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Hysteresis is an important technique for edge detection, but the unsupervised determination of its parameters is not an easy problem. In this paper, we propose a method for unsupervised determination of hysteresis thresholds using the advantages and disadvantages of two thresholding methods. The basic idea of our method is to look for the best hysteresis thresholds in a set of candidates. First, the method finds a subset and a overset of the unknown edge points set. Then, it determines the best edge map with the measure ??2. Compared with a general method to determine the parameters of an edge detector, our method performs well and is less computationally complex. The basic idea of our method can be generalized to other pattern recognition problems.