High Order Differentiation Filters that Work

Abstract

Reliable derivatives of digital images have always been hard to obtain, especially (but not only) at high orders. We present new filters that give more accurate derivatives than the traditional Gaussian ones. We show that the traditional filters give incorrect derivatives even for an analytic, noiseless, infinite image, because they smooth the image too much. For a finite interval, the effects of truncating the filter become intolerable for high derivatives. We derive filters that allow a higher amount of noise suppression with less compromise of accuracy than the Gaussian. The filters are easy to compute at arbitrary size. In addition, a general analytic (non-filter) solution is derived for the regularization problem on a finite interval.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1991
Accession Number
ADA234504

Entities

People

  • Isaac Weiss

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Computer Graphics
  • Computer Vision
  • Differential Equations
  • Digital Images
  • Discontinuities
  • Equations
  • Filters
  • Graphics
  • Image Processing
  • Interpolation
  • Intervals
  • Linear Differential Equations
  • Numerical Analysis
  • Polynomials
  • Universities

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Educational Psychology