Detection of edges in spectral data III-refinement of the concentration method

Anne Gelb, Dennis Cates

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Edge detection from Fourier spectral data is important in many applications including image processing and the post-processing of solutions to numerical partial differential equations. The concentration method, introduced by Gelb and Tadmor in 1999, locates jump discontinuities in piecewise smooth functions from their Fourier spectral data. However, as is true for all global techniques, the method yields strong oscillations near the jump discontinuities, which makes it difficult to distinguish true discontinuities from artificial oscillations. This paper introduces refinements to the concentration method to reduce the oscillations. These refinements also improve the results in noisy environments. One technique adds filtering to the concentration method. Another uses convolution to determine the strongest correlations between the waveform produced by the concentration method and the one produced by the jump function approximation of an indicator function. A zero crossing based concentration factor, which creates a more localized formulation of the jump function approximation, is also introduced. Finally, the effects of zero-mean white Gaussian noise on the refined concentration method are analyzed. The investigation confirms that by applying the refined techniques, the variance of the concentration method is significantly reduced in the presence of noise.

Original languageEnglish (US)
Pages (from-to)1-43
Number of pages43
JournalJournal of Scientific Computing
Volume36
Issue number1
DOIs
StatePublished - Jul 2008

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Refinement
Jump
Discontinuity
Oscillation
Edge detection
Convolution
Partial differential equations
Image processing
Piecewise Smooth Functions
Zero-crossing
Indicator function
Approximation of Functions
Function Approximation
Edge Detection
Gaussian White Noise
Post-processing
Waveform
Processing
Image Processing
Filtering

Keywords

  • Convolution
  • Edge detection
  • Filtering
  • Fourier data
  • Gaussian noise
  • Piecewise smooth functions

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Software

Cite this

Detection of edges in spectral data III-refinement of the concentration method. / Gelb, Anne; Cates, Dennis.

In: Journal of Scientific Computing, Vol. 36, No. 1, 07.2008, p. 1-43.

Research output: Contribution to journalArticle

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