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Unmixing based fusion aims at generating a high spectral-spatial resolution image (HSS) with the same surface features of the high spatial resolution multispectral image (MS) and low spatial resolution hyperspectral image (HS). In this paper, a new fusion method is proposed to improve the fusion performance by taking further advantage of the distribution characteristics of ground objects. First, we put forward a local adaptive sparse unmixing based fusion (LASUF) algorithm, in which the sparsity of the abundance matrices is appended as the constraint to the optimization fusion, considering the limited categories of ground objects in a specific range and the local correlation of their distribution. Then, to correct the possible original subpixel misregistrations or those introduced by the fusion procedures, a subpixel calibration method based on optimal matching adaptive morphology filtering (OM-AMF) is designed. Experiments on various datasets captured by different sensors demonstrate that the proposed fusion algorithm surpasses other typical fusion techniques in both spatial and spectral domains. The proposed method effectively preserves the spectral composition features of the isolated ground objects within a small area. In addition, the OM-AMF postprocessing is able to spatially correct the fusion results at a subpixel level and preserve the spectral features simultaneously.