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Related Experiment Video

Updated: Jul 7, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

A graph-theoretic approach for studying the convergence of fractal encoding algorithm.

J Mukherjee¹, P Kumar, S K Ghosh

¹Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India. jay@cse.iitkgp.ernet.in

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|February 8, 2008

Summary

This study introduces a graph-theoretic approach to fractal encoding convergence using partial iterated function systems (PIFS). It develops fast, linear-time decoding algorithms for both non-contracting and general fractal compression schemes.

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Area of Science:

Computer Science
Image Processing
Graph Theory

Background:

Fractal compression offers high compression ratios but often involves complex decoding.
Partial Iterated Function Systems (PIFS) provide a framework for fractal encoding.
Understanding the convergence properties of fractal encoding is crucial for efficient decoding.

Purpose of the Study:

To present a graph-theoretic interpretation of convergence in fractal encoding using PIFS.
To develop fast, linear-time decoding algorithms for fractal image compression.
To analyze decoding efficiency with and without spatial contraction.

Main Methods:

Graph-theoretic analysis of PIFS convergence.
Development of a linear-time decoding algorithm for non-contracting PIFS.
Extension of the algorithm for PIFS with spatial contraction (on averaging).

Main Results:

A novel graph-theoretic framework for PIFS convergence is established.
A linear-time decoding algorithm is proposed for fractal compression without spatial contraction.
An efficient linear-time decoding algorithm is developed for general fractal compression, yielding results comparable to iterative methods.

Conclusions:

Graph-theoretic interpretation provides insights into fractal encoding convergence.
Fast, linear-time decoding algorithms are achievable for PIFS-based fractal compression.
The proposed algorithms offer a significant improvement in decoding speed without substantial loss in image quality.