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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...
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A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
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Oriented Surfaces

A surface is called orientable if a consistent choice of unit normal vector can be made at every point on the surface. A thin soap film stretched across a wire loop provides a familiar example. The film separates the air on one side from the air on the other, so one side can be selected as positive and the opposite side as negative. Once this choice is made, a unit normal vector can be assigned smoothly across the entire surface.At each point on the soap film, a unit normal vector points...
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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 uniform...
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Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...

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Spherical demons: fast surface registration.

B T Thomas Yeo1, Mert Sabuncu, Tom Vercauteren

  • 1Computer Science and Artificial Intelligence Laboratory, MIT, USA. ythomas@csail.mit.edu

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
|November 5, 2008
PubMed
Summary
This summary is machine-generated.

We developed a fast Spherical Demons algorithm for accurate spherical image registration. This method efficiently registers cortical surfaces, enabling precise anatomical analysis and localization.

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Area of Science:

  • Medical image analysis
  • Computational anatomy
  • Neuroimaging

Background:

  • Accurate registration of spherical images, particularly cortical surfaces, is crucial for comparative neuroimaging studies.
  • Existing methods may lack speed or accuracy for large-scale analyses.

Purpose of the Study:

  • To introduce a novel, fast, and accurate algorithm for registering spherical images.
  • To enable efficient and precise analysis of cortical surface data.

Main Methods:

  • Developed the fast Spherical Demons algorithm utilizing spherical vector spline interpolation.
  • Implemented regularizers using convolution for efficient computation on the sphere.
  • Ensured registration is diffeomorphic using one-parameter subgroups of diffeomorphisms.

Main Results:

  • Achieved registration of cortical mesh models (100k+ nodes) in under 5 minutes.
  • Demonstrated comparable or superior accuracy to the FreeSurfer registration algorithm.
  • Successfully validated the method for in-vivo cortical surface parcellation and ex-vivo Brodmann area localization.

Conclusions:

  • The fast Spherical Demons algorithm offers a computationally efficient and accurate solution for spherical image registration.
  • This method facilitates advanced neuroimaging analyses, including cortical parcellation and anatomical localization.
  • The algorithm's speed and accuracy make it suitable for large-scale neuroimaging datasets.