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

Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

149
When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
149
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

1.2K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
1.2K
Castigliano's Theorem01:18

Castigliano's Theorem

349
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
349
Deconvolution01:20

Deconvolution

127
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
127

You might also read

Related Articles

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

Sort by
Same author

Optical Coherence Tomography Harmonization with Anatomy-Guided Latent Metric Schrödinger Bridges.

Advances in neural information processing systems·2026
Same author

Optical Coherence Tomography Harmonization via Dual Diffusion Implicit Bridges.

Proceedings of SPIE--the International Society for Optical Engineering·2026
Same author

Unsupervised OCT Image Interpolation Using Deformable Registration and generative models.

Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention·2026
Same author

An Unsupervised Approach for Artifact Severity Scoring in Multi-Contrast MR Images.

Proceedings of machine learning research·2026
Same author

Beyond the LUMIR challenge: The pathway to foundational registration models.

Medical image analysis·2026
Same author

DSHARP: Deep Incompressible Motion Estimation With Sinusoidal-Transformed Harmonic Phase for Tagged MRI.

IEEE transactions on medical imaging·2026

Related Experiment Video

Updated: May 24, 2025

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration
05:05

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

7.8K

On Finite Difference Jacobian Computation in Deformable Image Registration.

Yihao Liu1, Junyu Chen2, Shuwen Wei1

  • 1Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, Maryland, USA.

International Journal of Computer Vision
|March 3, 2025
PubMed
Summary

Ensuring spatial transformations are diffeomorphic is crucial for medical image registration. This study introduces a digital diffeomorphism criterion to accurately detect non-diffeomorphic transformations, improving upon traditional methods.

Keywords:
Deformable RegistrationDigital DiffeomorphismFinite DifferenceInterpolationJacobian DeterminantsNon-rigid registration

More Related Videos

Analyzing Dendritic Morphology in Columns and Layers
08:41

Analyzing Dendritic Morphology in Columns and Layers

Published on: March 23, 2017

9.3K
Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.3K

Related Experiment Videos

Last Updated: May 24, 2025

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration
05:05

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

7.8K
Analyzing Dendritic Morphology in Columns and Layers
08:41

Analyzing Dendritic Morphology in Columns and Layers

Published on: March 23, 2017

9.3K
Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

6.3K

Area of Science:

  • Medical image analysis
  • Computational geometry
  • Digital image processing

Background:

  • Diffeomorphic spatial transformations are essential for accurate deformable image registration.
  • Current methods using Jacobian determinant approximations can incorrectly identify non-diffeomorphic transformations.
  • Voxel-level analysis is critical for ensuring transformation integrity.

Purpose of the Study:

  • To investigate the limitations of finite difference approximations for digital Jacobian determinants.
  • To propose a novel criterion for assessing diffeomorphism in digital images.
  • To develop a method that accurately detects non-diffeomorphic transformations at the voxel level.

Main Methods:

  • Analysis of geometric interpretations of finite difference approximations.
  • Development of a digital diffeomorphism criterion based on multiple finite difference calculations.
  • Validation of the criterion for 2D and 3D transformations.

Main Results:

  • Individual finite difference approximations are insufficient to guarantee diffeomorphism.
  • Four unique finite difference approximations are required for 2D transformations.
  • Ten unique finite difference approximations are necessary for 3D transformations.
  • The proposed digital diffeomorphism criteria accurately identifies non-diffeomorphic transformations.

Conclusions:

  • The central difference approximation is inadequate for verifying digital diffeomorphism.
  • The proposed digital diffeomorphism criteria provides a robust method for ensuring transformation integrity in medical imaging.
  • Accurate detection of non-diffeomorphic transformations is vital for reliable image registration.