An Image Segmentation Algorithm Based On Internal Type-2 Fuzzy C-Means

Image segmentation is the basis of image analysis, recognition and understanding. It is mainly about the technology that we use to partition an image into some different regions with some specific properties and pick up the parts we are interested in. For many years, a lot of scholars focus on the study in this field. But because of the uncertainty of image itself and the presence of noise, image segmentation has always been a great problem. Nowadays, there is no a method could suitable for every kind of image to get best segmentation result. Recently some researchers have introduced fuzzy theory in to image segmentation field whereas fuzzy mathematics theory can describe uncertain information even better and fuzzy threshold methods and fuzzy clustering segmentation methods are the two kind methods which are developing rapidly. But the effect is not ideal because the fuzzy quality of traditional fuzzy set is not very high and the results of fuzzy C-Means (FCM) algorithm strongly depend on the initialization process. So we introduce type-2 fuzzy sets in this paper and make some improvement on traditional FCM based on type-2 fuzzy theory.The theory of type-2 fuzzy set was published by Professor Zadeh in 1965. Compared to traditional fuzzy sets, type-2 fuzzy sets have much higher fuzzy quality and can describe uncertain information even integrally. In this paper, we discuss the concept and qualities of type-2 fuzzy sets deeply and create internal type-2 fuzzy C-Means algorithm. Internal type-2 FCM has better performance in image segmentation field. We extend the patterns set into an internal type-2 fuzzy set by using two different weight exponents such as m₁ and m₂ and established the primary membership function. In the meantime, the two different exponents create a footprint of uncertainty which describe the uncertain information of image itself and we get a better result of segment- ation. We also have some analysis on type-reduction process of internal type-2 FCM which is the most complex part and character of this arithmetic, so it is also the most important part in this paper.Although internal type-2 FCM still has some problems but we should not ignore the advantage of type-2 fuzzy sets. Especially when we solve the problems with high uncertainties, type-2 fuzzy sets have much better performance than traditional fuzzy sets.