Cardinal interpolation and spline fucntions V. The B-splines for cardinal Hermite interpolation

Schoenberg, I. J.; Sharma, A.

doi:10.1016/0024-3795(73)90034-7

Cited by 30 publications

(20 citation statements)

References 8 publications

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“…First, we have to ensure that the Hermite interpolant s(·) exists for fixed s [·], s [·] and is uniquely defined. This is already ensured by Schoenberg's work dedicated to the cubic Hermite splines [23], [43]. Then, we have to show that, for any f satisfying the two interpolation constraints f (k) = s [k] and…”

Section: Appendix C Inherent Smoothness Propertymentioning

confidence: 99%

Hermite Snakes With Control of Tangents

Uhlmann

Fageot

Unser

2016

IEEE Trans. on Image Process.

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Abstract-We introduce a new model of parametric contours defined in a continuous fashion. Our curve model relies on Hermite spline interpolation and can easily generate curves with sharp discontinuities; it also grants direct access to the tangent at each location. With these two features, the Hermite snake distinguishes itself from classical spline-snake models and allows one to address certain bioimaging problems in a more efficient way. More precisely, the Hermite snake construction allows introducing sharp corners in the snake curve and designing directional energy functionals relying on local orientation information in the input image. Using the formalism of spline theory, the model is shown to meet practical requirements such as invariance to affine transformations and good approximation properties. Finally, the dependence on initial conditions and the robustness to the noise is studied on synthetic data in order to validate our Hermite snake model, and its usefulness is illustrated on real biological images acquired using brightfield, phase-contrast, differentialinterference-contrast, and scanning-electron microscopy.

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Section: Appendix C Inherent Smoothness Propertymentioning

confidence: 99%

Hermite Snakes With Control of Tangents

Uhlmann

Fageot

Unser

2016

IEEE Trans. on Image Process.

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“…[2,10,1]). In particular, the construction of fundamental splines and the existence and uniqueness of solutions have been studied.…”

Section: J=-oomentioning

confidence: 99%

Cardinal Hermite Spline Interpolation with Shifted Nodes

Plonka¹,

Tasche²

1994

Mathematics of Computation

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Abstract. Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be given. Furthermore, a new efficient algorithm for the computation of the cardinal Hermite spline interpolant is obtained, which is mainly based on fast Fourier transform. This algorithm is shown to be also applicable to computing the periodic Hermite spline interpolant. In both cases we only use necessary and sufficient conditions for the existence and uniqueness of the corresponding Hermite spline interpolant.

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“…One of the most important properties of the ß-splines (see [2], [11]) asserts that every Six) E SJ£_i. admits a unique representation of the form…”

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confidence: 99%

“…Substituting (2.3) into (2.2) and performing a change of variable after interchanging the order of integration and summation we obtain (11).…”

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confidence: 99%

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Fourier transforms of 𝐵-splines and fundamental splines for cardinal Hermite interpolations

Lee¹

1976

Proc. Amer. Math. Soc.

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Cardinal interpolation and spline fucntions V. The B-splines for cardinal Hermite interpolation

Cited by 30 publications

References 8 publications

Hermite Snakes With Control of Tangents

Hermite Snakes With Control of Tangents

Cardinal Hermite Spline Interpolation with Shifted Nodes

Fourier transforms of 𝐵-splines and fundamental splines for cardinal Hermite interpolations

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