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Related Concept Videos

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,...
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...
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...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...
Triple Integrals in Cylindrical Coordinates01:28

Triple Integrals in Cylindrical Coordinates

Cylindrical coordinates describe a point in three-dimensional space using three values: radial distance, angle, and height. The height gives the position above the xy-plane, the radial distance measures how far the point is from the z-axis, and the angle describes the point’s direction from the positive x-axis in the xy-plane. This system is especially useful for regions with circular symmetry because it matches the natural geometry of cylinders, disks, and circular tanks.To calculate volume,...
Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

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 time...

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Related Experiment Video

Updated: Jul 14, 2026

Optical Scatter Microscopy Based on Two-Dimensional Gabor Filters
14:58

Optical Scatter Microscopy Based on Two-Dimensional Gabor Filters

Published on: June 2, 2010

Recursive anisotropic 2-D Gaussian filtering based on a triple-axis decomposition.

Stanley Yiu Man Lam, Bertram E Shi

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |July 4, 2007
    PubMed
    Summary

    A novel recursive algorithm for anisotropic 2-D Gaussian filtering uses three 1-D filters, eliminating interpolation for improved kernel shape and DSP implementation. Computational complexity remains comparable to existing methods.

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    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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    Published on: August 30, 2013

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    Last Updated: Jul 14, 2026

    Optical Scatter Microscopy Based on Two-Dimensional Gabor Filters
    14:58

    Optical Scatter Microscopy Based on Two-Dimensional Gabor Filters

    Published on: June 2, 2010

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
    13:44

    Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

    Published on: August 30, 2013

    Area of Science:

    • Image processing
    • Computer vision
    • Digital signal processing

    Background:

    • Anisotropic 2-D Gaussian filtering is crucial for image analysis.
    • Existing methods often involve interpolation, leading to spatial inhomogeneity and less regular filter structures.
    • Efficient implementation on digital signal processing (DSP) chips is a key challenge.

    Discussion:

    • This study introduces a recursive algorithm that decomposes the 2-D filter into a cascade of three 1-D filters.
    • The filters operate along axes with integer pixel shifts, avoiding interpolation and its associated artifacts.
    • This approach results in more elliptically shaped kernels and a regular filter structure suitable for hardware implementation.

    Key Insights:

    • Eliminating interpolation preserves spatial homogeneity and produces more accurate elliptical filter kernels.
    • The proposed method enhances filter matching for identical eccentricity and width but varying orientations.
    • Computational complexity is comparable to two-axis algorithms, achieving under 11 ms for a 512x512 image on a 3.2-GHz Pentium 4 PC.

    Outlook:

    • Further research can explore optimizing the selection of basis filter axes to achieve desired aspect ratios.
    • This algorithm has potential applications in areas requiring precise anisotropic filtering, such as medical imaging and remote sensing.
    • Investigating hardware acceleration for DSP chips could further enhance performance and real-time applicability.