Fractal image compression with adaptive quadtree partitioning and non-linear affine map

Abstract

Fractal image compression techniques are now very popular for its high compression rates and resolution independence property. However, the qualities of decoded images of the existing techniques are not satisfactory. An adaptive partitioning scheme can improve the image quality significantly. These existing adaptive techniques use linear affine maps during encoding that have limited pixel intensity approximation ability. In order to increase the image quality further, non-linear affine maps can be used that generalizes the pixel intensity approximation and generates much better approximation. Here, a fractal based technique for image compression using non-linear contractive affine maps has been proposed that applies adaptive quadtree partitioning to partition image in a context dependent way to enhance decoded image quality. The technique partitions twice an image to be compressed to obtain collection of ranges and domains and finds the highest matching non-linear affine transformed domain of each range. The corresponding affine parameters are kept in the compressed file. However, a range may be broken into sub-ranges using adaptive quadtree partitioning for unavailability of enough matching domains and repeat the same on those. The comparative results show that the proposed technique greatly improves the decoded image quality than existing techniques and also maintains the high compression ratios. Two variants have also been proposed that improve compression ratio of the proposed technique without any degradation of image quality using loss-less coding.