How to Transform and Filter Images using Iterated Function Systems

TL;DR

This paper introduces a comprehensive theory of fractal transformations that enables advanced filtering and transforming of digital images, integrating fractal geometry and chaotic dynamics for novel image processing techniques.

Contribution

It generalizes previous fractal top methods by developing a unified framework for fractal-based image filtering and transformation.

Findings

Established the mathematical foundation for fractal image transformations.

Demonstrated applications to digital image filtering and transformation.

Showed how chaotic dynamics enhance fractal image processing.

Abstract

We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous representations. The underlying mathematics is established and applications to digital imaging are described and exemplified.