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The local fuzzy fractal dimension (LFFD) is proposed as a novel representation of local image complexity. The definition of LFFD is an extension of the box-counting dimension of discrete sets by incorporating the fuzzy set. The relationship between LFFD and local intensity changing is investigated by experiments, which proves that LFFD is an important feature of edges and is insensitive to noises. Multi-feature edge extraction is implemented with the LFFD and the Sobel operator. The experimental results show that the incorporation of LFFD in edge extraction improves the quality of edge extraction results.