On Trajectory Representation for Scientific Features

2006 ◽  
Author(s):  
Sameep Mehta ◽  
Srinivasan Parthasarathy ◽  
Raghu Machiraju
Keyword(s):  
Trajectory Representation

scholarly journals Trajectory representation and landmark projection for continuous-time structure from motion

2019 ◽  
Vol 38 (6) ◽  
pp. 686-701 ◽  
Author(s):  
Hannes Ovrén ◽  
Per-Erik Forssén
Keyword(s):  
Structure From Motion ◽  
Continuous Time ◽  
Spline Interpolation ◽  
Time Structure ◽  
Robot Arm ◽  
Good Sense ◽  
Trajectory Representation ◽  
Inertial Measurements ◽  
Derivatives Of ◽  
Fusion Framework

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 [Formula: see text]-continuous spline for the trajectory naturally incorporates inertial measurements, as derivatives of the sought trajectory. We analyze the behavior of split spline interpolation on [Formula: see text] and on [Formula: see text], and a joint spline on [Formula: see text], 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 [Formula: see text] is preferable over an [Formula: see text] 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.

scholarly journals A motor planning stage represents the shape of upcoming movement trajectories

2016 ◽  
Vol 116 (2) ◽  
pp. 296-305 ◽  
Author(s):  
Aaron L. Wong ◽  
Jeff Goldsmith ◽  
John W. Krakauer
Keyword(s):  
Motor Planning ◽  
Time Cost ◽  
Planning Stage ◽  
Movement Trajectories ◽  
Motor Behaviors ◽  
Task Requirements ◽  
Trajectory Representation ◽  
Stimulus Perception ◽  
Human Motor ◽  
Point To Point

Interactions with our environment require curved movements that depend not only on the final position of the hand but also on the path used to achieve it. Current studies in motor control, however, largely focus on point-to-point movements and do not consider how movements with specific desired trajectories might arise. In this study, we examined intentionally curved reaching movements that navigate paths around obstacles. We found that the preparation of these movements incurred a large reaction-time cost. This cost could not be attributed to nonmotor task requirements (e.g., stimulus perception) and was independent of the execution difficulty (i.e., extent of curvature) of the movement. Additionally, this trajectory representation cost was not observed for point-to-point reaches but could be optionally included if the task encouraged consideration of straight trajectories. Therefore, when the path of a movement is task relevant, the shape of the desired trajectory is overtly represented as a stage of motor planning. This trajectory representation ability may help explain the vast repertoire of human motor behaviors.

scholarly journals How can contemporary climate research help understand epidemic dynamics? Ensemble approach and snapshot attractors

2020 ◽  
Vol 17 (173) ◽  
pp. 20200648
Author(s):  
T. Kovács
Keyword(s):  
Complex Dynamics ◽  
Internal Variability ◽  
Climate Change Research ◽  
Contact Parameter ◽  
Epidemic Dynamics ◽  
Ensemble Approach ◽  
Statistical Measures ◽  
Trajectory Representation ◽  
Parameter Values ◽  
Contemporary Climate

Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed upon a monotonic decay needs a different description from that of the standard chaotic dynamics. The concept of snapshot attractors and their natural distribution has been adopted from the field of the latest climate change research. This shows the importance of the finite-time chaotic effect and ensemble interpretation while investigating the spread of a disease. By defining statistical measures over the ensemble, we can interpret the internal variability of the epidemic as the onset of complex dynamics—even for those values of contact parameters where originally regular behaviour is expected. We argue that anomalous outbreaks of the infectious class cannot die out until transient chaos is presented in the system. Nevertheless, this fact becomes apparent by using an ensemble approach rather than a single trajectory representation. These findings are applicable generally in explicitly time-dependent epidemic systems regardless of parameter values and time scales.

scholarly journals AN AUTOMATIC PROCEDURE FOR MOBILE LASER SCANNING PLATFORM 6DOF TRAJECTORY ADJUSTMENT

2018 ◽  
Vol XLII-1 ◽  
pp. 203-209 ◽  
Author(s):  
Z. Hussnain ◽  
S. Oude Elberink ◽  
G. Vosselman
Keyword(s):  
Image Matching ◽  
Point Cloud ◽  
Laser Scanning ◽  
Aerial Image ◽  
Second Step ◽  
Data Set ◽  
B Splines ◽  
Image Patches ◽  
Trajectory Representation ◽  
Previous Step

<p><strong>Abstract.</strong> In this paper, a method is presented to improve the MLS platform’s trajectory for GNSS denied areas. The method comprises two major steps. The first step is based on a 2D image registration technique described in our previous publication. Internally, this registration technique first performs aerial to aerial image matching, this issues correspondences which enable to compute the 3D tie points by multiview triangulation. Similarly, it registers the rasterized Mobile Laser Scanning Point Cloud (MLSPC) patches with the multiple related aerial image patches. The later registration provides the correspondence between the aerial to aerial tie points and the MLSPC’s 3D points. In the second step, which is described in this paper, a procedure utilizes three kinds of observations to improve the MLS platform’s trajectory. The first type of observation is the set of 3D tie points computed automatically in the previous step (and are already available), the second type of observation is based on IMU readings and the third type of observation is soft-constraint over related pose parameters. In this situation, the 3D tie points are considered accurate and precise observations, since they provide both locally and globally strict constraints, whereas the IMU observations and soft-constraints only provide locally precise constraints. For 6DOF trajectory representation, first, the pose [R, t] parameters are converted to 6 B-spline functions over time. Then for the trajectory adjustment, the coefficients of B-splines are updated from the established observations. We tested our method on an MLS data set acquired at a test area in Rotterdam, and verified the trajectory improvement by evaluation with independently and manually measured GCPs. After the adjustment, the trajectory has achieved the accuracy of RMSE X<span class="thinspace"></span>=<span class="thinspace"></span>9<span class="thinspace"></span>cm, Y<span class="thinspace"></span>=<span class="thinspace"></span>14<span class="thinspace"></span>cm and Z<span class="thinspace"></span>=<span class="thinspace"></span>14<span class="thinspace"></span>cm. Analysing the error in the updated trajectory suggests that our procedure is effective at adjusting the 6DOF trajectory and to regenerate a reliable MLSPC product.</p>

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