Image segmentation is a crucial step in image processing. The method based on fuzzy cluster is one of the most effective methods for image segmentation by which most images can be accurately segmented using algorithms. Many inevitable geometric noises are found in a remote sensing image with the improvement of resolution ratio. Generally

the geometric noises need to be ignored in the image segmentation because they usually belong to either the main cluster or those that cannot be considered as a cluster. The traditional FCM algorithm and its improved algorithms use the membership degree as the common segmentation criterion. If there are geometric noises in the image

the clustering centers of traditional algorithm are very susceptible to the effects of the geometrical noise which easily causes them to be located in the wrong position. As a result

the traditional algorithms are difficult to be correctly segmented in this kind of image. In order to segment the geometrical noises image well

a new clustering algorithm called the "remote sensing images Fuzzy segmentation algorithm using inclusion degree and membership degree" is being proposed in this paper. The inclusion degree is proposed as a new measure to describe the relationship between pixels and clusters. Normally

the clusters should possess inclusion degree for every pixel with different levels. The proposed algorithm uses the inclusion degree combined with the traditional membership degree to segment the remote sensing images by defining a new objective function. The proposed algorithm gets the optimum inclusion degree and membership degree through continuous iteration to minimize the objective function. The pixel is classified to the cluster with the maximum value of the product of membership degree and inclusion degree. Finally

the average gray value of pixels within a class is used to display the segmentation results. First

in order to prove the effect of the inclusion degree

some point sets are generated to simulate the cluster and the geometrical noises. The results show that FCM algorithm can segment the cluster well when there are no geometrical noises existing in the image and when the cluster centers are located at the right position

which is at the center of the two clusters' respective point sets. However

after adding the geometrical noises

the cluster centers are seriously affected and located to the wrong place

which is at the center of the noises. On the one hand

the proposed algorithm can resist the effects of the geometrical noise keeping the cluster center on their respective point sets. In addition

this paper uses the proposed algorithm to segment the simulated image and the real remote sensing images

which it is further compared with the traditional FCM algorithm and the FLICM algorithm. The proposed algorithm has higher accuracy than the FCM algorithm and the FLICM algorithm based on the results of the experiment. The results illustrate that the proposed algorithm can eliminate the effect of the geometric noises. On the other hand

the other two algorithms cannot overcome the effect of the geometric noises in the wrong segmentation results wherein the geometric noises were regarded as independent clusters. In order to quantitatively analyze the proposed algorithm

the producer

user and overall accuracies and Kappa coefficient are calculated from the confusion matrix

and they are compared with the proposed algorithm

FCM algorithm and FLICM algorithm. The results showed that the accuracy of the proposed algorithm is higher than the other two accuracies and the Kappa coefficient. This paper proposed a new measure to describe the relationship between the clusters and the pixels based on the traditional membership degree. The proposed fuzzy segmentation algorithm combines the respective advantages of membership degree and inclusion degree for remote sensing image. The advantages of proposed algorithm include fast running speed and an easily understandable theory. The experimental results show that the proposed algorithm is capable of resisting the effect of geometrical noises by considering the inclusion degree

and it can segment remote sensing images more accurately than other algorithms. Hence

the proposed algorithm is an appropriate algorithm for images with geometric noises. However

the proposed algorithm will be restricted because it does not quote the neighborhood information

which is necessary in the next steps of image processing.