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

Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...
Divergence and Curl01:15

Divergence and Curl

The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the vector...
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
First Derivatives and the Shape of a Graph01:22

First Derivatives and the Shape of a Graph

In calculus, the concept of the first derivative plays a crucial role in understanding the behavior of a function over its domain. The first derivative, denoted as f’(x), provides insight into how a function changes at any given point, much like a cyclist adjusting speed along a winding trail. By analyzing the first derivative, mathematicians can determine where a function is increasing, decreasing, or reaching critical points.The first derivative provides a precise method for classifying...

You might also read

Related Articles

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

Sort by
Same author

[Analysis of the prevalence and influencing factors of myopia among primary and secondary school students in Inner Mongolia Autonomous Region in 2022].

Beijing da xue xue bao. Yi xue ban = Journal of Peking University. Health sciences·2026
Same author

Generalized Legendre Transforms Have Roots in Information Geometry.

Entropy (Basel, Switzerland)·2026
Same author

Mirror Descent and Exponentiated Gradient Algorithms Using Trace-Form Entropies.

Entropy (Basel, Switzerland)·2025
Same author

Two Types of Geometric Jensen-Shannon Divergences.

Entropy (Basel, Switzerland)·2025
Same author

Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys-Fisher-Rao Center and the Gauss-Bregman Inductive Center.

Entropy (Basel, Switzerland)·2025
Same author

Symplectic Bregman Divergences.

Entropy (Basel, Switzerland)·2025

Related Experiment Video

Updated: May 7, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

Total Bregman Divergence and its Applications to Shape Retrieval.

Meizhu Liu1, Baba C Vemuri, Shun-Ichi Amari

  • 1CISE, University of Florida mliu,vemuri@cise.ufl.edu.

Proceedings. IEEE Computer Society Conference on Computer Vision and Pattern Recognition
|October 1, 2013
PubMed
Summary

Researchers introduce a new divergence measure, the total Bregman divergence (TBD), for efficient shape database searching. This method uses a novel t-center to represent shape classes, improving accuracy in biometric and CAD systems.

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: May 7, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

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:

  • Computer Science
  • Mathematics
  • Data Science

Background:

  • Shape database search is crucial for biometrics and CAD systems.
  • Explosive growth in shape data necessitates efficient retrieval methods.
  • Existing divergence measures like Bregman divergences have limitations.

Purpose of the Study:

  • To introduce a novel divergence measure for shape data.
  • To develop a new theory for estimating centers of vectors and distributions.
  • To present an improved shape retrieval scheme.

Main Methods:

  • Defined a novel divergence measuring orthogonal distance.
  • Redefined Bregman divergences as total Bregman divergence (TBD).
  • Developed an l1-norm based TBD center (t-center) for shape class representation.

Main Results:

  • The t-center acts as a robust cluster center, downplaying noise and outliers.
  • A shape retrieval scheme using TBD and t-center was developed.
  • Demonstrated competitive performance against state-of-the-art methods on the MPEG-7 database.

Conclusions:

  • The total Bregman divergence offers a new perspective on divergence measures.
  • The t-center provides a robust method for shape class representation.
  • The proposed shape retrieval scheme shows significant potential for large-scale shape databases.