Solving the process of hysteresis without determining the optimal thresholds

Hysteresis is an important edge detection technique, but the unsupervised determination of hysteresis thresholds is a difficult problem. Thus, hysteresis has limited practical applicability. Unimodal thresholding techniques are another edge detection method. They are useful, because the histogram of a feature image (usually the feature image is an approximation of the gradient image) is unimodal, and there are many unsupervised methods to solve this problem. But such techniques do not use spatial information to detect edge points, so their performance is worse than that of the hysteresis. In this paper, we show how to formulate the hysteresis process as a unimodal thresholding problem without determining the optimal hysteresis thresholds. Using similar steps of the Canny edge detector to obtain an approximation of the gradient image we compare the performance of our method against that of a method that determines the best parameters of an edge detector and show that our method performs relatively well. Additionally, our method can adjust its sensitivity by using different unimodal thresholding techniques.