Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Complete parameterization of piecewise-polynomial interpolation kernels.

Thierry Blu1, Philippe Thévenaz, Michael Unser

  • 1Biomed. Imaging Group, Swiss Fed. Inst. of Technol. Lausanne, Switzerland. thierry.blu@epfl.ch

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|February 5, 2008
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Revisiting deep information propagation: Fractal frontier and finite-size effects.

Neural networks : the official journal of the International Neural Network Society·2026
Same author

Revisiting PSF models: Unifying framework and high-performance implementation.

Journal of microscopy·2025
Same author

Perturbative Fourier ptychographic microscopy for fast quantitative phase imaging.

Optics express·2025
Same author

Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography.

Optics express·2025
Same author

Utilizing 3D fast spin echo anatomical imaging to reduce the number of contrast preparations in <math><semantics><mrow><msub><mrow><mi>T</mi></mrow> <mrow><mn>1</mn> <mi>ρ</mi></mrow></msub></mrow> <annotation>$$ {T}_{1\rho } $$</annotation></semantics></math> quantification of knee cartilage using learning-based methods.

Magnetic resonance in medicine·2025
Same author

Point-spread-function engineering in MINFLUX: optimality of donut and half-moon excitation patterns.

Optics letters·2024
Same journal

Change-Prior-Guided Unsupervised Change Detection of Heterogeneous Remote Sensing Images.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

AgonicDreamer: Enhancing Multi-View Consistency in Text-to-3D Generation via Rectified Score Distillation.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

BiCM-Prompt: Bidirectional Cross-Modal Prompt Tuning for Class-Incremental Learning on Multisource Remote Sensing Images.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

GoP-based Quality Enhancement on Video Compression.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Align then Tensorize: Multi-Level Consistent Anchor Graph Learning for Scalable Multi-View Clustering.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same journal

Beyond Fidelity: Diverse Image Synthesis via Retrieval-Augmented Diffusion.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
See all related articles

This study introduces an explicit formula for designing piecewise-polynomial interpolation kernels, simplifying the laborious traditional methods. The formula allows for easy tuning of kernel properties like degree, support, regularity, and approximation order.

Area of Science:

  • Numerical Analysis
  • Computer Graphics
  • Image Processing

Background:

  • Traditional interpolation kernel design is complex and computationally intensive.
  • Existing methods often involve solving large systems of linear equations analytically.
  • This presents a significant bottleneck in developing new interpolation kernels.

Purpose of the Study:

  • To present a novel, explicit formula for generating piecewise-polynomial interpolation kernels.
  • To simplify and streamline the kernel design process.
  • To offer a flexible method for tailoring kernels to specific design constraints.

Main Methods:

  • Derivation of a general explicit formula for piecewise-polynomial kernels.
  • The formula incorporates parameters for kernel degree, support, regularity, and order of approximation.

Related Experiment Videos

  • Introduces free coefficients for additional design flexibility.

    • Main Results:

    • The proposed formula generates all possible piecewise-polynomial kernels.
    • It bypasses the need for solving large analytical systems of linear equations.
    • The formula allows for independent tuning of kernel properties and additional constraints.

    Conclusions:

    • The explicit formula significantly eases the burden of interpolation kernel design.
    • It provides a powerful and flexible tool for researchers and practitioners.
    • Enables efficient creation of customized interpolation kernels for various applications.