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Related Concept Videos

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: 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...
Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The orientation of the...
Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
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,...

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Measuring Spatially- and Directionally-varying Light Scattering from Biological Material
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Published on: May 20, 2013

Curved glide-reflection symmetry detection.

Seungkyu Lee1, Yanxi Liu

  • 1Advanced Media Lab, Samsung Advanced Institute of Technology (SAIT), San14, Nongseo-dong, Giheung-gu, Yongin-si, Gyeonggi-do 446-712, South Korea. seungkyu74@gmail.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|June 15, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces curved glide-reflection symmetry, a generalization of reflection symmetry. The new method accurately detects this symmetry in 2D and 3D images, outperforming existing algorithms.

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Area of Science:

  • Computer Vision
  • Image Analysis
  • Geometric Symmetry

Background:

  • Classic reflection symmetry is limited in describing complex natural shapes.
  • A generalized symmetry detection method is needed for unsegmented real-world images.

Purpose of the Study:

  • To generalize bilateral reflection symmetry to curved glide-reflection symmetry.
  • To develop a local feature-based approach for detecting curved glide-reflection symmetry in 2D and 3D images.
  • To apply this detection for identifying curved reflection surfaces.

Main Methods:

  • Generalizing bilateral reflection symmetry to curved glide-reflection symmetry in 2D Euclidean space.
  • Proposing a local feature-based approach for symmetry detection in unsegmented 2D images.
  • Utilizing an Axis-Parameter-Space (APS) for discovering and connecting dominant local glide-reflection axes without preassumptions.

Main Results:

  • The proposed algorithm achieves promising average detection rates of 80% on a 64-test-image set and 40% on 1,125 leaf images.
  • Demonstrated superior performance compared to existing reflection symmetry detection algorithms.
  • Successfully applied curved glide-reflection axis detection for curved reflection surface detection in 3D images.

Conclusions:

  • The developed method effectively detects generalized curved glide-reflection symmetry in 2D and 3D images.
  • Potential applications include saliency detection and normality quantification in biomedical imaging.
  • The 64-test-image dataset is publicly available for further research.