Shiftable multiscale transforms

Eero Simoncelli, William T. Freeman, Edward H. Adelson, David Heeger

Research output: Contribution to journalArticle

Abstract

One of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal and, in two dimensions, rotations of the input signal. The authors formalize these problems by defining a type of translation invariance called shiftability. In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be applied in the context of other domains, particularly orientation and scale. Jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored. Two examples of jointly shiftable transforms are designed and implemented: a 1-D transform that is jointly shiftable in position and scale, and a 2-D transform that is jointly shiftable in position and orientation. The usefulness of these image representations for scale-space analysis, stereo disparity measurement, and image enhancement is demonstrated.

Original languageEnglish (US)
Pages (from-to)587-607
Number of pages21
JournalIEEE Transactions on Information Theory
Volume38
Issue number2 pt II
DOIs
StatePublished - 1992

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Invariance
Wavelet transforms
Image enhancement
lack
Sampling

ASJC Scopus subject areas

  • Information Systems
  • Electrical and Electronic Engineering

Cite this

Shiftable multiscale transforms. / Simoncelli, Eero; Freeman, William T.; Adelson, Edward H.; Heeger, David.

In: IEEE Transactions on Information Theory, Vol. 38, No. 2 pt II, 1992, p. 587-607.

Research output: Contribution to journalArticle

Simoncelli, Eero ; Freeman, William T. ; Adelson, Edward H. ; Heeger, David. / Shiftable multiscale transforms. In: IEEE Transactions on Information Theory. 1992 ; Vol. 38, No. 2 pt II. pp. 587-607.
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