A type-2 neutrosophic-entropy-fusion based multiple thresholding method for the brain tumor tissue structures segmentation

Abstract

In this paper, we introduce an extension theory of the neutrosophic set (NS) called type-2 neutrosophic set (T2NS). This new theory provides a granular representation of features and helps to model uncertainties with six different memberships very effectively. To demonstrate the real-time application of this theory, a new segmentation method for brain tumor tissue structures in magnetic resonance imaging (MRI) is presented. There are inconsistencies in the gray levels observed in MRIs due to their low illumination. The proposed theory addressed this problem by performing neutrosophication operation on gray levels based on six different membership functions called type-2 neutrosophic membership functions. During segmentation, a concept of T2NS entropy is used to quantify each gray level of MRIs. The proposed method is able to select multiple adaptive thresholds for segmentation of brain tumor tissue structures in MRIs from the locations of maximum entropy values of gray levels. Finally, an image fusion operation is performed on the segmented images with different thresholds to include all features and identify the location of brain tumor. The fusion images are compared with the segmented images obtained by five different methods, including fuzzy c-means algorithm, modified fuzzy c-means algorithm, fuzzy-K-means clustering algorithm, kernel intuitionistic fuzzy entropy c-means and neutrosophic entropy-based adaptive thresholding method. The proposed method achieves Jaccard similarity coefficients of 97.07%, 97.92% and 97.13% in the case of three different sets of MRIs, namely Set I, Set II and Set III, respectively. The proposed method exhibits correlation coefficients of 0.9638, 0.9698 and 0.9610 for the Set I, Set II and Set III of MRIs, respectively. Similarly, the proposed method shows uniformity measures of 0.9624, 0.9633 and 0.9660 for the Set I, Set II and Set III of MRIs, respectively. These three performance evaluation metrics show the effectiveness of the proposed method compared to the existing methods.