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Trends in Opto-electro & Optical Communication Original Research

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

  1. Dr. J.F. Peters Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6
  2. E. Cui1 Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, Manitoba R3T 5V6

Abstract

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 curves 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)) which 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 a walker or runner motion recorded in infrared videos.

Keywords

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