The　Markov　Random　Field　(MRF)　model,　whose　model　parameters　specify　the　amount　of　smoothness　in　an　image,　is　a　popular　approach　to　image　magnification.　The　model　parameters　must　be　estimated　accurately　in　order　to　obtain　an　elegant　solution.　The　conventional　parameter　estimation　methods　consider　an　image　to　be　homogeneous　and　have　a　high　computational　complexity.　However,　images　are　usually　not　homogenous;　using　only　one　set　of　parameters　cannot　describe　a　whole　image　effectively.　We　therefore　devise　an　adaptive　parameter　estimation　method　for　the　MRF　model　to　reduce　the　blocky　artifact　while　preserving　the　edges　in　the　(high-resolution)　HR　image.　In　our　method,　an　initial　estimated　HR　image　is　divided　into　small　blocks,　and　the　respective　parameters　are　then　estimated.　Their　values　are　defined　as　inversely　proportional　to　their　energy　in　the　corresponding　direction.　Then,　the　gradient　descent　algorithm　is　employed　iteratively　to　obtain　an　improved　HR　image　in　a　Bayesian　MAP　framework.　Experimental　results　show　that,　when　compared　to　the　MRF　model　with　a　fixed　set　of　parameters,　using　the　MRF　model　with　our　adaptive　parameter　estimation　method　can　produce　a　magnified　image　with　the　edges　and　texture　well　preserved.　Both　the　PSNR　and　visual　quality　of　our　proposed　method　are　much　better　than　the　fixed-parameter　method.　©　2005　IEEE.