Orthogonal Pyramid Transforms for Image Coding

Edward H. Adelson, Eero Simoncelli

Research output: Contribution to journalArticlepeer-review

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

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'Orthogonal Pyramid Transforms for Image Coding'. Together they form a unique fingerprint.

Cite this