For ’th point, there can be two different conditions: totally belonging to one cluster or belonging to several clusters at same time. When the normalized distance between this point and the ’th cluster center is small enough, this point shall totally belong to the ’th class as shown by Eqs. (13) and (14): Display Formula
(14)where represents the degree of the fuzzy membership with which the ’th point belongs to the ’th class and is a parameter introduced in the fuzzy function design to adjust the range of acceptance of fuzzy operation. Otherwise, when the distances between ’th point and every cluster center are all larger than , the point shall belong to several clusters and a judgment shall be made to choose the essential clusters as shown by Eqs. (15) and (16): Display Formula
(16)where means the minimum value of and , which can ensure the pixel far from the cluster center has no effect on the membership calculation. And means the distance between ’th point and ’th cluster is too large so that the membership of ’th point to ’th cluster shall be set to 0.