Image Segmentation Basing On Fuzzy Set Theory

Image segmentation is the basis of image analysis, recognition and understanding. Image segmentation, partitioning an image into different regions with some specific properties, has always been an important and challenging problem for many years. The main difficulties lie in the great variability of images and the presence of noises.Recently many researchers have introduced fuzzy set theory to image segmentation, which gets better results than traditional algorithm. This paper proposes some modified methods based on the study of fuzzy threshloding methods and fuzzy clustering segmentation methods:1. A thresholding method for image segmentation is presented, basing on two-dimensional maximum fuzzy entropy and genetic algorithm. Utilizing two-dimensional histogram, the method defines a membership function that is more fit for image characteristics, and then gives the description of image's fuzzy entropy. The procedure for finding the optimal combination of fuzzy parameters is implemented by genetic algorithm. Finally, the optimal threshold is determined by maximizing the fuzzy entropy. The experimental results show that the proposed method gives better performance and higher calculation speed, and the ability of resisting noise is improved. For multi-target image segmentation, a three-level thresholding method is presented, basing on fuzzy partition, probability analysis and entropy theory. The method defines different membership functions for dark part, gray part and bright part of the image, and then gives the definition of fuzzy entropy. The concept of exponential entropy is introduced. Finally, the optimal thresholds can be determined by maximizing the fuzzy entropy. A genetic algorithm is employed to reduce the computation time and the storage space. The experimental results show that the proposed method can segment the image effectively and fast.2. An image segmentation method via fuzzy c-means clustering algorithm with spatial information is presented. The method combines the standard fuzzy c-means clustering algorithm with two-dimensional histogram of the image, and modifies the membership function of the FCM for taking into account the spatial information of image data. Fuzzy membership matrix and clustering center is determined according to the principle of minimum square error sum. Finally, the optimal threshold is obtained by the principle of maximum membership, and the image pixels can be categorated into different regions. The experimental results show that the proposed method can segment noisy image effectively. Aiming at the problem of a lot of information loss during the process of image segmentation, this paper adopts MRF theory to integrate the pixels' gray information with the spatial correlation information. The prior spatial constraint is incorporated based on MRF theory and a new clustering object function is presented. Fuzzy membership matrix and clustering center is determined according to the principle of minimum square error sum. Finally, the optimal threshold is obtained by the principle of maximum membership, and the image pixels can be categorated into different regions. The experimental results show that the proposed method can segment the image effectively and properly, and has good performance of resisting noise.