IFS coding of non-homogeneous fractal images using Grobner bases

Toshimizu Abiko, Masayuki Kawamata

Research output: Contribution to conferencePaperpeer-review

4 Citations (Scopus)


This paper proposes a moment based encoding algorithm for iterated function system (IFS) 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 Grobner bases with floating-point coefficients in order to derive a numerically solvable equation with a single unknown. The algorithm also employs a varying associated-probabilities method for the purpose of decreasing the computational complexity of calculating Grobner bases. An experimental result shows that the computational time for encoding the non-homogeneous fractal image `Curl' of 256×256 pixels and 256 gray levels is 207 seconds on a PC with a 233 MHz Pentium II processor.

Original languageEnglish
Number of pages5
Publication statusPublished - 1999 Dec 1
EventInternational Conference on Image Processing (ICIP'99) - Kobe, Jpn
Duration: 1999 Oct 241999 Oct 28


OtherInternational Conference on Image Processing (ICIP'99)
CityKobe, Jpn

ASJC Scopus subject areas

  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


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