cvpr cvpr2013 cvpr2013-368 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Luc Oth, Paul Furgale, Laurent Kneip, Roland Siegwart
Abstract: 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.
Reference: text
sentIndex sentText sentNum sentScore
1 It is well known, that if a RS camera is used with a moving camera or scene, significant image distortions are introduced. [sent-9, score-0.338]
2 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. [sent-10, score-1.012]
3 The current state-of-the-art technique for calibrating the shutter timings requires specialised hardware. [sent-11, score-0.366]
4 We present a new method that only requires video of a known calibration pattern. [sent-12, score-0.249]
5 Introduction Most consumer electronic devices—such as smartphones—leave no room for a mechanical global shutter (GS). [sent-15, score-0.331]
6 The electronic shutter of CCD sensors exposes every row of the image during the same timespan, similar to a mechanical shutter. [sent-17, score-0.331]
7 CMOS sensors often only have a rolling shutter (RS). [sent-18, score-0.509]
8 The image rows are exposed and read sequentially, which introduces significant image distortions if either the camera or the scene are in motion. [sent-19, score-0.228]
9 Using this assumption, the timestamp of each line is uniquely defined by the line delay and the frame time. [sent-22, score-0.89]
10 The RS camera may be interpreted as a high frequency sensor returning sparse spatial information with a dense temporal coverage encoded by distortions [2]. [sent-24, score-0.232]
11 Conventional structure from motion (SfM) methods estimate a single camera pose per frame. [sent-25, score-0.333]
12 The reprojected chessboard corners after a continuoustime camera pose estimation. [sent-27, score-0.281]
13 The red dots show the corner positions for our continuous-time rolling shutter model. [sent-28, score-0.509]
14 The green dots show the results with a discrete-time global shutter model. [sent-29, score-0.305]
15 A common solution is to only estimate one pose per frame and perform a linear interpolation between consecutive camera poses to approximate the intermediate states. [sent-32, score-0.34]
16 However, to perform SfM using a rolling shutter camera, the line delay must be known accurately. [sent-36, score-1.221]
17 Hence, the line delay must be discovered through a calibration process. [sent-38, score-0.897]
18 This paper presents an offline calibration procedure to determine the rolling shutter line delay for use in high accuracy SfM, such as the work of [9]. [sent-39, score-1.406]
19 [9] shows that SfM on wobble-corrected images performs worse (in terms ofpose estimation accuracy) when compared to a continuous motion parametrisation operating on raw images with a calibrated RS model. [sent-43, score-0.225]
20 In light of this, high-accuracy rolling shutter calibration that does not need specialised hardware (as in [14, 15]) is highly desirable. [sent-44, score-0.829]
21 The current state of the art for line delay calibration 1 1 13 3 35 56 80 8 was proposed by Geyer et al. [sent-45, score-0.897]
22 The resulting images include light and dark lines whose spatial frequency is linked to the line delay and the known LED frequency. [sent-48, score-0.712]
23 We propose to use standard GS calibration means to also calibrate the RS line delay. [sent-50, score-0.378]
24 First, the intrinsics and distortion coefficients of a RS camera are determined with GS methods using still images and the help of a known pattern. [sent-51, score-0.306]
25 Next, RS distortion generating camera motion is produced in front of the known pattern. [sent-52, score-0.314]
26 The resulting video sequence is used to simultaneously estimate the camera pose in continuous-time and the line delay. [sent-53, score-0.406]
27 This method removes the dependency on expensive hardware and we are able to show that the resulting line delay estimates are more accurate than those produced by the method of Geyer et al. [sent-54, score-0.722]
28 we propose to use a continuous-time trajectory model combined with a rolling shutter camera model; 2. [sent-57, score-0.689]
29 we propose a new method for RS calibration that requires no additional hardware except for a known pattern e. [sent-58, score-0.291]
30 we parametrise the pose of the camera as a fourthorder B-spline and propose the first scheme for adaptively choosing the number of B-spline basis functions needed to represent different parts of the trajectory. [sent-62, score-0.24]
31 Additionally, they propose the current state-of-the-art method for line delay calibration. [sent-66, score-0.68]
32 The precise knowledge of the LED frequency is essential for a successful calibration and the authors suggest to remove the lens for best sensor illumination. [sent-68, score-0.256]
33 Besides the line delay calibration proposed by Geyer et al. [sent-70, score-0.897]
34 [1] propose a method to estimate the full calibration of a rigidly attached camera and gyroscope, including the camera’s line delay. [sent-72, score-0.553]
35 [2] stop considering the RS artefacts as drawback and exploit them to simultaneously extract the pose and velocity of an object relative to the camera frame from a single view. [sent-74, score-0.302]
36 They first estimate a constant camera velocity between two consecutive frames which is then used to undistort the RS keypoints. [sent-80, score-0.317]
37 The camera trajectory is described by linearly interpolating between the camera poses at the beginning of each frame. [sent-84, score-0.325]
38 For solving the perspective pose problem, they suggest to use a multi-frame PnP solver and simultaneously estimate the pose of the camera in multiple frames. [sent-96, score-0.361]
39 The pose parametrisations proposed in earlier publications are however not optimal as they assume a constant velocity between two consecutive discrete camera poses. [sent-98, score-0.38]
40 The camera motion is thus assumed to be linear, which stands in conflict with a general rapid motion. [sent-99, score-0.233]
41 We propose a new calibration approach involving only a known pattern as also used for the intrinsics and distortion coefficient calibration. [sent-106, score-0.352]
42 Next, we propose a continuous-time perspective projection model for RS cameras derived from the general projection equations, and give the related perspective localisation theory. [sent-109, score-0.296]
43 We derive the equations for line delay estimation and combine them with the perspective pose equations to simultaneously estimate the camera pose and the line delay based on a set of known landmarks. [sent-110, score-1.843]
44 Beginning the integration at the first line, and assuming that the line delay, d, remains constant, the time of exposure of the vth line becomes: t = t¯ + vd. [sent-146, score-0.367]
45 Reprojection Error Modelling In the following, we derive the reprojection error terms for the RS case and build the perspective localisation problem. [sent-153, score-0.304]
46 Perspective localisation is widely known and aims at minimising the squared reprojection error of a set of known landmarks (k) in every frame (i), weighted by the inverse covariance matrix ofthe error, R¯k,i. [sent-154, score-0.482]
47 Th∼e Nm(i0ni,mRum of (7) is found using a Gauss-Newton based optimisation which requires the linearisation of the error terms with respect to the estimated quantity, c: ek,i = yik π ? [sent-159, score-0.28]
48 (11) We define the nominal error ek,i = yik − π ? [sent-163, score-0.336]
49 Shutter Calibration To estimate the line delay, we linearise the error term (9) with respect to small changes? [sent-175, score-0.261]
50 (13) To simplify the expressions equation (13) is merged with (11) to obtain a single equation for simultaneous line delay and pose estimation: ek,i≈¯ ek,i−Jπ? [sent-184, score-0.75]
51 Error Term Standardisation The standardisation of the error terms aims at scaling every term by its inverse covariance matrix such that all terms end up with unit variance [17]. [sent-191, score-0.223]
52 We approximate the covariance of the error terms by linearisation of the measurement equations (8). [sent-199, score-0.286]
53 The expected value of the error terms is zero, E [ek,i] = 0, and the second condition—Gaussian error term variance—is given, as the Gaussian noise, nk,i, is linearly mapped onto the error terms. [sent-221, score-0.237]
54 The influence of the off-diagonal terms becomes significant for most fast motion patterns: small changes in the feature row may, under rapid motion, induce a large change in the camera position and propagate back to a large change in the feature position in the image plane. [sent-229, score-0.372]
55 (20) (21) Please note that the covariance is not constant in time and needs to be re-evaluated each time the line delay changes during estimation. [sent-238, score-0.77]
56 To visualise the effect of motion on the error covariance ellipse we plot several examples in Figure 2. [sent-239, score-0.248]
57 In this example, the camera x-axis is aligned with the image u coordinates, parallel to the sensor rows, the camera y-axis is aligned with the v coordinates, aligned with the line scanning direction, and the camera z-axis points towards the landmarks in the scene. [sent-240, score-0.72]
58 If the camera moves along the x-axis, the position of the camera also changes. [sent-243, score-0.347]
59 Figure 2 (b) shows the covariance ellipses if the cam1 1 13 3 36 6 613 1 era motion is parallel to the line scanning direction. [sent-245, score-0.379]
60 If the camera motion has the same direction as the line scanning, the timespan during which a landmark is projected onto a specific line is enlarged. [sent-246, score-0.682]
61 The covariance matrix may, however, become degenerate for fast motion along the line scanning direction. [sent-248, score-0.379]
62 Moving the camera in the opposite direction reduces the timespan during which a feature is projected onto a same line. [sent-250, score-0.223]
63 We show that a weak motion model is important in continuous-time estimation and discuss the problems related to a prior in the context of line delay calibration. [sent-279, score-0.768]
64 Finally, we propose our adaptive knot placement algorithm which enables precise calibration results despite a motion prior. [sent-280, score-0.406]
65 Furthermore, we assume a zero frame-delay to initialise the line delay as d0 = fp1s N1R, where fps is the average number of Frames Per Second and NR the number of rows of the sensor. [sent-288, score-0.68]
66 The cost is constantly reduced by overfitting the reprojection errors while the estimated line delay starts to deviate from the nominal value. [sent-341, score-0.928]
67 shows how a motion prior improves the stability of the estimated camera position in a general setup. [sent-344, score-0.29]
68 Figure 4 shows the line delay estimates for an increasing number ofuniformly spaced knots. [sent-351, score-0.68]
69 As the line delay is a physical parameter, we expect its value to be independent of the motion parametrisation as long as enough representational power is available to accurately describe the motion. [sent-352, score-0.905]
70 However, in Figure 4 we see that the line delay estimate stabilises between 600 and 1000 knots but then begins to diverge as more knots allow the curve to over fit. [sent-353, score-0.954]
71 We conclude that the selection of an appropriate number of knots becomes important for line delay calibration. [sent-355, score-0.802]
72 We propose an adaptive knot placement method that avoids over-fitting by adaptively adjusting the number of knots until the residuals agree with their theoretical expected value. [sent-356, score-0.223]
73 When J > E [J] for some segment of the trajectory, this implies that the spline does not have enough knots to be able to represent the motion in that segment. [sent-374, score-0.252]
74 This adaptive knot picking scheme was crucial for us to be able to estimate the line delay over a wide range of datasets. [sent-376, score-0.786]
75 Calibration Algorithm Finally, we can outline our complete algorithm for line delay calibration: 1. [sent-379, score-0.68]
76 Collect a video sequence of a known calibration pattern and extract keypoint measurements. [sent-380, score-0.249]
77 For all three types we collected a series of datasets by moving the camera in front of a calibration pattern for 30– 60s. [sent-391, score-0.362]
78 The camera is attached to a large rig equipped with Vicon motion capture system markers for ground truth. [sent-393, score-0.257]
79 The calibration process as well as the 1 1 13 3 36 6 635 3 perspective localisation datasets used chessboard corners, with known relative positions as landmarks, extracted using OpenCV. [sent-394, score-0.447]
80 The camera-rig transformation and the time synchronisation are only required for validation against the ground truth and have no influence on the calibration or localisation tasks themselves. [sent-397, score-0.328]
81 For the calibration of the intrinsics and the distortion coefficients of the RS camera the OpenCV tools were used. [sent-398, score-0.491]
82 Continuous-Time Localisation Our first experiment is designed to show that our algorithm is capable of estimating the motion of a rolling shutter camera; simultaneous calibration ofthe line delay is not performed. [sent-402, score-1.494]
83 The line delay is first calibrated using the approach proposed by Geyer et al. [sent-403, score-0.68]
84 We chose a low framerate (≈ 7fps) for which the line delay lies around d = 137μs. [sent-405, score-0.68]
85 A significant increase of the position error is however unpreventable as no information on the camera pose is available. [sent-413, score-0.342]
86 As this publication only presents a calibration method a thorough analysis of the required motion patterns for a successful calibration is left for future research. [sent-418, score-0.522]
87 The nominal values were obtained using the relation between the pixel clock (P [Hz]) and the time required for reading a single line containing NP pixels given in the data sheet: 3to quantify the errors an Euler Roll-Pitch-Yaw parametrisation is used Position SSE Error m]m[1200000 d]ra[000. [sent-421, score-0.49]
88 Deviation of the calibration results with our approach and the Geyer approach from the nominal values based on 40 real datasets at different values of pixel-clock. [sent-433, score-0.363]
89 The numerical values in Table 1 and the error histogram in Figure 6 both confirm that our approach delivers line delay estimates close to the nominal values. [sent-436, score-0.896]
90 We expect a linear relation between the line delay and the pixel timing (μs) passing through the origin. [sent-438, score-0.68]
91 The behaviour of the line delay as a function of the pixel clock is more accurately described with our results. [sent-440, score-0.726]
92 t7o2y81i0m3e2nrpai- son between our approach, the Geyer calibration and the nominal values. [sent-454, score-0.363]
93 The line delay d and the standard deviation σ are given in μs. [sent-468, score-0.68]
94 Conclusion and Future Work In this paper, we derived a new method of estimating the line delay of a rolling shutter camera, using only video images of a chessboard or other calibration pattern with known geometry. [sent-475, score-1.504]
95 The line delay calibration method outperforms the current state-of-the-art technique [14] without requiring any specialised hardware. [sent-477, score-0.958]
96 The complexity of the simultaneous calibration of the camera intrinsics and distortion parameters remains an open problem which should be addressed by further research. [sent-478, score-0.465]
97 Besides that, a series of RS cameras influence the line delay by tuning the exposure while recording a video. [sent-479, score-0.794]
98 We believe that our approach could be modified to an online line delay estimation to take full advantage of the sensors. [sent-480, score-0.68]
99 Digital video stabilization and rolling shutter correction using gyroscopes. [sent-488, score-0.509]
100 Simultaneous object pose and velocity computation using a single view from a rolling shutter camera. [sent-495, score-0.641]
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