Differentiation of discrete multidimensional signals

Hany Farid, Eero P. Simoncelli

Research output: Contribution to journalArticle

Abstract

We describe the design of finite-size linear-phase separable kernels for differentiation of discrete multidimensional signals. The problem is formulated as an optimization of the rotation-invariance of the gradient operator, which results in a simultaneous constraint on a set of one-dimensional low-pass prefilter and differentiator filters up to the desired order. We also develop extensions of this formulation to both higher dimensions and higher order directional derivatives. We develop a numerical procedure for optimizing the constraint, and demonstrate its use in constructing a set of example filters. The resulting filters are significantly more accurate than those commonly used in the image and multidimensional signal processing literature.

Original languageEnglish (US)
Pages (from-to)496-508
Number of pages13
JournalIEEE Transactions on Image Processing
Volume13
Issue number4
DOIs
StatePublished - Apr 1 2004

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Keywords

  • Derivative
  • Digital filter design
  • Discrete differentiation
  • Gradient
  • Steerability

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design

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