B-spline signal processing. I. Theory

Unser, Michaël; Aldroubi, Akram; Eden, Murray

doi:10.1109/78.193220

Cited by 889 publications

(605 citation statements)

References 26 publications

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“…This can be done either by matrix manipulations [20,27], or by means of recursive filtering techniques [55][56][57], the latter of which are easier to implement and computationally much more efficient. When using the latter approach, nth-degree spline interpolation is carried out by evaluating the following expression:…”

Section: Cardinal Spline Kernelsmentioning

confidence: 99%

“…where (b n ) −1 denotes the recursive prefilter, also known as the direct B-spline filter [55][56][57]. Note that the resulting interpolant is an element of C n−1 .…”

Section: Cardinal Spline Kernelsmentioning

confidence: 99%

“…We also note that for n → ∞, the cardinal spline converges to the sinc function [1,50]. For further details regarding the theoretical and implementational aspects of B-spline interpolation, we refer to Unser et al [56,57].…”

Section: Cardinal Spline Kernelsmentioning

confidence: 99%

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Quantitative evaluation of convolution-based methods for medical image interpolation

Meijering

Niessen

Viergever

2001

Medical Image Analysis

249

165

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Abstract-Interpolation is required in a variety of medical image processing applications. Although many interpolation techniques are known from the literature, evaluations of these techniques for the specific task of applying geometrical transformations to medical images are still lacking. In this paper we present such an evaluation. We consider convolution-based interpolation methods and rigid transformations (rotations and translations). A large number of sincapproximating kernels are evaluated, including piecewise polynomial kernels and a large number of windowed sinc kernels, with spatial supports ranging from two to ten grid intervals. In the evaluation we use images from a wide variety of medical image modalities. The results show that spline interpolation is to be preferred over all other methods, both for its accuracy and its relatively low computational cost.

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Section: Cardinal Spline Kernelsmentioning

confidence: 99%

“…where (b n ) −1 denotes the recursive prefilter, also known as the direct B-spline filter [55][56][57]. Note that the resulting interpolant is an element of C n−1 .…”

Section: Cardinal Spline Kernelsmentioning

confidence: 99%

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Quantitative evaluation of convolution-based methods for medical image interpolation

Meijering

Niessen

Viergever

2001

Medical Image Analysis

249

165

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“…In fact any window function may be used. B-splines were used here since they are inexpensive and their derivatives are easily obtainable [23]. The advantages of post-Parzen windowing are that it improves on the basic sampling method using a computationally cheap operation: O(i 2 max w 2 ).…”

Section: Different Sampling Methodsmentioning

confidence: 99%

“…A more detailed description of B-spline functions and their numerical computation is given by Unser et alin [23]. Firstly, the sum of a B-spline function for all integral distances from a real value is one, i.e.…”

Section: B-splinesmentioning

confidence: 99%

A Unifying Framework for Mutual Information Methods for Use in Non-linear Optimisation

Dowson

Bowden

2006

Computer Vision – ECCV 2006

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Abstract. Many variants of MI exist in the literature. These vary primarily in how the joint histogram is populated. This paper places the four main variants of MI: Standard sampling, Partial Volume Estimation (PVE), In-Parzen Windowing and Post-Parzen Windowing into a single mathematical framework. Jacobians and Hessians are derived in each case. A particular contribution is that the non-linearities implicit to standard sampling and post-Parzen windowing are explicitly dealt with. These non-linearities are a barrier to their use in optimisation. Side-byside comparison of the MI variants is made using eight diverse data-sets, considering computational expense and convergence. In the experiments, PVE was generally the best performer, although standard sampling often performed nearly as well (if a higher sample rate was used). The widely used sum of squared differences metric performed as well as MI unless large occlusions and non-linear intensity relationships occurred. The binaries and scripts used for testing are available online.

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Spatial Registration of Images

Ashburner

Good

2003

Quantitative MRI of the Brain

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B-spline signal processing. I. Theory

Cited by 889 publications

References 26 publications

Quantitative evaluation of convolution-based methods for medical image interpolation

Quantitative evaluation of convolution-based methods for medical image interpolation

A Unifying Framework for Mutual Information Methods for Use in Non-linear Optimisation

Spatial Registration of Images

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