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We propose and evaluate a number of novel improvements to the mesh-based coding scheme for 3-D brain magnetic resonance images. This includes: 1) elimination of the clinically irrelevant background leading to meshing of only the brain part of the image; 2) content-based (adaptive) mesh generation using spatial edges and optical flow between two consecutive slices; 3) a simple solution for the aperture problem at the edges, where an accurate estimation of motion vectors is not possible; and 4) context-based entropy coding of the residues after motion compensation using affine transformations. We address only lossless coding of the images, and compare the performance of uniform and adaptive mesh-based schemes. The bit rates achieved (about 2 bits per voxel) by these schemes are comparable to those of the state-of-the-art three-dimensional (3-D) wavelet-based schemes. The mesh-based schemes have been shown to be effective for the compression of 3-D brain computed tomography data also. Adaptive mesh-based schemes perform marginally better than the uniform mesh-based methods, at the expense of increased complexity.