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Related Concept Videos

Principal Moments of Area01:14

Principal Moments of Area

1.1K
In mechanics, the product of inertia and moments of inertia of area help to calculate the stability and performance of various structures and components. The coordinate transformation relations are used to calculate the moments and products of inertia for an area about the inclined axes. Further, the moments and products of inertia with respect to the principal axes can be determined using the moments and products of inertia about the inclined axes.
The principal moment of inertia axes are the...
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Moments of Inertia for Areas01:17

Moments of Inertia for Areas

1.2K
The second moment of area, also known as the moment of inertia of an area, is a geometric property of a shape that reflects its resistance to change. The moment of inertia of an area is expressed in terms of a single number and can be calculated for both two-dimensional and three-dimensional shapes. The moment of inertia of an area is calculated by taking the sum of the product of the area and the square of its distance from a chosen axis of rotation. The moment of inertia is expressed in units...
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Principle of Moments01:20

Principle of Moments

1.8K
The principle of moments, also known as Varignon's theorem, is a fundamental concept in physics and engineering that describes the equilibrium of a rigid body under the influence of external forces. The principle states that the moment of a force about a point is equal to the sum of the moments of the components of the force about the same point.
The moment is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of application to the point about...
1.8K
Moment of Inertia about an Arbitrary Axis01:20

Moment of Inertia about an Arbitrary Axis

323
The moment of inertia is typically associated with principal axes, but it can also be computed for any random axis. When an arbitrary axis is under consideration, the moment of inertia is determined by integrating the mass distribution of the object along that specific axis. It is crucial in applications like the design of machinery, where components rotate about various axes, and balance and stability are essential.
In this scenario, the perpendicular distance between the chosen arbitrary axis...
323
Mohr's Circle for Moments of Inertia01:10

Mohr's Circle for Moments of Inertia

660
Mohr's circle is a graphical method to determine an area's principal moments of inertia by plotting the moments and product of inertia on a rectangular coordinate system.
660
Mohr's Circle for Moments of Inertia: Problem Solving01:14

Mohr's Circle for Moments of Inertia: Problem Solving

2.2K
Mohr's circle is a graphical method for determining an area's principal moments by plotting the moments and product of inertia on a rectangular coordinate system. This circle can also be used to calculate the orientation of the principal axes.
Consider a rectangular beam. The moments of inertia of the beam about the x and y axis are 2.5(107) mm4 and 7.5(107) mm4, respectively. The product of inertia is 1.5(107) mm4. Determine the principal moments of inertia and the orientation of the major and...
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Updated: Jul 28, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Local Orthogonal Moments for Local Features.

Jianwei Yang, Zezhi Zeng, Timothy Kwong

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |May 30, 2023
    PubMed
    Summary
    This summary is machine-generated.

    A new method, local orthogonal moment (LOM), offers improved control over image feature extraction. LOM precisely adjusts basis function zeros, leading to more accurate local feature identification compared to existing methods.

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    Area of Science:

    • Computer Vision
    • Image Processing
    • Mathematical Imaging

    Background:

    • Orthogonal moments are used for image local feature extraction.
    • Existing methods lack precise control over feature localization due to parameter limitations in basis function zero distribution.

    Purpose of the Study:

    • To introduce a novel framework, transformed orthogonal moment (TOM), for enhanced local feature extraction.
    • To propose local orthogonal moment (LOM) with adjustable basis function zeros for improved accuracy.

    Main Methods:

    • Developed a new framework, transformed orthogonal moment (TOM).
    • Designed a novel local constructor to control basis function zeros distribution.
    • Proposed local orthogonal moment (LOM) based on the new constructor.

    Main Results:

    • Local orthogonal moment (LOM) allows precise adjustment of basis function zeros.
    • LOM demonstrates more accurate local feature extraction compared to fractional-order orthogonal moments (FOOMs).
    • LOM exhibits order-insensitive feature extraction range, outperforming Krawtchouk and Hahn moments.

    Conclusions:

    • Local orthogonal moment (LOM) provides superior control and accuracy in image local feature extraction.
    • The proposed LOM framework overcomes limitations of existing orthogonal moments.
    • LOM is a viable method for effective local feature extraction in images.