An analysis of isometry transforms in frequency domain for fast fractal encoding

A new fast fractal encoding algorithm, which minimizes the iterations of isometry transforms for each domain block, is proposed. The effects of isometry transforms are analyzed in the Walsh-Hadamard transform (WHT) domain, and the search for the minimum Euclidean-distance isometry transform to a range block starts with the one having the minimum feature distance. The search is then terminated with the test reports that the remaining isometry transforms have larger distances than current minimum distance. The second and third low frequency coefficients of WHT are used as the features of the image blocks. The simulation results confirmed that our algorithm produces a completely identical fractal code, including minimum distance isometry transform, to that of the conventional full search in reduced time.