Smoothing with Cubic Splines

Pollock, D.S.G.

doi:10.1016/b978-012560990-6/50013-0

Cited by 38 publications

(25 citation statements)

References 13 publications

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“…Thereafter, to obtain a smooth curve for movement of each knot throughout the heart cycle, as well as a smooth transition between adjacent knots, cubic spline smoothing is performed in both space and time. This smoothing procedure is explained and illustrated in more detail elsewhere [15]. …”

Section: Methodsmentioning

confidence: 99%

Is strain by Speckle Tracking Echocardiography dependent on user controlled spatial and temporal smoothing? An experimental porcine study

Moen

Salminen

Dahle

et al. 2013

Cardiovasc Ultrasound

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BackgroundSpeckle Tracking Echocardiography (STE) strain analysis relies on both spatial and temporal smoothing. The user is often allowed to adjust these smoothing parameters during analysis. This experimental study investigates how different degrees of user controllable spatial and temporal smoothing affect global and regional STE strain values in recordings obtained from normal and ischemic myocardium.MethodsIn seven anesthetized pigs, left ventricular short- and long-axis B-mode cineloops were recorded before and after left anterior descending coronary artery occlusion. Peak- and postsystolic global STE strain in the radial, circumferential and longitudinal direction as well as corresponding regional strain in the anterior and posterior walls were measured. During post-processing, strain values were obtained with three different degrees of both spatial and temporal smoothing (minimum, factory default and maximum), resulting in nine different combinations.ResultsAll parameters for global and regional longitudinal strain were unaffected by adjustments of spatial and temporal smoothing in both normal and ischemic myocardium. Radial and circumferential strain depended on smoothing to a variable extent, radial strain being most affected. However, in both directions the different combinations of smoothing did only result in relatively small changes in the strain values. Overall, the maximal strain difference was found in normal myocardium for peak systolic radial strain of the posterior wall where strain was 22.0 ± 2.2% with minimal spatial and maximal temporal smoothing and 30.9 ± 2.6% with maximal spatial and minimal temporal smoothing (P < 0.05).ConclusionsLongitudinal strain was unaffected by different degrees of user controlled smoothing. Radial and circumferential strain depended on the degree of smoothing. However, in most cases these changes were small and would not lead to altered conclusions in a clinical setting. Furthermore, smoothing did not affect strain variance. For all strain parameters, variance remained within the corresponding interobserver variance.

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Section: Methodsmentioning

confidence: 99%

Is strain by Speckle Tracking Echocardiography dependent on user controlled spatial and temporal smoothing? An experimental porcine study

Moen

Salminen

Dahle

et al. 2013

Cardiovasc Ultrasound

View full text Add to dashboard Cite

show abstract

“…As a result of this segmental interpolation, a curve composed of parts of the polynomial, which is not smooth, is obtained. In order for the curve to be smooth, it is necessary to satisfy the continuity conditions of the first derivatives, and for the higher derivatives to be continuous [4].…”

Section: Cubic Spline Interpolationmentioning

confidence: 99%

Deflection Calculation for Beam-type Structures from Measured Strain Dana

Flajs¹,

Veg

Gubeljak

et al. 2020

Teh. vjesn

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Behavior of structures under various load types is determined by their deformation characteristics, global deformation characteristics-deflections and rotations, and local deformation characteristics-strains / stresses in structure base material. If we know global and local deformation characteristics of a structure, then it is possible to determine the structure behavior under acting loads, on the whole structure or at some part of that structure. The main objective of this research is to verify calculation algorithm for obtaining vertical displacements-the deflection of the structure, based on the known strain values in the structure base material, under acting load. The verification of the calculation algorithm is performed by comparing the numerical and experimental results.

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“…To have a continuous junction between a previously planned path and a new planned path segment the spline formulation must be capable to ascertain the starting position with its first derivative and the curvature as boundary conditions. With more than two boundary conditions the system of linear equations of the spline representation would be overdetermined [12]. To cope with this problem we introduce an extra point (red cross on spline without blue box in Fig.…”

Section: B the New Combined Approachmentioning

confidence: 99%

Real-time capable path planning for energy management systems in future vehicle architectures

Brembeck¹,

Winter

2014

2014 IEEE Intelligent Vehicles Symposium Proceedings

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In this paper an energy optimal path planning and velocity profile generation for our highly maneuverable Robotic Electric Vehicle research platform ROboMObil is presented. The ROMO [1] is a development of the German Aerospace Center's Robotics and Mechatronics Center to cope with several research topics, like energy efficient, autonomous or remote controlled driving for future (electro-) mobility applications. The main task of the proposed algorithms is to calculate an energy optimal trajectory in a real-time capable way. It is designed to incorporate data from actual traffic situations (e.g. oncoming traffic) or changed conditions (e.g. snowy conditions). The resulting trajectory is then fed forward to a lower level time independent path following control [2] that calculates the motion demands for our energy optimal control allocation. This in turn distributes the demand to the actuators of the over-actuated vehicle. We show a numerical reliable way to formulate the energy optimal path planning optimization objective, which is able to provide a consistent replanning feature considering the actual vehicle states. Besides this, different types of optimization methods are evaluated for their real-time capabilities. The velocity profile will be calculated afterwards and the generation of the profile is also enabled to handle dynamic replanning. Finally, we show several experimental results, using a virtual road definition and tests on a commercial real-time platform.

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Smoothing with Cubic Splines

Cited by 38 publications

References 13 publications

Is strain by Speckle Tracking Echocardiography dependent on user controlled spatial and temporal smoothing? An experimental porcine study

Is strain by Speckle Tracking Echocardiography dependent on user controlled spatial and temporal smoothing? An experimental porcine study

Deflection Calculation for Beam-type Structures from Measured Strain Dana

Real-time capable path planning for energy management systems in future vehicle architectures

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