Robust Intuitionistic Fuzzy c-Means Clustering Algorithm for Brain Image Segmentation
03 Apr 2018-pp 0781-0785
TL;DR: A novel approach, namely the Robust and improved intuitionistic fuzzy c-means clustering algorithm (RIIFCM) is proposed, which is robust to noise as it considers local spatial information and outperforms the other existing algorithms by calculating the similarity indices, false positive ratio (FPR) and false negative ratio (fNR).
Abstract: The segmentation of the human brain magnetic resonance imaging (MRI) plays a highly decisive role in diagnosing numerous diseases like tumors, Alzheimer's disease, edema, dementia etc. But it is a very challenging task because of presence of noise in the MRI images and also because the boundaries between different tissues of the brain cannot be easily distinguished. Standard fuzzy c-means clustering (FCM) method is proposed to segment the brain MRI accurately and to handle the noise. There are many variants of FCM and one such variant is the Intuitionistic fuzzy c-means clustering algorithm (IFCM). It incorporates the advantages of intuitionistic fuzzy set theory. The IFCM handles the uncertainty, but is not robust to noise as it does not consider any local spatial information. Hence, in this paper a novel approach, namely the Robust and improved intuitionistic fuzzy c-means clustering algorithm (RIIFCM) is proposed. This algorithm is robust to noise as it considers local spatial information. We have demonstrated the efficiency of the RIIFCM algorithm compared to six other algorithms used for the brain image segmentation. The segmentation is carried out on a simulated MRI brain image and we demonstrate that the RIIFCM algorithm outperforms the other existing algorithms by calculating the similarity indices, false positive ratio (FPR) and false negative ratio (FNR).
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TL;DR: The goal of the proposed work is to identify the tumors in MR images using segmentation methods and to locate the affected regions of the brain more accurately and these results are compared with the conventional fuzzy C means (FCM) method.
Abstract: In the field of medical sciences, automatic detection of tumor using magnetic resonance (MR) brain images is a major research area. The goal of the proposed work is to identify the tumors in MR images using segmentation methods and to locate the affected regions of the brain more accurately. Medical images have vast information but they are difficult to examine with lesser computational time. An innovative process is proposed to extract tumor cells using the discrete wavelet transform (DWT). After extracting features with DWT feature reduction is carried out with the principal component analysis (PCA). Modified fuzzy C means (MFCM) technique is used for segmenting the tumor cells. The efficiency of the proposed method to identify different abnormalities in real MR images for intracranial neoplasm detection, tuberculoma, and bilateral thalamic fungal granulomas identification is tested. The results obtained are shown in‐terms of Accuracy, Dice Similarity Index (DSI), and Jaccard Index (JI) measures. The performance of the proposed method is tested in terms of performance measures like Accuracy, DSI, and JI. These results are compared with the conventional fuzzy C means (FCM) method.
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01 Jan 1967
TL;DR: The k-means algorithm as mentioned in this paper partitions an N-dimensional population into k sets on the basis of a sample, which is a generalization of the ordinary sample mean, and it is shown to give partitions which are reasonably efficient in the sense of within-class variance.
Abstract: The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = {S1, S2, * *, Sk} is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends to be low for the partitions S generated by the method. We say 'tends to be low,' primarily because of intuitive considerations, corroborated to some extent by mathematical analysis and practical computational experience. Also, the k-means procedure is easily programmed and is computationally economical, so that it is feasible to process very large samples on a digital computer. Possible applications include methods for similarity grouping, nonlinear prediction, approximating multivariate distributions, and nonparametric tests for independence among several variables. In addition to suggesting practical classification methods, the study of k-means has proved to be theoretically interesting. The k-means concept represents a generalization of the ordinary sample mean, and one is naturally led to study the pertinent asymptotic behavior, the object being to establish some sort of law of large numbers for the k-means. This problem is sufficiently interesting, in fact, for us to devote a good portion of this paper to it. The k-means are defined in section 2.1, and the main results which have been obtained on the asymptotic behavior are given there. The rest of section 2 is devoted to the proofs of these results. Section 3 describes several specific possible applications, and reports some preliminary results from computer experiments conducted to explore the possibilities inherent in the k-means idea. The extension to general metric spaces is indicated briefly in section 4. The original point of departure for the work described here was a series of problems in optimal classification (MacQueen [9]) which represented special
24,320 citations
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
13,376 citations
TL;DR: A novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data and estimation of intensity inhomogeneities using fuzzy logic and the neighborhood effect acts as a regularizer and biases the solution toward piecewise-homogeneous labelings.
Abstract: We present a novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data and estimation of intensity inhomogeneities using fuzzy logic. MRI intensity inhomogeneities can be attributed to imperfections in the radio-frequency coils or to problems associated with the acquisition sequences. The result is a slowly varying shading artifact over the image that can produce errors with conventional intensity-based classification. Our algorithm is formulated by modifying the objective function of the standard fuzzy c-means (FCM) algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel (voxel) to be influenced by the labels in its immediate neighborhood. The neighborhood effect acts as a regularizer and biases the solution toward piecewise-homogeneous labelings. Such a regularization is useful in segmenting scans corrupted by salt and pepper noise. Experimental results on both synthetic images and MR data are given to demonstrate the effectiveness and efficiency of the proposed algorithm.
1,786 citations
TL;DR: Use of the expectation-maximization (EM) algorithm leads to a method that allows for more accurate segmentation of tissue types as well as better visualization of magnetic resonance imaging data, that has proven to be effective in a study that includes more than 1000 brain scans.
Abstract: Intensity-based classification of MR images has proven problematic, even when advanced techniques are used. Intrascan and interscan intensity inhomogeneities are a common source of difficulty. While reported methods have had some success in correcting intrascan inhomogeneities, such methods require supervision for the individual scan. This paper describes a new method called adaptive segmentation that uses knowledge of tissue intensity properties and intensity inhomogeneities to correct and segment MR images. Use of the expectation-maximization (EM) algorithm leads to a method that allows for more accurate segmentation of tissue types as well as better visualization of magnetic resonance imaging (MRI) data, that has proven to be effective in a study that includes more than 1000 brain scans. Implementation and results are described for segmenting the brain in the following types of images: axial (dual-echo spin-echo), coronal [three dimensional Fourier transform (3-DFT) gradient-echo T1-weighted] all using a conventional head coil, and a sagittal section acquired using a surface coil. The accuracy of adaptive segmentation was found to be comparable with manual segmentation, and closer to manual segmentation than supervised multivariant classification while segmenting gray and white matter.
1,328 citations
01 Aug 2004
TL;DR: Two variants of fuzzy c-means clustering with spatial constraints, using the kernel methods, are proposed, inducing a class of robust non-Euclidean distance measures for the original data space to derive new objective functions and thus clustering theNon-E Euclidean structures in data.
Abstract: Fuzzy c-means clustering (FCM) with spatial constraints (FCM/spl I.bar/S) is an effective algorithm suitable for image segmentation. Its effectiveness contributes not only to the introduction of fuzziness for belongingness of each pixel but also to exploitation of spatial contextual information. Although the contextual information can raise its insensitivity to noise to some extent, FCM/spl I.bar/S still lacks enough robustness to noise and outliers and is not suitable for revealing non-Euclidean structure of the input data due to the use of Euclidean distance (L/sub 2/ norm). In this paper, to overcome the above problems, we first propose two variants, FCM/spl I.bar/S/sub 1/ and FCM/spl I.bar/S/sub 2/, of FCM/spl I.bar/S to aim at simplifying its computation and then extend them, including FCM/spl I.bar/S, to corresponding robust kernelized versions KFCM/spl I.bar/S, KFCM/spl I.bar/S/sub 1/ and KFCM/spl I.bar/S/sub 2/ by the kernel methods. Our main motives of using the kernel methods consist in: inducing a class of robust non-Euclidean distance measures for the original data space to derive new objective functions and thus clustering the non-Euclidean structures in data; enhancing robustness of the original clustering algorithms to noise and outliers, and still retaining computational simplicity. The experiments on the artificial and real-world datasets show that our proposed algorithms, especially with spatial constraints, are more effective.
1,077 citations