In this paper, edge based fractal image compression is proposed for various frequency domains. Range and domain blocks of similar edge property are mapped to lowest DCT coefficient in a vertical and horizontal direction into 2D coordinate System. The proposed algorithm is hybrid approaches which exercise fast Fourier transform (FFT), discrete cosine transform (DCT) and real DCT on edge based FIC. Range and domain block pool searching is proposed using k-nearest neighbor search method. Here dissimilarity or distance measure is used in K-NN search for domain and range block. Three frequency transform is used to compare the performance of edge based FIC for K-NN search strategies. The proposed algorithm focuses on image encoding time consumed in edge based FIC with minimal distortion in the resultant image. Proposed algorithm shows improvement in the quality of decoded image with same encoding time and compression ratio as compared to the existing algorithm. The quality of the decoded image was measured regarding PSNR. Keywords: Fractal image compression, Edge property, Frequency domain, Nearest neighbor, DCT, FFT