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Related Concept Videos

Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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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...
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Symmetry in Maxwell's Equations01:28

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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...
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Gauss's Law: Spherical Symmetry01:26

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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...
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Gauss's Law: Cylindrical Symmetry01:20

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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,...
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

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Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
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Updated: Jan 22, 2026

Normothermic Ex Vivo Kidney Perfusion for the Preservation of Kidney Grafts prior to Transplantation
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Symmetry prior for epipolar consistency.

Alexander Preuhs1, Andreas Maier2, Michael Manhart3

  • 1Pattern Recognition Lab, Friedrich-Alexander Universität Erlangen-Nürnberg, Erlangen, Germany. alexander.preuhs@fau.de.

International Journal of Computer Assisted Radiology and Surgery
|July 14, 2019
PubMed
Summary

This study introduces a novel method for estimating symmetry planes from projection images, enabling accurate in-plane motion estimation. This approach leverages symmetry to overcome limitations in medical imaging analysis, particularly for detecting abnormalities like tumors or strokes.

Keywords:
Cone-beam CTConsistency conditionsData completenessMotion compensationSymmetryTomographic reconstruction

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Area of Science:

  • Medical imaging analysis
  • Computational geometry
  • Computer vision

Background:

  • Plane symmetric objects produce identical mirrored views.
  • A single image and camera calibration can yield a virtual image if the symmetry plane is known.
  • Symmetry breakers are crucial for detecting pathologies like tumors and strokes.

Purpose of the Study:

  • To develop a method for estimating the symmetry plane from projection images.
  • To utilize the estimated symmetry plane for robust in-plane motion estimation.
  • To overcome inherent limitations in current in-plane motion estimation techniques.

Main Methods:

  • Symmetry plane estimation via consistency maximization based on epipolar consistency.
  • Exploiting symmetry for in-plane motion estimation using an X-trajectory.
  • Acquiring data with a conventional short-scan trajectory by tilting the acquisition plane.

Main Results:

  • Demonstrated robustness of symmetry plane estimation on a human head phantom and synthetic data.
  • Showcased the advantage of the method for in-plane motion estimation.
  • Validated the approach using acquired projection data.

Conclusions:

  • A fast, outlier-robust symmetry plane estimation method is provided, computed directly from projections.
  • Coupling symmetry prior with epipolar consistency overcomes in-plane motion estimation limitations.
  • The method enhances the detection of symmetry breakers for medical diagnostic applications.