IFS coding of non-homogeneous fractal images using gröbner basis techniques

Toshimizu Abiko, Masayuki Kawamata

Research output: Contribution to journalArticlepeer-review


This paper proposes a moment based encoding algorithm for iterated function system (IPS) coding of nonhomogeneous fractal images with unequal probabilities. Moment based encoding algorithms for IFS coding of non-homogeneous fractal images require a solution of simultaneous algebraic equations that are difficult to handle with numerical root-finding methods. The proposed algorithm employs a variable elimination method using Gröbner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associatedprobabilities method for the purpose of decreasing the computational complexity of calculating Gröbner bases. Experimental results show that the average computation time for encoding a non-homogeneous fractal image of 256 x 256 pixels and 256 gray levels is about 200 seconds on a PC with a 400MHz AMD K6-III processor.

Original languageEnglish
Pages (from-to)1575-1581
Number of pages7
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number8
Publication statusPublished - 2000
Externally publishedYes


  • Fractal
  • Gröbner basis
  • Image coding
  • Inverse problem
  • Iterated function system

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


Dive into the research topics of 'IFS coding of non-homogeneous fractal images using gröbner basis techniques'. Together they form a unique fingerprint.

Cite this