In this paper, a fast encoding algorithm is developed for fractal image com
pression, At each search entry in the domain pool, the mean square error (M
SE) calculations of the given range block and the eight dihedral symmetries
of the domain block are obtained simultaneously in the frequency domain, i
n which the redundant computations are all eliminated in the new encoding a
lgorithm. It is shown in software simulation that the encoding time is abou
t sis times faster than that of the baseline method with almost the same PS
NR for the retrieved image. The fast algorithm is performed to deal with th
e eight dihedral symmetries at each search entry. Therefore, it can be appl
ied to various enhanced algorithms which are equipped with quadtree, classi
fication, and other mechanism.