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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Spherical and Cylindrical Capacitor01:26

Spherical and Cylindrical Capacitor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
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...
Triple Integrals in Spherical Coordinates01:27

Triple Integrals in Spherical Coordinates

Triple integrals in spherical coordinates provide an efficient method for evaluating volumes over regions with central symmetry, such as spheres. Instead of describing points by rectangular coordinates, spherical coordinates use three variables: 𝜌, 𝜃, and 𝜑. Here, 𝜌 is the distance from the origin, 𝜃 is the angle in the xy-plane measured from the positive x-axis, and 𝜑 is the angle measured downward from the positive z-axis.To derive the volume of a sphere, the solid region can be divided...
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Curl and Divergence of Vector Fields

Curl and divergence describe two fundamental ways a vector field can behave. A vector field assigns both magnitude and direction to each point in space, such as the velocity of water flowing in a river. Leaves floating on the surface may reveal regions where the water swirls and other regions where it spreads outward or gathers inward. These motions correspond to curl and divergence.Curl measures the tendency of a vector field to rotate around a point. If leaves circle around a small whirlpool,...
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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Mechanical Mapping of Spheroids Using Brillouin Spectroscopy
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Level set fiber bundle segmentation using spherical harmonic coefficients.

Mohammad-Reza Nazem-Zadeh1, Esmaeil Davoodi-Bojd, Hamid Soltanian-Zadeh

  • 1Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. m.nazemzadeh@ece.ut.ac.ir

Computerized Medical Imaging and Graphics : the Official Journal of the Computerized Medical Imaging Society
|October 23, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for segmenting brain white matter fiber bundles using spherical harmonic coefficients from High Angular Resolution Diffusion Imaging. The technique offers improved accuracy and robustness, particularly in challenging low signal-to-noise ratio conditions.

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Area of Science:

  • Neuroscience
  • Medical Imaging
  • Computational Biology

Background:

  • Classifying brain white matter fiber bundles is crucial for understanding neurological conditions.
  • Quantifying diffusion characteristics aids in tracking disease progression, treatment efficacy, and surgical planning.

Purpose of the Study:

  • To present a novel method for segmenting white matter fiber bundles using spherical harmonic coefficients (SHC).
  • To demonstrate the advantages of SHC-based similarity measures over traditional Diffusion Tensor Imaging (DTI) indices.
  • To offer a more direct and efficient approach by analyzing diffusion signals instead of complex orientation distribution functions (ODF).

Main Methods:

  • Utilized spherical harmonic coefficients (SHC) to represent diffusion signals from High Angular Resolution Diffusion Imaging (HARDI).
  • Developed a novel similarity measure based on SHC.
  • Integrated this similarity measure into a level set framework as a speed function for segmentation.
  • Compared the proposed method against DTI-based measures.

Main Results:

  • The proposed SHC-based method demonstrated superior accuracy and robustness, especially in low signal-to-noise ratio (SNR) environments, when tested on synthetic data.
  • Application to real HARDI MRI data confirmed its enhanced performance, particularly in areas with complex diffusion patterns and low anisotropy.
  • The method avoids complex mathematical calculations and assumptions inherent in ODF reconstruction.

Conclusions:

  • The novel SHC-based segmentation method provides a more accurate, robust, and efficient approach for analyzing white matter fiber bundles.
  • This technique offers significant advantages over existing DTI-based methods, especially in challenging neuroimaging scenarios.
  • The findings have implications for advanced neuroimaging analysis in clinical and research settings.