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 Concept Videos

Extended Versions of Green’s Theorem01:27

Extended Versions of Green’s Theorem

Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...
Green’s Theorem01:27

Green’s Theorem

Green’s Theorem establishes a relationship between a line integral around a closed plane curve and a double integral over the region enclosed by that curve. It applies to a vector field F(x, y) = 〈P(x, y), Q(x, y)〉, where P and Q have continuous first partial derivatives on an open set containing the region.Let C be a positively oriented, simple, closed, piecewise smooth curve, and let R be the plane region bounded by C. Green’s Theorem states that\begin{equation*}\oint_C P\,dx+Q\,dy =\iint_R...
Area Between Curves: Integrating With Respect to x01:25

Area Between Curves: Integrating With Respect to x

Consider two continuous functions defined on a closed interval from a to b. The region between these curves is bounded vertically by their graphs and horizontally by the endpoints of the interval. The objective is to measure the area of this region.An initial estimate of the area can be obtained by dividing the interval into a large number of narrow vertical strips of equal width. Each strip is approximated by a rectangle whose height is given by the vertical difference between the two...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
Elevation of Intermediate Points on Vertical Curves01:20

Elevation of Intermediate Points on Vertical Curves

Vertical curves are essential in roadway design because they provide smooth transitions between varying roadway grades. Designing vertical curves involves calculating intermediate elevations and identifying the curve's highest or lowest point, which is essential for optimal roadway performance.Intermediate elevations on a vertical curve are determined using the tangent offset method. This method considers the initial elevation at the start of the curve, the grades, and the curve's geometry. The...
Area Between Curves: Integrating With Respect to y01:29

Area Between Curves: Integrating With Respect to y

Consider a planar region bounded by two curves that are both written as functions of the vertical variable, y. The left and right boundary curves are continuous between y = c and y = d, and these two horizontal lines define the vertical limits of the region. Because the boundaries depend on y rather than x, the area is most appropriately evaluated using horizontal slices.The area is obtained using the Riemann sum method. The region is divided into many thin horizontal strips, each having an...

You might also read

Related Articles

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

Sort by
Same author

Macro Monte Carlo dose calculation for very high energy electron (VHEE) radiotherapy.

Medical physics·2026
Same author

Robust optimized dynamic mixed-beam arc radiotherapy for left-sided breast radiotherapy under deep inspiration breath-hold variations.

Physics in medicine and biology·2026
Same author

Treatment planning comparison of focused very high energy electron and volumetric modulated arc therapy.

Physics and imaging in radiation oncology·2026
Same author

A dual-layer quality assurance approach leveraging dose prediction for efficient review of automated contours of organs at risk in the brain in radiotherapy.

Physics and imaging in radiation oncology·2026
Same author

Evaluation of compartmentalized automatic segmentation for definition of the GTV in glioblastoma radiotherapy.

Radiotherapy and oncology : journal of the European Society for Therapeutic Radiology and Oncology·2025
Same author

"The Fact [Is] That There Is No Easy Way". A Qualitative Study of the Experiences of Aotearoa New Zealand Clinicians with Opioid Tapering for Chronic Non-Cancer Pain.

Journal of pain research·2025
Same journal

Effective contrast-enhanced preprocessing for intracranial artery segmentation in digital subtraction angiography.

Physics in medicine and biology·2026
Same journal

Improving Plan Quality in Adaptive Proton Therapy Using an Interactive Dose Modification Tool.

Physics in medicine and biology·2026
Same journal

Technical Note: Real-Time MLC Control and Latency Measurement Optimization with External Verification.

Physics in medicine and biology·2026
Same journal

Fetus-Specific Hematopoietic Stem Cell Dosimetry Framework for Leukemia-Relevant Target Cells During Prenatal Development.

Physics in medicine and biology·2026
Same journal

Deep learning-based dose prediction to enhance planning efficiency in cervical brachytherapy with hybrid applicators.

Physics in medicine and biology·2026
Same journal

Corrigendum: Referenceless MR thermometry-a comparison of five methods (2017<i>Phys. Med. Biol</i>.<b>62</b>1-16).

Physics in medicine and biology·2026
See all related articles

Related Experiment Video

Updated: Jun 28, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

An integral conservative gridding--algorithm using Hermitian curve interpolation.

Werner Volken1, Daniel Frei, Peter Manser

  • 1Division of Medical Radiation Physics, Inselspital and University of Bern, Switzerland. werner.volken@vsw.ch

Physics in Medicine and Biology
|October 17, 2008
PubMed
Summary
This summary is machine-generated.

A new gridding algorithm uses Hermitian interpolation to accurately re-sample spatial data, reducing overestimation and underestimation common in traditional methods. This improves data processing for applications like medical imaging.

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Related Experiment Videos

Last Updated: Jun 28, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Data processing and scientific visualization
  • Computational imaging and signal processing

Background:

  • Gridding or re-binning spatially distributed data is crucial for data processing, requiring algorithms to conserve integrals and avoid negative values for positive definite quantities.
  • Traditional gridding methods using high-order polynomial interpolation can lead to significant overshoots or undershoots, causing inaccurate data representation.

Purpose of the Study:

  • To develop a novel gridding algorithm that overcomes the limitations of existing methods, particularly concerning interpolation errors.
  • To introduce a controllable parameter for adjusting interpolation behavior, minimizing deviations from original data.

Main Methods:

  • Developed a gridding algorithm employing a parametrized Hermitian interpolation curve to approximate integrated data, offering user control over interpolation behavior.
  • Extended the algorithm for application to multidimensional grids.
  • Compared the new algorithm against linear and cubic interpolation methods.

Main Results:

  • The new algorithm significantly reduces interpolation errors compared to standard methods, which can overestimate or underestimate data by 10-20%.
  • Demonstrated improved accuracy on medical imaging datasets (x-ray CT scans) using metrics like mean square error and a quality index.
  • The algorithm's parameter allows tuning to minimize deviations, enhancing the fidelity of re-sampled data.

Conclusions:

  • The proposed gridding algorithm offers superior accuracy and control over data re-sampling compared to conventional techniques.
  • The method is effective for processing various datasets, including medical images, leading to more reliable results.
  • This approach provides a valuable tool for scientific data processing where accurate data representation is critical.