Differentiation of discrete multidimensional signals

Hany Farid, Eero 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 2004

Fingerprint

Invariance
Mathematical operators
Signal processing
Filter
Derivatives
Multidimensional Signal Processing
Rotation Invariance
Directional derivative
Higher order derivative
Numerical Procedure
Higher Dimensions
kernel
Gradient
Optimization
Formulation
Operator
Demonstrate

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

Differentiation of discrete multidimensional signals. / Farid, Hany; Simoncelli, Eero.

In: IEEE Transactions on Image Processing, Vol. 13, No. 4, 04.2004, p. 496-508.

Research output: Contribution to journalArticle

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