Segmentation of step-like signals using fuzzy clustering

Segmentation of step-like signals arises in several application areas; e.g., well-log signal segmentation, ionic-channel signal detection and image segmentation. The objective in processing these signals is to optimally segment the measured signal based on optimization of a criterion function. Recently a sequentially optimum segmentation algorithm is proposed by Moghaddamjoo [13, 14] which performs a reasonable segmentation with affordable computation. This approach, at intermediate and low signal-to-noise ratios (SNRs) has large variances in its estimates. In this work, we apply fuzzy clustering approaches to improve the performance of the aforementioned algorithm at any SNR. In our first approach, we associate a degree of uncertainty to each of the intermediate decisions made by assigning fuzzy membership functions to samples of the signal. These uncertainties, i.e., membership functions, are updated whenever a new decision is made. At the end, a defuzzification approach is used to crystallize the final segmentation of the signal. In the second approach, the fuzzy algorithm starts when the sequentially optimum approach completes its segmentation. Based on this initial segmentation, the fuzzy algorithm defines a set of membership values for each sample point of the signal. The segmentation is then updated by using these membership values. Based on the new estimates of the parameters of the signal, the memberships are recalculated. This updating is continued iteratively until the parameters of the signal converge. At this time a defuzzification algorithm finalizes the segmentation results. Improvement of the results, due to these modifications is significant, especially at low SNRs.