Curve Similarity via Signatures

Author(s):  
Joseph O'Rourke ◽  
Richard Washington
Keyword(s):  
Author(s):  
Anne Driemel ◽  
André Nusser ◽  
Jeff M. Phillips ◽  
Ioannis Psarros

AbstractThe Vapnik–Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation through the use of sampling bounds. We analyze set systems where the ground set X is a set of polygonal curves in $$\mathbb {R}^d$$ R d and the sets $$\mathcal {R}$$ R are metric balls defined by curve similarity metrics, such as the Fréchet distance and the Hausdorff distance, as well as their discrete counterparts. We derive upper and lower bounds on the VC dimension that imply useful sampling bounds in the setting that the number of curves is large, but the complexity of the individual curves is small. Our upper and lower bounds are either near-quadratic or near-linear in the complexity of the curves that define the ranges and they are logarithmic in the complexity of the curves that define the ground set.


2004 ◽  
Vol 49 (3-4) ◽  
pp. 165-172 ◽  
Author(s):  
Wladimir Rodriguez ◽  
Mark Last ◽  
Abraham Kandel ◽  
Horst Bunke

2010 ◽  
Vol 26 (4) ◽  
pp. 407-414 ◽  
Author(s):  
Rebecca E. Fellin ◽  
Kurt Manal ◽  
Irene S. Davis

Researchers conduct gait analyses utilizing both overground and treadmill modes of running. Previous studies comparing these modes analyzed discrete variables. Recently, techniques involving quantitative pattern analysis have assessed kinematic curve similarity in gait. Therefore, the purpose of this study was to compare hip, knee and rearfoot 3-D kinematics between overground and treadmill running using quantitative kinematic curve analysis. Twenty runners ran at 3.35 m/s ± 5% during treadmill and overground conditions while right lower extremity kinematics were recorded. Kinematics of the hip, knee and rearfoot at footstrike and peak were compared using intraclass correlation coefficients. Kinematic curves during stance phase were compared using the trend symmetry method within each subject. The overall average trend symmetry was high, 0.94 (1.0 is perfect symmetry) between running modes. The transverse plane and knee frontal plane exhibited lower similarity (0.86–0.90). Other than a 4.5 degree reduction in rearfoot dorsiflexion at footstrike during treadmill running, all differences were ≤1.5 degrees. 17/18 discrete variables exhibited modest correlations (>0.6) and 8/18 exhibited strong correlations (>0.8). In conclusion, overground and treadmill running kinematic curves were generally similar when averaged across subjects. Although some subjects exhibited differences in transverse plane curves, overall, treadmill running was representative of overground running for most subjects.


2013 ◽  
Vol 29 (5) ◽  
pp. 622-627 ◽  
Author(s):  
Elena Bergamini ◽  
Pélagie Guillon ◽  
Valentina Camomilla ◽  
Hélène Pillet ◽  
Wafa Skalli ◽  
...  

The proper execution of the sprint start is crucial in determining the performance during a sprint race. In this respect, when moving from the crouch to the upright position, trunk kinematics is a key element. The purpose of this study was to validate the use of a trunk-mounted inertial measurement unit (IMU) in estimating the trunk inclination and angular velocity in the sagittal plane during the sprint start. In-laboratory sprint starts were performed by five sprinters. The local acceleration and angular velocity components provided by the IMU were processed using an adaptive Kalman filter. The accuracy of the IMU inclination estimate and its consistency with trunk inclination were assessed using reference stereophotogrammetric measurements. A Bland-Altman analysis, carried out using parameters (minimum, maximum, and mean values) extracted from the time histories of the estimated variables, and curve similarity analysis (correlation coefficient > 0.99, root mean square difference < 7 deg) indicated the agreement between reference and IMU estimates, opening a promising scenario for an accurate in-field use of IMUs for sprint start performance assessment.


Author(s):  
Fan ZHANG ◽  
Liang-kun LIAO ◽  
Hui HUANG ◽  
Yi-jun LIU ◽  
Ji-hua LI ◽  
...  

2015 ◽  
Vol 798 ◽  
pp. 576-581
Author(s):  
Hao Xu ◽  
Fu Ting Bao ◽  
Chen Cheng ◽  
Bin Hang Wang

In the assessment of internal ballistic performance reliability of Solid Rocket Motor (SRM), eigenvalue discriminance method has long been used. In order to avoid the limitations of the traditional methods, a curve similarity discriminance modification combined with Hausdorff Distance was introduced. A Monte-Carlo simulation model of internal ballistic performance was established, and several uncertain parameters were chosen. A sample analysis of performance reliability of a designed SRM was presented. The result was credible, which proved the modification is feasible and it can meet the needs of the assessment of the internal ballistic performance reliability.


Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6610
Author(s):  
Andrea Mariscotti

Electrified transportation systems (ETSs) are affected by stray current problems impacting within and outside the right of way on reinforcement, buried metal structures and foundations. Stray current protection systems have recently been integrated in the track structure. Track electrical quantities are, thus, usually measured to assess track insulation and protection efficiency but should be backed up by additional measurements at the affected structures and installations, in order to assess their exposure and risk of corrosion. Ideally, a stray current monitoring system proceeds from the measurement of these quantities, to data collection and archival, to data presentation, analysis and prediction. Feasible sensors and probes, the impact of environmental conditions and uncertainty are considered for the measurement at the physical level. Data analysis is critically reviewed considering the variability of operating conditions and the effectiveness of each quantity as indicator of track insulation and protection efficiency. Given the normal spread of values, for data presentation and interpretation, suitable techniques are considered based on averaging, curve similarity and feature extraction, and also for the task of assessing compliance to limits or reference values and establishing a trend that may drive informed maintenance decision.


2020 ◽  
Vol 30 (4) ◽  
pp. 721-733
Author(s):  
Paul Faya ◽  
Adam P. Rauk ◽  
Kristi L. Griffiths ◽  
Bhavin Parekh
Keyword(s):  

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