Studies On Clustering Algorithms Based On Weak Fuzzy Partition And Image Segmentation Methods Based On Fuzzy Set Theory

Fuzzy set(FS)theory is an effective tool for dealing with uncertainty and inaccuracy issues.Fuzzy partition and its related theory are an important aspect of the study of fuzzy set.The application of the classification fuzzy partition has some limitations due to its probabilistic constraints.The possibilitic partition or the weak partitioin lose the constraints and have more flexibility.Therefore,this paper mainly studied fuzzy set theory,weak partition theory,and possibilistic c-mean clustering algorithm and their application on the noisy image segmentation.The main work of this paper is as follows:1.Considering the limitation of the application of the classical fuzzy partition on the image segmentation,a one-dimensional(1D)weak fuzzy partition and two-dimensional(1D)weak fuzzy partition and their corresponding fuzzy partition entropies are constructed based on a generalized fuzzy complement operator.Moreover a nest optimization method for segmenting gray image based on the proposed 1D weak fuzzy partition entropy(1DWFPE),2D fuzzy partition entropy(2DWFPE)and an improved uniformity measure.2.A novel adaptive algorithm for segmenting uneven lighting images with strong noise injection is proposed based on fuzzy theory,wave transformation and non-local spatial information.To reduce the influence of the uneven lighting on the image segmentation,the relative characteristics of a pixel in different direction are determined utilizing the fuzzy membership,thus achieving wave transform.Finally,a global method based on intuitionistic fuzzy entropy is employed on the wave transformation image to obtain the segmented result.3.To solve the coincident clustering problem of the possibilistic c-means clustering(PCM)algorithm based on possibilistic partition,a cutset-type possibilistic c-means clustering(C-PCM)algorithm is proposed by introducing the cutset idea in the fuzzy set theory.Meanwhile,an adaptive method for determining the cutset threshold is given and the impact of the penalty factor on the performance of the proposed C-PCM algorithm is also studied.In addition,a novel segmentation method for images corrupted by salt-and-pepper noise is proposed by taking advantage of strong robustness to outliers and good noise-identification ability of the C-PCM algorithm.4.To solve the coincident clustering problem of PCM,a suppressed possibilistic clustering(S-PCM)algorithm is presented by introducing a suppressed competitive learning strategy from another perspective to improve the between-class relationship.Two determination methods are given to adaptively determine the suppressed rate and the penalty factor.Moreover,a suppressed possibilistic Gustafson-kessel clustering(S-PGK)algorithm is proposed which is more applicable for ellipsoidal dataset than S-PCM.A new method for segmenting color images with salt&pepper noise is also proposed based on the S-PCM and S-PGK algorithms.