shutter cameras and a constrained global optimization of its parameters. This is done by means of a semidefinite programming problem obtained from the generalized problem of moments method. Contrarily to previous work, our optimization does not require an initialization and ensures that the global minimum is achieved. This allows us to build automatically robust 2D-3D correspondences using a template to provide an initial set of correspondences. Experiments show that our method slightly improves previous work on both simulated and real data. This is due to local minima into which previous methods get trapped. We also successfully experimented building 2D-3D correspondences automatically with both simulated and real data.
@cite_4: It is well known that the rolling shutter effect in images captured with a moving rolling shutter camera causes inaccuracies to 3D reconstructions. The problem is further aggravated with weak visual connectivity from wide baseline images captured with a fast moving camera. In this paper, we propose and implement a pipeline for sparse to dense 3D construction with wide baseline images captured from a fast moving rolling shutter camera. Specifically, we propose a cost function for Bundle Adjustment (BA) that models the rolling shutter effect, incorporates GPS INS readings, and enforces pairwise smoothness between neighboring poses. We optimize over the 3D structures, camera poses and velocities. We also introduce a novel interpolation scheme for the rolling shutter plane sweep stereo algorithm that allows us to achieve a 7× speed up in the depth map computations for dense reconstruction without losing accuracy. We evaluate our proposed pipeline over a 2.6km image sequence captured with a rolling shutter camera mounted on a moving car.
@cite_22: A huge fraction of cameras used nowadays is based on CMOS sensors with a rolling shutter that exposes the image line by line. For dynamic scenes cameras this introduces undesired effects like stretch, shear and wobble. It has been shown earlier that rotational shake induced rolling shutter effects in hand-held cell phone capture can be compensated based on an estimate of the camera rotation. In contrast, we analyse the case of significant camera motion, e.g. where a bypassing street level capture vehicle uses a rolling shutter camera in a 3D reconstruction framework. The introduced error is depth dependent and cannot be compensated based on camera motion rotation alone, invalidating also rectification for stereo camera systems. On top, significant lens distortion as often present in wide angle cameras intertwines with rolling shutter effects as it changes the time at which a certain 3D point is seen. We show that naive 3D reconstructions (assuming global shutter) will deliver biased geometry already for very mild assumptions on vehicle speed and resolution. We then develop rolling shutter dense multiview stereo algorithms that solve for time of exposure and depth at the same time, even in the presence of lens distortion and perform an evaluation on ground truth laser scan models as well as on real street-level data.
@cite_7: 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.
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@cite_1: An original concept for computing instantaneous 3D pose and 3D velocity of fast moving objects using a single view is proposed, implemented and validated. It takes advantage of the image deformations induced by rolling shutter in CMOS image sensors. First of all, after analysing the rolling shutter phenomenon, we introduce an original model of the image formation when using such a camera, based on a general model of moving rigid sets of 3D points. Using 2D-3D point correspondences, we derive two complementary methods, compensating for the rolling shutter deformations to deliver an accurate 3D pose and exploiting them to also estimate the full 3D velocity. The first solution is a general one based on non-linear optimization and bundle adjustment, usable for any object, while the second one is a closed-form linear solution valid for planar objects. The resulting algorithms enable us to transform a CMOS low cost and low power camera into an innovative and powerful velocity sensor. Finally, experimental results with real data confirm the relevance and accuracy of the approach.
@cite_9: This paper presents a method for rectifying video sequences from rolling shutter (RS) cameras. In contrast to previous RS rectification attempts we model distortions as being caused by the 3D motion of the camera. The camera motion is parametrised as a continuous curve, with knots at the last row of each frame. Curve parameters are solved for using non-linear least squares over inter-frame correspondences obtained from a KLT tracker. We have generated synthetic RS sequences with associated ground-truth to allow controlled evaluation. Using these sequences, we demonstrate that our algorithm improves over to two previously published methods. The RS dataset is available on the web to allow comparison with other methods.
@cite_3: The vast majority of modern consumer-grade cameras employ a rolling shutter mechanism. In dynamic geometric computer vision applications such as visual SLAM, the so-called rolling shutter effect therefore needs to be properly taken into account. A dedicated relative pose solver appears to be the first problem to solve, as it is of eminent importance to bootstrap any derivation of multi-view geometry. However, despite its significance, it has received inadequate attention to date. This paper presents a detailed investigation of the geometry of the rolling shutter relative pose problem. We introduce the rolling shutter essential matrix, and establish its link to existing models such as the push-broom cameras, summarized in a clean hierarchy of multi-perspective cameras. The generalization of well-established concepts from epipolar geometry is completed by a definition of the Sampson distance in the rolling shutter case. The work is concluded with a careful investigation of the introduced epipolar geometry for rolling shutter cameras on several dedicated benchmarks.
@cite_16: We present a novel algorithm for efficient removal of rolling shutter distortions in uncalibrated streaming videos. Our proposed method is calibration free as it does not need any knowledge of the camera used, nor does it require calibration using specially recorded calibration sequences. Our algorithm can perform rolling shutter removal under varying focal lengths, as in videos from CMOS cameras equipped with an optical zoom. We evaluate our approach across a broad range of cameras and video sequences demonstrating robustness, scaleability, and repeatability. We also conducted a user study, which demonstrates preference for the output of our algorithm over other state-of-the art methods. Our algorithm is computationally efficient, easy to parallelize, and robust to challenging artifacts introduced by various cameras with differing technologies.
@cite_19: Artefacts that are present in images taken from a moving rolling shutter camera degrade the accuracy of absolute pose estimation. To alleviate this problem, we introduce an addition linear velocity in the camera projection matrix to approximate the motion of the rolling shutter camera. In particular, we derive a minimal solution using the Grobner Basis that solves for the absolute pose as well as the motion of a rolling shutter camera. We show that the minimal problem requires 5-point correspondences and gives up to 8 real solutions. We also show that our formulation can be extended to use more than 5-point correspondences. We use RANSAC to robustly get all the inliers. In the final step, we relax the linear velocity assumption and do a non-linear refinement on the fuli motion, i.e. linear and angular velocities, and pose of the rolling shutter camera with all the inliers. We verify the feasibility and accuracy of our algorithm with both simulated and real-world datasets.
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@cite_12: We describe a spatio-temporal triangulation method to be used with rolling shutter cameras. We show how a single pair of rolling shutter images enables the computation of both structure and motion of rigid moving objects. Starting from a set of point correspondences in the left and right images, we introduce the velocity and shutter characteristics in the triangulation equations. This results in a non-linear error criterion whose minimization in the least square sense provides the shape and velocity parameters. Unlike previous work on rolling shutter cameras, the constraining assumption of a-priori knowledge about the object geometry is removed and a full 3D motion model is considered. The aim of this work is thus to make the use of rolling shutter cameras of a broader interest. Experimental evaluation results confirm the feasibility of the approach.
@cite_11: This paper introduces a bundle adjustment (BA) method that obtains accurate structure and motion from rolling shutter (RS) video sequences: RSBA. When a classical BA algorithm processes a rolling shutter video, the resultant camera trajectory is brittle, and complete failures are not uncommon. We exploit the temporal continuity of the camera motion to define residuals of image point trajectories with respect to the camera trajectory. We compare the camera trajectories from RSBA to those from classical BA, and from classical BA on rectified videos. The comparisons are done on real video sequences from an iPhone 4, with ground truth obtained from a global shutter camera, rigidly mounted to the iPhone 4. Compared to classical BA, the rolling shutter model requires just six extra parameters. It also degrades the sparsity of the system Jacobian slightly, but as we demonstrate, the increase in computation time is moderate. Decisive advantages are that RSBA succeeds in cases where competing methods diverge, and consistently produces more accurate results.
A number of studies have been conducted to deal with RS distortion in single or multi-view images. Depending on the type of problems, they are classified into absolute pose problem @cite_1 @cite_26 @cite_21 @cite_19 , relative pose problem @cite_3 , multi-view optimization (bundle adjustment) @cite_11 @cite_29 @cite_4 , stereo @cite_12 @cite_22 , and rectification stabilization @cite_9 @cite_20 @cite_7 @cite_16 .