Polynomial fitting for edge detection in irregularly sampled signals and images

Rick Archibald, Anne Gelb, Jungho Yoon

Research output: Contribution to journalArticle

75 Citations (Scopus)

Abstract

We propose a new edge detection method that is effective on multivariate irregular data in any domain. The method is based on a local polynomial annihilation technique and can be characterized by its convergence to zero for any value away from discontinuities. The method is numerically cost efficient and entirely independent of any specific shape or complexity of boundaries. Application of the minmod function to the edge detection method of various orders ensures a high rate of convergence away from the discontinuities while reducing the inherent oscillations near the discontinuities. It further enables distinction of jump discontinuities from steep gradients, even in instances where only sparse nonuniform data is available. These results are successfully demonstrated in both one and two dimensions.

Original languageEnglish (US)
Pages (from-to)259-279
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume43
Issue number1
DOIs
StatePublished - 2005

Fingerprint

Edge Detection
Edge detection
Discontinuity
Polynomials
Polynomial
Local Polynomial
Annihilation
One Dimension
Costs
Irregular
Two Dimensions
Jump
Rate of Convergence
Oscillation
Gradient
Zero

Keywords

  • Minmod function
  • Multivariate edge detection
  • Newton divided differencing
  • Non-uniform grids

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Polynomial fitting for edge detection in irregularly sampled signals and images. / Archibald, Rick; Gelb, Anne; Yoon, Jungho.

In: SIAM Journal on Numerical Analysis, Vol. 43, No. 1, 2005, p. 259-279.

Research output: Contribution to journalArticle

Archibald, Rick ; Gelb, Anne ; Yoon, Jungho. / Polynomial fitting for edge detection in irregularly sampled signals and images. In: SIAM Journal on Numerical Analysis. 2005 ; Vol. 43, No. 1. pp. 259-279.
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