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Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
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Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments.

Chunpeng Wang1,2,3, Hongling Gao1,2, Meihong Yang1,2

  • 1School of Computer Science and Technology (School of Cyber Security), Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China.

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|March 6, 2021
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Summary

This study introduces fractional-order polar harmonic Fourier moments (FrPHFMs) to enhance image reconstruction and noise resistance. FrPHFMs demonstrate superior performance in image recognition and description compared to existing methods.

Keywords:
continuous orthogonal momentsfractional-order polar harmonic Fourier momentsgeometric invarianceimage reconstructionobject recognition

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Area of Science:

  • Image processing
  • Computer vision
  • Applied mathematics

Background:

  • Continuous orthogonal moments offer rotation and scaling invariance.
  • Polar harmonic Fourier moments (PHFMs) exhibit strong image description capabilities.
  • Existing integer-order PHFMs have limitations in noise resistance and reconstruction.

Purpose of the Study:

  • To extend integer-order PHFMs to fractional-order polar harmonic Fourier moments (FrPHFMs).
  • To improve noise resistance and image reconstruction performance.
  • To evaluate the effectiveness of FrPHFMs against other moment invariants.

Main Methods:

  • Modification of radial polynomials to achieve fractional orders.
  • Construction of FrPHFMs using fractional-order radial polynomials.
  • Mathematical proof of orthogonality, geometric invariance, and reconstruction ability.
  • Comparative performance analysis with integer-order PHFMs and other fractional-order moments.

Main Results:

  • FrPHFMs exhibit strong reconstruction ability, orthogonality, and geometric invariance.
  • Experimental results confirm FrPHFMs outperform integer-order PHFMs.
  • FrPHFMs show superiority over other fractional-order moments like FrRHFMs, FrPHTs, and FrZMs.
  • The proposed FrPHFMs demonstrate robust image description and stability.

Conclusions:

  • Fractional-order polar harmonic Fourier moments (FrPHFMs) offer enhanced performance.
  • FrPHFMs provide superior image reconstruction, object recognition, and description capabilities.
  • The developed FrPHFMs present a significant advancement in image analysis techniques.