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Related Concept Videos

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,...
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...
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...
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...
Gradient and Del Operator01:14

Gradient and Del Operator

In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The gradient is a mathematical operator that gives both the magnitude and direction of the maximum spatial rate of change. Consider a person standing on a mountain. The slope of the mountain at any given point is not defined unless it is quantified in a particular direction. For this reason, a "directional derivative" is defined, which is a vector...
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...

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Related Experiment Video

Updated: May 12, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Single-image vignetting correction from gradient distribution symmetries.

Yuanjie Zheng1, Stephen Lin, Sing Bing Kang

  • 1Department of Radiology, University of Pennsylvania, 3600 Market St., Suite 370, Philadelphia, PA 19104-2644, USA. Yuanjie.Zheng@uphs.upenn.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 20, 2013
PubMed
Summary
This summary is machine-generated.

We developed new methods for single-image vignetting correction using image gradient symmetries. These techniques automatically estimate the optical center and correct vignetting more accurately and faster than existing approaches.

Related Experiment Videos

Last Updated: May 12, 2026

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

Area of Science:

  • Computer Vision
  • Image Processing

Background:

  • Vignetting is a common optical distortion in images.
  • Existing single-image vignetting correction methods often require image segmentation and can lack accuracy.

Purpose of the Study:

  • To introduce novel techniques for single-image vignetting correction.
  • To develop an automatic optical center estimation algorithm.
  • To present accurate and efficient vignetting estimation methods.

Main Methods:

  • Utilizing symmetries of semicircular tangential gradients (SCTG) and radial gradients (RG).
  • Developing an automatic optical center estimation by minimizing SCTG distribution asymmetry.
  • Implementing two vignetting estimation methods based on RG distribution asymmetry.

Main Results:

  • The proposed methods achieve accurate optical center and vignetting estimation.
  • The techniques do not rely on image segmentation.
  • Experimental results demonstrate effectiveness across diverse images.
  • Achieved a 3-5 times speed-up compared to a state-of-the-art method.

Conclusions:

  • Novel techniques based on image gradient symmetries offer accurate and efficient single-image vignetting correction.
  • The methods provide a robust alternative to existing approaches, particularly those requiring segmentation.