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Compared with ID grayscale histogram analysis, 2D entropic thresholding makes use of local average as well as pixel gray level. However, it is time consuming to search the threshold vector in the 2D histogram. In the paper, a fast algorithm using wavelet decomposition is proposed, with which a set of candidates of the vector was first obtained in the decomposed histogram. The optimal threshold vector is then obtained without exhaustive searching. Experimental results have shown that our algorithm not only finds the threshold vector as well as Brink's method (1992) but also saves computation costs, using up only 0.53% of the processing time taken by exhaustive searching.