Fractal　image　compression　is　a　relatively　recent　image　compression　method,　which　is　simple　to　use　and　often　leads　to　a　high　compression　ratio.　These　advantages　make　it　suitable　for　the　situation　of　a　single　encoding　and　many　decoding,　as　required　in　video　on　demand,　archive　compression,　etc.　There　are　two　fundamental　fractal　compression　methods,　namely,　the　cube-based　and　the　frame-based　methods,　being　commonly　studied.　However,　there　are　advantages　and　disadvantages　in　both　methods.　This　paper　gives　an　extension　of　the　fundamental　compression　methods　based　on　the　concept　of　adaptive　partition.　Experimental　results　show　that　the　algorithms　based　on　adaptive　partition　may　obtain　a　much　higher　compression　ratio　compared　to　algorithms　based　on　fixed　partition　while　maintaining　the　quality　of　decompressed　images.　(c)　2006　Elsevier　Ltd.　All　rights　reserved.