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A method is presented to interpolate 3D grey-scale image data transformed by elastic deformation. For each new voxel, the Delaunay triangle enclosing this voxel is constructed. The vertices of Delaunay triangles are transformed voxels of the source 3D image data. The new voxel value can be obtained by inverse distance-weighted interpolation using the vertices of Delaunay triangles. Moreover, this method is suitable for two dimensional interpolation problem also. Experiments for 2D and 3D medical image elastic deformation show the feasibility of our method.