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The reconstruction quality of binary ghost imaging depends on the speckle binarization process. In order to obtain better binarization speckle and improve the reconstruction quality of binary ghost imaging, a local adaptive binarization method based on the fuzzy integral is proposed in this study. There are three steps in the proposed binarization process. The first step is to calculate the integral image of the speckle with the summed-area table algorithm. Secondly, the fuzzy integral image is calculated through the discrete Choquet integral. Finally, the binarization threshold of each pixel of the speckle is selected based on the calculated fuzzy integral result. The experiment results verify the feasibility of the proposed method. Compared with other methods qualitatively and quantitatively, the proposed method has high performance in reconstructing image of target.