Sparse Regularization-Based Fuzzy C-Means Clustering Incorporating Morphological Grayscale Reconstruction and Wavelet Frames

Abstract

Instead of directly utilizing an observed image including some outliers, noise or intensity inhomogeneity, the use of its ideal value (e.g. noise-free image) has a favorable impact on clustering. Hence, the accurate estimation of the residual (e.g. unknown noise) between the observed image and its ideal value is an important task. To do so, we propose an ℓ0 regularization-based Fuzzy C-Means (FCM) algorithm incorporating a morphological reconstruction operation and a tight wavelet frame transform. To achieve a sound trade-off between detail preservation and noise suppression, morphological reconstruction is used to filter an observed image. By combining the observed and filtered images, a weighted sum image is generated. Since a tight wavelet frame system has sparse representations of an image, it is employed to decompose the weighted sum image, thus forming its corresponding feature set. Taking it as data for clustering, we present an improved FCM algorithm by imposing an ℓ0 regularization term on the residual between the feature set and its ideal value, which implies that the favorable estimation of the residual is obtained and the ideal value participates in clustering. Spatial information is also introduced into clustering since it is naturally encountered in image segmentation. Furthermore, it makes the estimation of the residual more reliable. To further enhance the segmentation effects of the improved FCM algorithm, we also employ the morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, the segmented image is reconstructed by using a tight wavelet frame reconstruction operation. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.

AFCM-LSMA: New intelligent model based on Lévy slime mould algorithm and adaptive fuzzy C-means for identification of COVID-19 infection from chest X-ray images

“…Then it is crucial to have a robust technique that permits handling the challenges of medical images. Based on this fact, the Fuzzy C-Means (FCM) is considered one of the most popular approaches for image clustering [26] , [27] , [28] , [29] , [30] , [31] . The FCM is regarded as a part of the unsupervised clustering techniques, and it has been widely used to solve complex problems.…”

“…One of the most common algorithms for clustering is the fuzzy c-means (FCM) [26] ; it is an unsupervised learning method that is simple and can maintain more information than other methods. In medical images, the FCM has been applied in different clustering problems such as [27] , [28] , [29] , [30] , [31] , [32] . The main drawbacks of the FCM are that easily affected by noise and highly time-consuming.…”

Fuzzy STUDENT’S T-Distribution Model Based on Richer Spatial Combination

“…However, FCM performs image segmentation similarly to normal data classification without considering image local spatial information, which leads to the fact that FCM only provides tolerable image segmentation for images with simple objects and backgrounds since it is sensitive to noise, brightness, image details, etc. To improve the performance of FCM on image segmentation, many variants of FCM algorithm have been proposed, we roughly divide these algorithms into three categories: FCM with spatial distance constraints [10][11][12][13][14][15][16][17][18][19], FCM with filtering [20][21][22][23][24][25][26][27][28][29], and FCM with Markov random field (MRF) [31][32][33][34][35].…”

Kernel Probabilistic K-Means Clustering

“…Clustering is an important unsupervised method, and the purpose of clustering is to divide a dataset into multiple clusters (or classes) with high intra-cluster similarity and low inter-cluster similarity. There have been many clustering algorithms, such as k-means (KM) and its variants [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ]. Others are based on minimal spanning trees [ 17 , 18 , 19 ], density analysis [ 20 , 21 , 22 , 23 , 24 , 25 ], spectral analysis [ 26 , 27 ], subspace clustering [ 28 , 29 ], etc.…”

“…The higher the membership degree, the greater the possibility of the data point belonging to the cluster. Although FCM is more flexible in applications [ 11 , 12 , 13 , 14 , 15 , 16 ], it is primarily suitable for linearly separable datasets. Kernel fuzzy c-means (KFCM) [ 34 ] is a significantly improved version of fuzzy c-means for clustering linearly inseparable datasets.…”