Radon Transform Analysis of a Probabilistic Method for Image Generation

Abstract

The research performed for this grant over the past year involved affine iterated function system (IFS) encoding and IFS mixing for digital images. This relates to a technique of Michael Barnsley's for generating fractal and other images by randomly iterating affine transformations of the plane into itself. By this technique an image is both generated and represented as the long-term probability distribution for a 2-D or 3-D Markov chain. The encoding involves finding an affine 'collage' of the image, whereby it is identified as a convex combination of affinely scaled versions of itself. This permits some remarkable data compression. The mixing involves a merging of IFS's so as to produce images with combined textures. It ties in with the encoding in that a broader class of images can then be efficiently encoded, and there are more degrees of freedom in the encoding search. The mathematical methods used involve stochastic optimization, computational geometry, the Radon transform, dynamical systems and ergodic theory for Markov chains. Keywords: Encoding, Image compression, Image processing, Markov chain.

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Document Details

Document Type
Technical Report
Publication Date
Apr 12, 1989
Accession Number
ADA207814

Entities

People

  • Marc A. Berger

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Algorithms
  • Applied Mathematics
  • Coding
  • Computational Science
  • Computer Graphics
  • Data Compression
  • Digital Images
  • Geometry
  • Image Processing
  • Mathematical Models
  • Mathematics
  • Probability
  • Probability Distributions
  • Three Dimensional
  • Two Dimensional

Readers

  • Artificial Intelligence
  • Computer Vision.
  • Mathematical Modeling and Probability Theory.