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A non-rigid and precise image registration algorithm based on finite element method (FEM) is presented. The algorithm require to model image as the free-form deformation elastic material, construct the physical model and generate meshes from image datasets. Its characteristic is achieved through a finite-element based scheme and thus control the mesh deformation field to fit the differences of elastic deformation from the moving image to fixed image. Result shows that the algorithm can get accurate result in the problem of elastic image registration.