The Deduction of Coefficient Matrix for Cubic Non-Uniform B-Spline Curves

Huixian, Yang; Yue, Wen Long; He, Yabin; Huang, Huixian; Xia, Haixia

doi:10.1109/etcs.2009.396

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…The recurrence formula allows to compute the basis functions for different degrees. By developing the formula as in [22] or using Toeplitz matrix [17], the basis function can be expressed as a matrix product as in [19] for cubic B-Spline. Unlike the UTD case, the coefficient matrix used in the expression of basis functions is dependent on the CP timestamps.…”

Section: Non Uniform Time Distribution For B-splinesmentioning

confidence: 99%

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Spatiotemporal Optimization for Rolling Shutter Camera Pose Interpolation

Gohard

Vandeportaele

Devy

2019

Communications in Computer and Information Science

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Rolling Shutter cameras are predominant in the tablet and smart-phone market due to their low cost and small size. However, these cameras require specific geometric models when either the camera or the scene is in motion to account for the sequential exposure of the different lines of the image. This paper proposes to improve a state-of-the-art model for RS cameras through the use of Non Uniformly Time-Sampled B-splines. This allows to interpolate the pose of the camera while taking into account the varying dynamic of its motion, using higher density of control points where needed while keeping a low number of control points where the motion is smooth. Two methods are proposed to determine adequate distributions for the control points, using either an IMU sensor or an iterative reprojection error minimization. The non-uniform camera model is integrated into a Bundle Adjustment optimization which is able to converge even from a poor initial estimate. A routine of spatiotemporal optimization is presented in order to optimize both the spatial and temporal positions of the control points. Results on synthetic and real datasets are shown to prove the concepts and future works are introduced that should lead to the integration of our model in a SLAM algorithm.

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Section: Non Uniform Time Distribution For B-splinesmentioning

confidence: 99%

“…Details on coefficient matrix M are given in [22], it is however substantial to note that M is now relative to the 6 CP timestamps t i to t i+5 .…”

Section: Non Uniform Time Distribution For B-splinesmentioning

confidence: 99%

Spatiotemporal Optimization for Rolling Shutter Camera Pose Interpolation

Gohard

Vandeportaele

Devy

2019

Communications in Computer and Information Science

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show abstract

“…This formula is called the de Boor-Cox formula [27]. Where T is called the control point sequence or control point vector, and t i is called the control point.…”

Section: Measurements Of Metatarsale Girthmentioning

confidence: 99%

A 3D foot shape feature parameter measurement algorithm based on Kinect2

Wang

Fan

et al. 2018

J Image Video Proc.

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Accurate measurement of foot shape feature parameters is extremely important in the process of customized shoemaking. A 3D foot's depth image collected by second-generation Kinect is used to propose a foot shape feature parameter measurement algorithm. Through 3D reconstruction of foot based on improved interactive closest points algorithm, the coordinate transformation, feature point selection, and B-spline curve fitting algorithm, the foot length, foot width, metatarsale girth, and other foot feature parameters were calculated. The 3D foot measurement system using this algorithm is tested, and the results of multiple measurements have a mean variance of less than 0.3 mm. The average error between the algorithm calculation result and the manual measurement result is less than 0.85 mm. The stability and accuracy of the system meet the requirements of custom shoes. It lays a good foundation for the automation and standardization of customized shoemaking.

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“…In the present work, we adopt cubic B-splines as base (expansion) functions [20] because of their high-order nature and ability to handle knots of higher multiplicity. The function   n Sz employed in (6) can be each written as a combination of four polynomial terms:…”

Section: Cubic B-spline Eigenfunctionsmentioning

confidence: 99%