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In this paper, spatially and intensity adaptive morphology is introduced and studied in the context of the General Adaptive Neighborhood Image Processing (GANIP) approach. The combination of GAN (General Adaptive Neighborhood)-based filtering and semi-flat morphology is particularly efficient in the sense that the filtering is adaptive to the image spatial structures (structuring elements are spatially variant) and its activity is controlled according to the image intensities (level sets are processed at different scales). The resulting morphological filters show a high image processing performance while preserving the image regions and details without damaging its transitions. The effectiveness of these adaptive operators are practically highlighted on real application examples for image background removing, image restoration and image enhancement.