Self-Similarities in Hilbert Envelope Energy Regions on Motion Waveforms Application in Detecting Motion Irregularities in Video Frames

Notice

This is an unedited manuscript accepted for publication and provided as an Article in Press for early access at the author’s request. The article will undergo copyediting, typesetting, and galley proof review before final publication. Please be aware that errors may be identified during production that could affect the content. All legal disclaimers of the journal apply.

Year : 2024 | Volume :14 | Issue : 03 | Page : 1-10
By
vector

Dr. J.F. Peters,

vector

E. Cui1,

  1. Student,, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Manitoba, Canada
  2. Student,, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6, Manitoba, Canada

Abstract document.addEventListener(‘DOMContentLoaded’,function(){frmFrontForm.scrollToID(‘frm_container_abs_114033’);});Edit Abstract & Keyword

This paper introduces self-similar Hilbert envelope energy regions that are commonly found in oscillating spectral curves.  The time-varying amplitudes and peak-value frequencies in typical spectral curve reflect the response of a system to external stimuli.  A Hilbert envelope is a smooth curve connected between spectral curve peak values.  Each peak value  on an envelope curve  at time  identifies an envelope-bounded region with interior area (called Hilbert envelope energy region (denoted by)) provides a measure of the size of a system response to a time-varying stimulus. A planar curve tangent to the peak values of an oscillating waveform is called a Hilbert envelope. Such an envelope is a series of pathways that extend between a nonlinear waveform’s maximum values. In other words, a Hilbert envelope provides a ‘Fingerprint’ of the spectral flow of an oscillating waveform  in as much as an envelope is tangent to every maximal value of the waveform. This paper includes an application of Hilbert energy envelope regions in tracking the self-similarities of either walker or runner motion recorded in infrared videos.

Keywords: Aperiodic Waveform, Envelope, Hilbert energy region, Infrared (IR), Motion Waveform, Peak Value, Self-Similarity, Signal energy, Spectral Curve

[This article belongs to Trends in Opto-electro & Optical Communication (toeoc)]

How to cite this article:
Dr. J.F. Peters, E. Cui1. Self-Similarities in Hilbert Envelope Energy Regions on Motion Waveforms Application in Detecting Motion Irregularities in Video Frames. Trends in Opto-electro & Optical Communication. 2024; 14(03):1-10.
How to cite this URL:
Dr. J.F. Peters, E. Cui1. Self-Similarities in Hilbert Envelope Energy Regions on Motion Waveforms Application in Detecting Motion Irregularities in Video Frames. Trends in Opto-electro & Optical Communication. 2024; 14(03):1-10. Available from: https://journals.stmjournals.com/toeoc/article=2024/view=0

Full Text PDF

Full Text PDF

References
document.addEventListener(‘DOMContentLoaded’,function(){frmFrontForm.scrollToID(‘frm_container_ref_114033’);});Edit

  1. Al-Ahmari A, Sinha JK, Asnaashari E. A Comparison Between Hilbert Transform and a New Method for Signal Enveloping. InVibration Engineering and Technology of Machinery: Proceedings of VETOMAC X 2014, held at the University of Manchester, UK, September 9-11, 2014 2015 (pp. 163-172). Springer International Publishing.
  2. Andrade AO, Kyberd P, Nasuto SJ. The application of the Hilbert spectrum to the analysis of electromyographic signals. Information Sciences. 2008 May 1;178(9):2176-93.
  3. Boudraa AO, Salzenstein F. Teager–Kaiser energy methods for signal and image analysis: A review. Digital Signal Processing. 2018 Jul 1;78:338-75.
  4. Cui E, Peters JF. Self-similarities in optical flows: Voxel lumens flux fractality in moving shapes in triangulated video frames. Chaos, Solitons & Fractals. 2022 Nov 1;164:112722.
  5. Deng H, Liu J, Li H. EMD based infrared image target detection method. Journal of Infrared, Millimeter, and Terahertz Waves. 2009 Nov;30:1205-15.
  6. Feldman M. Hilbert transform applications in mechanical vibration. John Wiley & Sons; 2011 Mar 8.
  7. Feldman M, Braun S. Nonlinear vibrating system identification via Hilbert decomposition. Mechanical Systems and Signal Processing. 2017 Feb 1;84:65-96.
  8. Haider MS, Peters JF. Temporal proximities: Self-similar temporally close shapes. Chaos, Solitons & Fractals. 2021 Oct 1;151:111237.
  9. Kaiser JF. On a simple algorithm to calculate the’energy’of a signal. InInternational conference on acoustics, speech, and signal processing 1990 Apr 3 (pp. 381-384). IEEE.
  10. Kido KI. Digital Fourier Analysis: Advanced Techniques. New York, NY: Springer New York. doi. 2015;10:978-1.
  11. Kim AH, Kim IH. Essential spectra of quasisimilar-quasihyponormal operators. Journal of Inequalities and Applications. 2006 Dec;2006:1-7.
  12. Lathi BP, Green RA. Linear systems and signals. New York: Oxford University Press; 2005.
  13. Oppenheim AV. AS Willsky with SH Nawab, Signals and Systems.
  14. Råde L, Westergren B. Mathematics handbook for science and engineering. Berlin: Springer; 1999 May.
  15. Ulrich T. Envelope calculation from the Hilbert transform. Los Alamos Nat. Lab., Los Alamos, NM, USA, Tech. 2006 Mar 17.
  16. W. Weisstein, Self similarity, Wolfram MathWorld 1 (2024), 1, https://mathworld.wolfram.com/Self-Similarity.html.
  17. Krantz S, Rosen KH, Zwillinger D. Standard Mathematical Tables and Formulae.
Regular Issue Subscription Original Research
Volume 14
Issue 03
Received 21/09/2024
Accepted 22/10/2024
Published 18/11/2024
217