图像分割是计算机视觉领域中的经典任务之一，本文从模糊数学领域着手，以模糊C 均值算法作为出发点，根据实际应用场景中数据集形状分布以及借鉴模糊数学中直觉模糊集（Intuitionistic fuzzy set）的概念，提出了改进的基于马氏距离的直觉模糊C 均值算法。其次利用了The Oxford-III Pet Dataset数据集中呈椭圆状分布的彩色图片像素集，选用马氏距离作为模糊聚类目标函数中的距离测度。最后针对无噪声和含噪声的情况下对包含改进的基于马氏距离的直觉模糊C 均值算法在内的4 种算法进行对比，表明了我们的算法在一定场景下能够帮助聚类效果得到一定提升。本文的创新点主要表现在：

• 在模糊聚类算法的目标函数中，提出了基于香农熵的正则项，提升了一定的聚类表现；

• 引入了直觉模糊集来进一步刻画不确定性信息，基于此基础提出了基于马氏距离的直觉模糊C 均值算法，以符合实际应用场景中常见的椭圆型分布数据；

实验表明，本文提出的改进的基于马氏距离的直觉模糊C 均值算法在无噪声和含噪声的影响下均能提升一定效果并提高抗噪的鲁棒性。

Image segmentation is one of the classic tasks in computer vision. Our paper starts from the field of fuzzy mathematics, takes the fuzzy C-mean algorithm (FCM) as the starting point, and proposes an improved intuitionistic FCM algorithm based on the Mahalanobis distance (Mah_IFCM) according to the distribution of the dataset in the practical scenarios as well as by drawing on the concept of the Intuitionistic fuzzy set. Secondly, using the elliptically distributed image in The Oxford-III Pet Dataset, the Mahalanobis distance is chosen as the distance measure in the objective function. Finally, four algorithms including our Mah_IFCM are compared for noise-free and noise-containing scenarios, which shows that our algorithm can help to improve the clustering performance in certain scenarios. The innovations of this paper are mainly shown in:

• In the objective function of the fuzzy clustering algorithm, a regular term based on Shannon entropy is proposed, which improves the clustering performance to a certain extent;

• Intuitionistic fuzzy sets are introduced to characterize the uncertainty. Then our Mah_IFCM is proposed to conform to the ellipsoidal distribution data;

Experiments show that the Mah_IFCM algorithm proposed in this paper can enhance certain effects and improve the robustness of anti-noise under the influence of both noise-free and noise-containing.