Fuzzy Clustering Algorithms For Image Segmentation

Classic image segmentation involves an analysis or manipulation of image data defined in regular Euclidean spaces.Over the past two decades,a Fuzzy C-Means(FCM)algorithm has been widely applied to classic image segmentation.Due to the diversity and uncertainty of noise in an observed image,the FCM-related algorithms able to remove noise and require less time are not well exploited.G-images refer to image data defined on irregular graph domains.Differing from classic image segmentation,G-image segmentation focuses on developing techniques and tools for segmenting image data defined in irregular graph domains.So far,FCM has never been extended from classic image segmentation to G-image one.To do so,this dissertation work investigates two aspects,i.e.,proposing new FCMs that exhibit excellent segmentation effects and require less time for classic image segmentation,and extending the existing FCMs from classic image segmentation to G-image one.For the two investigations,this dissertation work makes the following four contributions as follows:1)Considering the impact of a feature space on FCM's segmentation performance,it elaborates on excellent FCM algorithms incorporating image filtering and feature extraction for classic image segmentation.First,it presents an FCM framework that consists of four basic stages,i.e.,image filtering,feature decomposition,fuzzy clustering,and feature reconstruction.Morphological grayscale reconstruction is employed for image filtering.Tight wavelet frame transform is used to realize feature decomposition and reconstruction.Second,to enhance FCM's computational efficiency,this work reports sparse regularizationbased FCM(SRFCM)where a sparse regularization term on a partition matrix is introduced into FCM's objective function.Third,to improve FCM's segmentation accuracy,this work comes up with Kullback-Leibler divergence-based FCM(KLDFCM)by introducing a Kullback-Leibler divergence term on a partition matrix into FCM's objective function.Experimental results for synthetic,medical and real-world images indicate that SRFCM and KLDFCM have great ability for multiphase image segmentation,and perform better than other FCM-related algorithms.Moreover,they require less time than most of the existing ones.2)This work reveals the impact of noise estimation on FCM's segmentation performance.First,by integrating into FCM a residual-related regularization term derived from the distribution characteristic of different types of noise,it elaborates a residual-driven FCM(RFCM)framework for classic image segmentation,which is the first approach that realizes accurate residual(noise/outliers)estimation and makes it possible for noise-free image to participate in clustering.Built on the RFCM framework,this work presents a weighted l2norm regularization term by weighting mixed noise distribution,thus resulting in a universal RFCM algorithm in presence of mixed or unknown noises,i.e.,Residual-driven FCM with weighted l2-norm regularization(WRFCM).Supporting experiments on synthetic,medical,and real-world images are conducted.The results demonstrate the higher effectiveness and efficiency of the proposed algorithm than its peers.To demonstrate RFCM's high effectiveness and efficiency over other noise-estimation-based FCM algorithms,this work makes a comparative study of deviation-sparse FCM(DSFCM)and RFCM.It demonstrates that an RFCM framework can realize more accurate noise estimation than DSFCM when different types of noise are involved.It also shows that DSFCM is a particular case of RFCM theoretically.By approximating Poisson noise with a normal distribution,this work models a novel regularization term suitable for Poisson noise estimation.Built on the RFCM framework,it proposes a new RFCM algorithm in presence of Poisson noise.Moreover,the augmented regularization term is extended to mixed Poisson-Gaussian noise estimation,thus resulting in an RFCM algorithm in presence of mixed Poisson-Gaussian noise.3)Since noise or outliers are sparse in some transformed domain,this work develops a residual-sparse FCM algorithm for image segmentation,which overcomes DSFCM's defect that noise sparsity is not fully analyzed.Morphological reconstruction is first used to filter an observed image.By combining the observed and filtered images,a weighted sum image is generated.Tight wavelet frame decomposition is used to transform the weighted sum image into its corresponding feature set.Taking such feature set as data for clustering,this work proposes l0-norm regularization-based FCM(LRFCM)by imposing an l0-norm regularization term on residual to FCM's objective function.With a spatial information constraint,LRFCM's segmentation accuracy is improved.To further enhance its segmentation accuracy,morphological reconstruction is employed to smoothen the generated labels.Based on the prototypes and smoothed labels,a segmented image is reconstructed by using tight wavelet frame reconstruction.Experimental results reported for synthetic,medical,and real-world images show that the proposed algorithm is effective and efficient,and outperforms its peers.4)For the first time,this work elaborates FCM algorithms for G-image segmentation.First,it presents the concept and mathematical definition of G-image.A G-image can be modelled as a real-valued function residing on vertices of a graph.Second,this work proposes an FCM framework incorporating spatial information and feature extraction for G-image segmentation.It commonly consists of four stages,i.e.,G-image filtering,feature decomposition,fuzzy clustering,and feature reconstruction.Tight wavelet frame transform is used to realize feature decomposition and reconstruction.Built on the FCM framework,this work develops two excellent FCM algorithms for G-image segmentation.A waveletframe-based FCM(W-FCM)algorithm is first proposed,where a filtered term is introduced into FCM's objective function.To make FCM robust to noise,an observed G-image is first filtered by using its spatial information.Experimental results reported for synthetic and real images on graphs demonstrate that W-FCM is effective and efficient.To further improve W-FCM's segmentation accuracy,this work elaborates on a similarity-preserving FCM algorithm.To preserve the membership similarity between an arbitrary image pixel and its neighbors,a Kullback-Leibler divergence term on a partition matrix is introduced as a part of FCM.As a result,similarity-preserving FCM is developed by considering spatial information of image pixels for its robustness enhancement.Experiments on synthetic and real-world G-images demonstrate that it indeed achieves higher robustness and performance than the state-of-the-art segmentation algorithms.Moreover,it requires less computation than most of them.