Fractal image compression (FIC) is a lossy compression method that has the potential to improve the performance of image transmission and image storage and provide security against illicit monitoring. The important features of FIC are high compression ratio and high resolution of decompressed images but the main problem of FIC is the computational complexity of the algorithm. Besides that, the FIC also suffers from a high number of Mean Square Error (MSE) computations for the best matching search between range blocks and domain blocks, which limits the algorithm. In this thesis, two approaches are proposed. Firstly, a new algorithm based on Imperialist competitive algorithm (ICA) is introduced. This is followed by a two-tier algorithm as the second approach to improve further the performance of the algorithm and reduce the MSE computation of FIC. In the first tier, based on edge property, all the range and domain blocks are classified using Discrete Cosine Transform. In the second tier, ICA is used according to the classified blocks. In the ICA, the solution is divided into two groups known as developed and undeveloped countries to maintain the quality of the retrieved image and accelerate the algorithm operation. The MSE value is only calculated for the developed countries. Experimental results show that the proposed algorithm performed better than Genetic algorithms (GAs) and Full-search algorithm in terms of MSE computation. Moreover, in terms of Peak Signal-to-Noise Ratio, the approaches produced high quality decompressed image which is better than that of the GAs
