Before revision:  We generalize DMA to multifractal detrending moving average (MFDMA) , and then extend one-dimensional MFDMA to two-dimensional version. In the paper, we elaborate one-dimensional and two-dimensional MFDMA theoretically and apply the methods to synthetic multifractal measures  .
After revision:  We generalize DMA to multifractal detrending moving average (MFDMA) , and then extend one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA theoretically and apply the methods to synthetic multifractal measures .