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Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
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...

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Related Experiment Video

Updated: Jun 22, 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

Object recognition using cylindrical harmonic filter.

Jáder Guerrero Bermúdez

    Optics Express
    |June 2, 2009
    PubMed
    Summary
    This summary is machine-generated.

    We developed a cylindrical harmonic filter for 3D range data correlation. This filter ensures consistent correlation peak intensity during target rotation, improving 3D object recognition.

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    Last Updated: Jun 22, 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

    Motion-Acuity Test for Visual Field Acuity Measurement with Motion-Defined Shapes
    06:25

    Motion-Acuity Test for Visual Field Acuity Measurement with Motion-Defined Shapes

    Published on: February 23, 2024

    Area of Science:

    • Computer Vision
    • Signal Processing
    • 3D Data Analysis

    Background:

    • 3D discrete correlation is crucial for analyzing range data in various applications.
    • Target rotation can significantly affect the accuracy and reliability of correlation-based recognition methods.
    • Existing methods often struggle with maintaining correlation peak intensity under rotational variations.

    Purpose of the Study:

    • To introduce a novel cylindrical harmonic filter for 3D discrete correlation.
    • To achieve invariance of correlation peak intensity under target rotation around the z-axis.
    • To enhance the robustness and accuracy of 3D object recognition using range data.

    Main Methods:

    • The proposed filter utilizes harmonic decomposition in cylindrical coordinates.
    • It operates on the 3D Fourier spectrum of the target data.
    • Discrete correlation techniques are employed for analysis.

    Main Results:

    • The cylindrical harmonic filter demonstrates invariance of correlation peak intensity under in-plane rotation.
    • Simulation results confirm the filter's effectiveness in maintaining peak intensity.
    • The filter shows strong discrimination capabilities, distinguishing targets effectively.

    Conclusions:

    • The cylindrical harmonic filter offers a robust solution for 3D discrete correlation with rotational invariance.
    • This method significantly improves the performance of 3D object recognition systems dealing with rotated targets.
    • The filter's harmonic decomposition approach provides a powerful tool for analyzing 3D spectral information.