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Related Concept Videos

Transformation of Plane Strain01:12

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
Vector Transformation in Rotating Coordinate Systems01:16

Vector Transformation in Rotating Coordinate Systems

Consider a vector rotating about an axis with an angular velocity, such that its tip sweeps a circular path.
Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it instrumental in...
Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
Here, in order to determine the magnitude of velocity and acceleration for point...
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...

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Related Experiment Video

Updated: Jun 13, 2026

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

Real-time deformation invariant optical pattern recognition using coordinate transformations.

D Casasent, S F Xia, A J Lee

    Applied Optics
    |May 11, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study uses a polar-logarithmic coordinate transformation for distortion-invariant pattern recognition. Computer-generated holograms and liquid crystal TVs enable real-time processing for improved optical pattern recognition systems.

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    Medical-grade Sterilizable Target for Fluid-immersed Fetoscope Optical Distortion Calibration
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    Published on: February 23, 2017

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    Last Updated: Jun 13, 2026

    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

    Medical-grade Sterilizable Target for Fluid-immersed Fetoscope Optical Distortion Calibration
    07:03

    Medical-grade Sterilizable Target for Fluid-immersed Fetoscope Optical Distortion Calibration

    Published on: February 23, 2017

    Area of Science:

    • Optics and Photonics
    • Computer Vision
    • Image Processing

    Background:

    • Pattern recognition often struggles with in-plane distortions like scale and rotation.
    • Traditional methods require complex algorithms or hardware for distortion invariance.

    Purpose of the Study:

    • To develop a distortion-invariant pattern recognition system using a polar-logarithmic coordinate transformation.
    • To enable real-time processing of transformed patterns for optical correlators.

    Main Methods:

    • A computer-generated hologram, printed via laser, performs the polar-logarithmic coordinate transformation.
    • Weighting terms in the output are analyzed for their impact on resolution and pixel data.
    • A pocket liquid crystal TV interfaces the transformed pattern to a correlator for real-time analysis.

    Main Results:

    • The system successfully achieves in-plane distortion invariance.
    • Analysis of weighting terms demonstrates their effect on output resolution and data reduction.
    • Experimental results validate the real-time processing capability.

    Conclusions:

    • The polar-logarithmic coordinate transformation is effective for distortion-invariant pattern recognition.
    • Computer-generated holograms and liquid crystal TVs provide a viable pathway for real-time optical pattern recognition.