Partitioned Fractal Interpolation

Abstract

This chapter studies the application of fractal image coding to interpolate images. It focuses on partitioned fractal image (PFI) representation based on iterated function system (IFS). The convergence of the IFS defined by a contractive transformation is the result of the “fixed‐point theorem”. The direct application of the IFS suggests the representation of any given image as contractive transformation of itself. The main idea of the fractal image interpolation is rather simple. It is based on the assumption that the fractal coding is really a fractal process and the fractal code's attractor is a fractal object. Fractal image representation technique is a block‐based technique, and hence blocking fractal artifact is observed to be heavy and considered to be the most important visual artifact in the decoded image. When this technique is applied to interpolate an image, the blocking artifact is emphasized and is usually highly visible.