Spline kernels for continuous-space image processing

Horbelt, Stefan; Munoz, A.; Blu, Thierry; Unser, Michaël

doi:10.1109/icassp.2000.859272

Cited by 9 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It decreases with distance and ranges between 0 (in the limit) and 1 (when x = y). The polynomial kernel is widely applied in natural language processing Goldberg and Elhadad (2008) while Spline Kernel is usually reserved for continuous-space image processing Horbelt et al (2000). Because classification accuracy heavily depends on kernel selection, researchers had proposed to have kernel functions based on a general purpose learning and domain specific.…”

Section: Loss Reserves Data For Israelmentioning

confidence: 99%

The Kummer Beta Normal: A New Useful-Skew Model

Pescim¹,

Nadarajah²

2021

Journal of Data Science

View full text Add to dashboard Cite

Probabilistic topic models have become a standard in modern machine learning to deal with a wide range of applications. Representing data by dimensional reduction of mixture proportion extracted from topic models is not only richer in semantics interpretation, but could also be informative for classification tasks. In this paper, we describe the Topic Model Kernel (TMK), a topicbased kernel for Support Vector Machine classification on data being processed by probabilistic topic models. The applicability of our proposed kernel is demonstrated in several classification tasks with real world datasets. TMK outperforms existing kernels on the distributional features and give comparative results on nonprobabilistic data types.

show abstract

Section: Loss Reserves Data For Israelmentioning

confidence: 99%

The Kummer Beta Normal: A New Useful-Skew Model

Pescim¹,

Nadarajah²

2021

Journal of Data Science

View full text Add to dashboard Cite

show abstract

“…12 The matrix A is Hermitian and positive-definite. 6 The system B = Ag can be solved using Cholesky decomposition.…”

Section: Continuous Errormentioning

confidence: 99%

Continuous criterion for parallel MRI reconstruction using B-spline approximation (PROBER)

Petr

Kybic

2007

SPIE Proceedings

View full text Add to dashboard Cite

Parallel MRI is a way to use multiple receiver coils with distinct spatial sensitivities to increase the speed of the MRI acquisition. The acquisition is speeded up by undersampling in the phase-encoding direction and the resulting data loss and aliasing is compensated for by the use of the additional information obtained from several receiver coils.The task is to reconstruct an unaliased image from a series of aliased images. We have proposed an algorithm called PROBER that takes advantage of the smoothness of the reconstruction transformation in space. B-spline functions are used to approximate the reconstruction transformation. Their coefficients are estimated at once minimizing the total expected reconstruction error. This makes the reconstruction less sensitive to noise in the reference images and areas without signal in the image. We show that this approach outperforms the SENSE and GRAPPA reconstruction methods for certain coil configurations.In this article, we propose another improvement, consisting of a continuous representation of the B-splines to evaluate the error instead of the discretely sampled version. This solves the undersampling issues in the discrete B-spline representation and offers higher reconstruction quality which has been confirmed by experiments. The method is compared with the discrete version of PROBER and with commercially used algorithms GRAPPA and SENSE in terms of artifact suppression and reconstruction SNR.

show abstract

“…In the original paper, the exact form of this kernel was only worked out for . More recently, we were able to obtain an explicit kernel formula [30].…”

Section: A Relation To Previous Workmentioning

confidence: 99%

Least-squares image resizing using finite differences

Munoz

Blu

Unser

2001

IEEE Trans. on Image Process.

Self Cite

103

View full text Add to dashboard Cite

Abstract-We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree . A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor . For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives.

show abstract

Spline kernels for continuous-space image processing

Cited by 9 publications

References 9 publications

The Kummer Beta Normal: A New Useful-Skew Model

The Kummer Beta Normal: A New Useful-Skew Model

Continuous criterion for parallel MRI reconstruction using B-spline approximation (PROBER)

Least-squares image resizing using finite differences

Contact Info

Product

Resources

About