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The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
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Related Experiment Video

Updated: Dec 25, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Multivariate locally stationary 2D wavelet processes with application to colour texture analysis.

Sarah L Taylor1, Idris A Eckley1, Matthew A Nunes1

  • 1Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF UK.

Statistics and Computing
|April 1, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a new framework for analyzing non-stationary multivariate lattice processes. The novel method accurately estimates localized spectrum and cross-covariance, improving texture classification in image processing.

Keywords:
Colour textureLocal coherenceLocal spectrumRandom fieldWavelets

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Area of Science:

  • Statistical Signal Processing
  • Image Analysis
  • Multivariate Data Modeling

Background:

  • Non-stationary multivariate lattice processes require advanced modeling techniques.
  • Existing methods lack the ability to estimate localized spatial properties.
  • Wavelet-based approaches offer potential for analyzing complex spatial data.

Purpose of the Study:

  • To develop a novel framework for modeling non-stationary multivariate lattice processes.
  • To extend the locally stationary wavelet paradigm to a multivariate 2D setting.
  • To enable estimation of spatially localized spectrum and cross-covariance.

Main Methods:

  • Extension of the locally stationary wavelet paradigm.
  • Development of a multivariate two-dimensional framework.
  • Estimation of localized spectrum and cross-covariance.
  • Establishment of associated estimation theory and convergence properties.

Main Results:

  • A novel framework for modeling non-stationary multivariate lattice processes is proposed.
  • The framework allows for estimation of spatially localized spectrum and cross-covariance.
  • Estimation theory confirms the framework's proper definition and convergence.
  • Successful application in classifying color textures, outperforming state-of-the-art methods.

Conclusions:

  • The developed multivariate spatial framework is robust and effective.
  • This model-based approach significantly enhances texture classification accuracy.
  • The framework provides a powerful tool for analyzing complex spatial data.