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

Oriented Surfaces01:30

Oriented Surfaces

A surface is called orientable if a consistent choice of unit normal vector can be made at every point on the surface. A thin soap film stretched across a wire loop provides a familiar example. The film separates the air on one side from the air on the other, so one side can be selected as positive and the opposite side as negative. Once this choice is made, a unit normal vector can be assigned smoothly across the entire surface.At each point on the soap film, a unit normal vector points...
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
Torsion in Vector Calculus01:20

Torsion in Vector Calculus

A toy train ascending a winding track that curves and tilts offers an intuitive view of torsion, a key geometric concept in the study of space curves. While curvature measures how sharply a path bends, torsion captures how the path twists out of the plane of bending. This twisting behavior is crucial in understanding three-dimensional motion and is precisely described using the Frenet–Serret framework.At each point along a space curve, the Frenet–Serret frame consists of three orthogonal unit...

You might also read

Related Articles

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

Sort by
Same author

Revisiting the Grain and Valence Effect of Oxide-Derived Copper on Electrocatalytic CO<sub>2</sub> Reduction Using Single Crystal Cu(111) Foils.

The journal of physical chemistry letters·2021
Same author

Red Light-Triggered Intracellular Carbon Monoxide Release Enables Selective Eradication of MRSA Infection.

Angewandte Chemie (International ed. in English)·2021
Same author

Ghrelin Inhibits Intestinal Epithelial Cell Apoptosis Through the Unfolded Protein Response Pathway in Ulcerative Colitis.

Frontiers in pharmacology·2021
Same author

Effect of temperature stress on gut-brain axis in mice: Regulation of intestinal microbiome and central NLRP3 inflammasomes.

The Science of the total environment·2021
Same author

Disparities of weather type and geographical location in the impacts of temperature variability on cancer mortality: A multicity case-crossover study in Jiangsu Province, China.

Environmental research·2021
Same author

Temporal trends of the association between extreme temperatures and hospitalisations for schizophrenia in Hefei, China from 2005 to 2014.

Occupational and environmental medicine·2021

Related Experiment Video

Updated: Jun 13, 2026

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

A Riemannian framework for orientation distribution function computing.

Jian Cheng1, Aurobrata Ghosh, Tianzi Jiang

  • 1LIAMA Research Center for Computational Medicine, Institute of Automation, Chinese Academy of Sciences, China. Jian.Cheng@sophia.inria.fr

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
|April 30, 2010
PubMed
Summary
This summary is machine-generated.

High Angular Resolution Imaging (HARDI) offers superior white matter microstructure analysis. This study introduces a novel Riemannian framework for Orientation Distribution Function (ODF) computation, enabling robust parameter estimation and a new Geometric Anisotropy measure.

More Related Videos

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
08:59

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Published on: October 28, 2018

Related Experiment Videos

Last Updated: Jun 13, 2026

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

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
08:59

Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps

Published on: October 28, 2018

Area of Science:

  • Medical Imaging
  • Computational Neuroscience
  • Information Geometry

Background:

  • High Angular Resolution Imaging (HARDI) provides detailed white matter microstructure insights, surpassing Diffusion Tensor Imaging (DTI).
  • Orientation Distribution Functions (ODFs) represent fiber direction probabilities, crucial for understanding white matter complexity.
  • Information Geometry offers tools for analyzing probability distributions, previously applied to DTI tensor computing.

Purpose of the Study:

  • To develop a novel Riemannian framework for computing Orientation Distribution Functions (ODFs) using Information Geometry and sparse orthonormal bases.
  • To introduce a new scalar metric, Geometric Anisotropy (GA), derived from Riemannian geodesic distance.
  • To establish Affine-Euclidean and Log-Euclidean frameworks for ODF analysis in Euclidean space.

Main Methods:

  • A state-of-the-art Riemannian framework for ODF computation utilizing Information Geometry and sparse orthonormal bases.
  • Closed-form solutions for exponential map, logarithmic map, and geodesic on the ODF manifold.
  • Development of Geometric Anisotropy (GA) as the Riemannian geodesic distance to the isotropic ODF.
  • Implementation of Affine-Euclidean and Log-Euclidean frameworks for simplified ODF analysis.
  • Application of Lagrange interpolation on ODF fields using weighted Frechet mean.

Main Results:

  • The proposed Riemannian framework is model-free, offering robust and linear estimation of Riemannian coordinates.
  • The weighted Frechet mean on the ODF manifold is shown to exist uniquely.
  • Geometric Anisotropy (GA) provides a novel scalar measure, enabling computation of Renyi entropy (H1/2).
  • Validation on synthetic and real data demonstrates the framework's effectiveness compared to existing methods.

Conclusions:

  • The novel Riemannian framework advances ODF computation in HARDI, providing a robust, model-free approach.
  • Geometric Anisotropy (GA) offers a new quantitative measure for white matter microstructure analysis.
  • The theoretical results are generalizable to any probability density function represented by orthonormal bases.