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Related Concept Videos

Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Symmetry01:26

Symmetry

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Torsion of Noncircular Members01:16

Torsion of Noncircular Members

Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...

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

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Published on: August 30, 2013

Irregular shape symmetry analysis: theory and application to quantitative galaxy classification.

Qi Guo1, Falei Guo, Jiaqing Shao

  • 1Strangeways Research Laboratory, University of Cambridge, Worts Causeway, Cambridge CB1 8RN, UK. qi.guo@srl.cam.ac.uk

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 21, 2010
PubMed
Summary

This study introduces new geometric measures to quantify the symmetry of arbitrary shapes. These measures enable novel shape characterization and effective galaxy classification.

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Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Published on: October 28, 2018

Area of Science:

  • Mathematics
  • Computer Science
  • Astronomy

Background:

  • Analyzing the geometric properties of arbitrary shapes is crucial in various scientific fields.
  • Existing symmetry measures often struggle with imperfect or complex shapes.

Purpose of the Study:

  • To develop novel, imperfectly symmetric measures for quantifying the degree of symmetry in arbitrary shapes.
  • To introduce new definitions for bilateral and rotational symmetricity for enhanced shape analysis.
  • To establish criteria for quantitative galaxy classification using these symmetry measures.

Main Methods:

  • Utilizing a series of geometric transformation operations to define symmetry measures.
  • Developing quantitative criteria for irregular shape symmetry.
  • Applying these measures to galaxy classification tasks.

Main Results:

  • Successfully quantified the "amount" of symmetry for arbitrary shapes.
  • Provided new insights into analyzing geometrical properties through bilateral and rotational symmetricity.
  • Demonstrated the effectiveness of the proposed method for celestial body shape characterization.

Conclusions:

  • The proposed imperfectly symmetric measures offer a robust way to characterize arbitrary shapes.
  • The developed criteria are effective for quantitative galaxy classification.
  • The concepts have broad applicability across disciplines like AI, robotics, and biomedicine.