Pythagorean fuzzy C-means algorithm for image segmentation

In recent decades, image segmentation has aroused great interest of many researchers, and has become an important part of machine learning, pattern recognition, and computer vision. Among many methods of image segmentation, fuzzy C-means (FCM) algorithm is undoubtedly a milestone in unsupervised method. With the further study of FCM, various different kinds of FCM algorithms are put forward to deal with the specific problems in image segmentation. Because there exist uncertainties in different regions of the image and similarity in the same region, reducing the uncertainty is still the main problem in image segmentation. Considering that Pythagorean fuzzy set (PFS) is a powerful tool to deal with uncertainty, in this paper, we use PFS to describe the uncertainty of image segmentation, including introducing fuzzification and defuzzification process and Pythagorean fuzzy element to describe the membership degree of pixel, combine the neighborhood information with weights and Pythagorean fuzzy distance, and propose Pythagorean fuzzy C-means (PFCM) algorithm. Finally, we apply PFCM algorithm in image segmentation, such as different size images and Berkeley Segmentation Data Set to illustrate the effectiveness and applicability of our proposed algorithm. Meanwhile, we do comparison analysis between PFCM, fully convolution network and Deep-image-Prior networks, these results show that our proposed PFCM has good intuition and effectiveness.

Automated summary

This paper introduces the Pythagorean fuzzy set (PFS) to handle uncertainty in image segmentation, proposing the Pythagorean fuzzy C-means (PFCM) algorithm. Experimental results on different images and datasets demonstrate the effectiveness and applicability of the proposed algorithm.