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

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The Global Positioning System (GPS) has become an indispensable tool in fieldwork, offering unparalleled precision and efficiency for surveying, navigation, and infrastructure development. By harnessing signals from a constellation of satellites, GPS receivers determine the location of objects with remarkable speed and accuracy, often completing calculations within a second.Advantages of Modern GPS TechnologyContemporary GPS receivers are designed to meet the practical demands of field...
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Gauss's Law01:07

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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
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Spatially varying registration using Gaussian processes.

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    Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
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    This study introduces a novel spatially-varying registration method using Gaussian process priors and spectral tempering. The approach enhances registration accuracy and robustness against noise in medical imaging, particularly for cone beam CT scans.

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    Area of Science:

    • Medical Imaging
    • Computational Anatomy
    • Machine Learning

    Background:

    • Accurate medical image registration is crucial for diagnosis and treatment planning.
    • Existing registration methods often struggle with spatially varying image noise and artifacts.
    • Spatially-varying registration requires adaptable smoothness constraints.

    Purpose of the Study:

    • To develop a novel approach for spatially-varying registration using Gaussian process priors.
    • To enhance robustness against noise in medical image datasets, such as cone beam CT scans.
    • To provide a flexible method applicable to various registration algorithms.

    Main Methods:

    • Implementation of spectral tempering to modify Gaussian process spectra.
    • Creation of non-stationary Gaussian processes with user-defined tempering functions.
    • Integration of the modified prior into existing registration frameworks without altering the core algorithm.

    Main Results:

    • Demonstrated robustness against noise in atlas-based skull registration of cone beam CT images.
    • Achieved accurate correspondence in noise-free regions of the datasets.
    • Showcased the method's applicability to spline-based models and statistical shape/deformation models.

    Conclusions:

    • The proposed Gaussian process prior with spectral tempering offers an effective solution for spatially-varying registration.
    • This method significantly improves registration performance in the presence of noise, a common challenge in medical imaging.
    • The approach is versatile, allowing for spatially-varying adaptations of various registration techniques.