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相关概念视频

Spherical Coordinates01:23

Spherical Coordinates

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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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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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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...
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Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

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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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Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

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In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
389
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

14.7K
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
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Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

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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...
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相当的球体解卷:从球体数据中学习稀疏方向分布函数.

Axel Elaldi1, Neel Dey1, Heejong Kim1

  • 1Department of Computer Science and Engineering, New York University, New York, USA.

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概括
此摘要是机器生成的。

我们开发了一种旋转等价的自我监督学习方法,用于扩散MRI (dMRI),以改善白质纤维的重建. 这种方法提高了解决复杂纤维结构的准确性,推进了神经成像分析.

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相关实验视频

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科学领域:

  • 医疗成像医学成像
  • 神经成像是一种神经成像.
  • 机器学习 机器学习

背景情况:

  • 扩散核磁共振 (dMRI) 数据包含复杂的信号在每一个voxel由于异性质组织结构,如白质.
  • 目前的线性球形解卷方法难以准确地解决交叉纤维配置,并估计dMRI中的部分体积分数.
  • 对白质纤维方向的准确重建对于理解大脑结构和功能至关重要.

研究的目的:

  • 引入一个新的旋转等值自主监督学习框架,用于dMRI中球形信号的稀疏解卷.
  • 通过解决现有线性方法的局限性,改进白质纤维结构的非线性估计.
  • 为了提高纤维通道图的准确性和dMRI中的部分体积估计.

主要方法:

  • 开发了一个自主监督的球形卷积神经网络,具有保证的旋转等差.
  • 将框架应用于单元球上的非负标量场的稀疏解卷.
  • 使用单个和多合成dMRI数据集和人类受试者数据集验证了该方法.

主要成果:

  • 拟议的方法证明了与合成基准标准的常见基准方法相比具有竞争力的性能.
  • 在使用 Tractometer 基准数据集的纤维曲谱测量上取得了下游性能改进.
  • 从人类受试者的多数据集上显示了增强的路径图和部分体积估计.

结论:

  • 旋转等值自主监督学习框架为dMRI球形解卷提供了一个有希望的非线性方法.
  • 这种方法可以提高复杂的白质结构的分辨率,包括交叉纤维.
  • 该框架有可能推进神经成像分析和dMRI的临床应用.