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Related Concept Videos

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...
Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
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...
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 Axes - Acceleration01:22

Relative Motion Analysis using Rotating Axes - Acceleration

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. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...

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Related Experiment Video

Updated: Jul 7, 2026

A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers
12:39

A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers

Published on: January 18, 2020

Partial rotation-invariant pattern matching and face recognition with a joint transform correlator.

S Chang, S A Boothroyd, J Chrostowski

    Applied Optics
    |April 10, 1997
    PubMed
    Summary

    This study introduces circular-harmonic (CH) images for rotationally invariant pattern recognition. Filtering these images enables partial or full rotation invariance, demonstrated for human face recognition.

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    Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data
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    Published on: October 18, 2024

    Related Experiment Videos

    Last Updated: Jul 7, 2026

    A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers
    12:39

    A Methodology for Capturing Joint Visual Attention Using Mobile Eye-Trackers

    Published on: January 18, 2020

    Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data
    06:36

    Three-Dimensional Mapping of the Rotation of Interactive Virtual Objects with Eye-Tracking Data

    Published on: October 18, 2024

    Area of Science:

    • Computer Vision
    • Image Processing
    • Pattern Recognition

    Background:

    • Traditional pattern recognition methods struggle with rotational variations.
    • Achieving rotation invariance is crucial for robust object identification.

    Purpose of the Study:

    • To introduce and evaluate circular-harmonic (CH) images for rotationally invariant pattern recognition.
    • To demonstrate the effectiveness of CH images in recognizing objects with partial rotational invariance.

    Main Methods:

    • Utilized circular-harmonic (CH) components derived from images in polar coordinates.
    • Constructed a two-dimensional CH(mr) image space incorporating the radial variable r.
    • Applied various filters (narrow-pass, all-pass, low-pass) to CH(mr) images.
    • Conducted numerical simulations and optical experiments using a joint transform correlator.

    Main Results:

    • Narrow-pass filtering yielded full rotation invariance.
    • All-pass filtering resulted in no rotational invariance (original image).
    • Low-pass filtering produced partial rotation invariance by combining multiple circular harmonics.
    • Successfully demonstrated partial-rotation-invariant recognition of human face images.

    Conclusions:

    • Circular-harmonic (CH) images offer a viable approach for rotationally invariant pattern recognition.
    • The filtering strategy applied to CH images allows for tunable levels of rotational invariance.
    • The method shows promise for applications like human face recognition.