Manual determination of hysteresis thresholds is time-consuming. Several methods approach the problem of unsupervised determination of edge detector parameters, but they require human intervention to establish the initial range of values in which to detect the best parameter value and the result depends on the range of values initially used.In this paper, a method is proposed to determine candidates to hysteresis thresholds in an unsupervised manner. The method provides a criterion to reduce in a significant way the number of initial values to be considered as threshold candidates. The proposed method can be applied to any feature image provided by an edge detector upon which hysteresis must be implemented.