目的 传统FCM算法及其改进算法均只采用隶属度作为分割判据实现图像分割。然而，在分割过程中聚类中心易受到同质区域内几何噪声的影响，导致此类算法难以有效分割具有几何噪声的图像。为了解决这一类问题，提出一种利用包含度和隶属度的遥感影像模糊分割算法。方法 该算法假设同一聚类对每个像素都有不同程度的包含度，将包含度作为一种新测度来描述聚类与像素间关系，并将包含度纳入目标函数中。该算法通过迭代最小化目标函数来得到最优的隶属度和包含度，然后，通过反模糊化隶属度和包含度之积实现带有几何噪声的遥感图像的分割。结果 采用本文算法分别对模拟图像，真实遥感影像进行分割实验，并与FCM算法和FLICM算法进行对比，定性结果表明，对含有几何噪声的区域，提出算法的用户精度和产品精度均高于FCM算法和FLICM算法，且总精度和Kappa值也高于对比算法。实验结果表明，本文算法能够抵抗几何噪声对图像分割的影响，且分割精度远远高于其他两种算法的分割精度。结论 提出算法通过考虑聚类对像素的包含性，能够有效抵抗几何噪声对图像分割的影响，使得算法具有较高的抗几何噪声能力，进而提高该算法对含有几何噪声图像的分割精度。提出算法适用于包含几何噪声的高分辨率遥感图像，具有很好的抗几何噪声性。

Objective 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. Method 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. Result 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. Conclusion 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.