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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...
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...
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...
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...
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,...
Rotation of Asymmetric Top01:11

Rotation of Asymmetric Top

By definition, a spherically symmetric body has the same moment of inertia about any axis passing through its center of mass. This situation changes if there is no spherical symmetry. Since most rigid bodies are not spherically symmetric, these require special treatment.
The relationship between the angular momentum of any rigid body and its angular velocity, both of which are vectors, involves the moment of inertia. The moment of inertia is a scalar quantity only for spherically symmetric...

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Automated Midline Shift and Intracranial Pressure Estimation based on Brain CT Images
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Published on: April 13, 2013

Symmetry constraint for foreground extraction.

Huazhu Fu, Xiaochun Cao, Zhuowen Tu

    IEEE Transactions on Cybernetics
    |June 26, 2013
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel method for foreground object extraction by incorporating image symmetry. The approach enhances segmentation accuracy, particularly for objects with weak or complex symmetry.

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    Area of Science:

    • Computer Vision
    • Image Processing
    • Artificial Intelligence

    Background:

    • Symmetry is a common characteristic of natural objects.
    • Accurate foreground object extraction is crucial in image analysis.
    • Existing methods may struggle with objects exhibiting weak or complex symmetry.

    Purpose of the Study:

    • To enhance foreground object extraction by leveraging image symmetry.
    • To develop a method that consistently extracts objects with symmetric parts.
    • To improve segmentation of weakly or complexly symmetric objects.

    Main Methods:

    • A symmetry foreground map is created to represent image symmetry structure.
    • A symmetry constraint model is integrated into graph-based segmentation.
    • Graph cuts are employed to obtain the final segmentation results.

    Main Results:

    • The proposed method improves the quality of foreground object extraction.
    • Consistent extraction of objects with symmetric parts is achieved.
    • Enhanced performance is demonstrated on benchmark datasets, especially for challenging symmetry cases.

    Conclusions:

    • Explicitly considering symmetry constraints significantly enhances foreground object extraction.
    • The developed model is effective for segmenting objects with weak and complex symmetries.
    • The approach offers a robust solution for image segmentation tasks involving natural objects.