Orthogonal Pyramid Transforms for Image Coding

Edward H. Adelson, Eero Simoncelli

Research output: Contribution to journalArticle

Abstract

We describe a set of pyramid transforms that decompose an image into a set of basis functions that are (a) spatial frequency tuned, (b) orientation tuned, (c) spatially localized, and (d) self-similar. For computational reasons the set is also (e) orthogonal and lends itself to (f) rapid computation. The systems are derived from concepts in matrix algebra, but are closely connected to decompositions based on quadrature mirror filters. Our computations take place hierarchically, leading to a pyramid representation in which all of the basis functions have the same basic shape, and appear at many scales. By placing the high-pass and low-pass kernels on staggered grids, we can derived odd-tap QMF kernels that are quite compact. We have developed pyramids using separable, quincunx, and hexagonal kernels. Image data compression with the pyramids gives excellent results, both in terms of MSE and visual appearance. A non-orthogonal variant allows good performance with 3-tap basis kernels and the appropriate inverse sampling kernels.

Original languageEnglish (US)
Pages (from-to)50-58
Number of pages9
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume845
DOIs
StatePublished - Oct 13 1987

Fingerprint

Image Coding
Pyramid
pyramids
Image coding
coding
Mathematical transformations
Transform
kernel
taps
Data compression
Digital filters
Basis Functions
Sampling
Decomposition
data compression
Inverse Sampling
Decompose
Staggered Grid
quadratures
Matrix Algebra

ASJC Scopus subject areas

  • Applied Mathematics
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Electrical and Electronic Engineering
  • Computer Science Applications

Cite this

Orthogonal Pyramid Transforms for Image Coding. / Adelson, Edward H.; Simoncelli, Eero.

In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 845, 13.10.1987, p. 50-58.

Research output: Contribution to journalArticle

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