# Unsupervised Image Classification Based on Fully Fuzzy Voronoi Tessellation
## 1 Introduction  
Image classification plays an important role in image interpretation and is widely used in many fields, such as military reconnaissance, geographic survey, and disaster assessment [1; 2]. In recent years, with the rise of deep learning, a large number of image classification methods based on deep convolutional neural networks have been studied, such as FCN [3; 4], U-Net [5; 6], and DeepLab [7; 8; 9]. However, it has high requirements for the quantity and quality of samples. The generalization performance is insufficient [10]. Therefore, many researchers proposed a new idea of using unsupervised classification methods to generate pseudo-labels before deep learning [11; 12]. It is beneficial for expanding the sample size and improving model performance. Thus, unsupervised image classification, as a crucial prerequisite step for the methods, is still worth challenging. Fuzzy C-means (FCM) is of the commonly used unsupervised methods [13; 14; 15]. It extends hard relationships to fuzzy relationships to improve the uncertainty problem of classification. However, it has many problems when applied to image classification, such as misclassification and the salt/pepper noise phenomenon. That is because the same category in the image is not homogeneous, especially remote sensing images that havethe special characteristics of the same object but different spectra [16; 17]. Fortunately, images have spatial constraint characteristics, i.e., adjacent pixels in space often belong to a category. Therefore, numerous scholars focus on improving classification performance by introducing spatial constraint [18; 19]. To incorporate local spatial information, [PERSON] et al. proposed FCM with a spatial constraint algorithm (FCM_S) [20], which introduced a regularization term modeled by the dissimilarity of neighborhood pixels. FCM_S is more robust to noise than FCM. However, FCM_S needs to calculate neighborhood terms at each iteration, which is very time-consuming. Focusing on this problem, [PERSON] and [PERSON] proposed FCM_S1 and FCM_S2 [21]. They replace the neighborhood term by introducing the mean image and median image in advance, respectively, which can reduce the computational cost. The classification performance of FCM_S1 and FCM_S2 is equivalent to that of FCM_S. Referring to the idea of mean image, [PERSON] et al. proposed the enhanced FCM (EnFCM) [22]. EnFCM constructed a linear weighted image of the original image based on the neighborhood information, and then the image classification was implemented based on the gray level of the linear weighted image. EnFCM is difficult to adaptively determine the strength of neighborhood effects. Thus, [PERSON] et al. proposed the fast generalized FCM (FGFCM) [23]. FGFCM constructed a non-linear weighted image based on both spatial and gray-level information. However, EnFCM and FGFCM all need a parameter to balance detailed information and noise. The selection of this parameter is very important and difficult. To deal with this problem, [PERSON] and [PERSON] proposed the robust fuzzy local information C-means method (FLICM) [24]. The FLICM defined a novel fuzzy factor that is directly derived from the image, which can automatically determine the spatial and gray level relationship. However, FLICM ignored the situation where the central pixel is noisy. [PERSON] et al. [25] proposed the reformulated FLICM (RFLICM). The RFLICM proposed a local coefficient of variation parameter to regulate this situation. RFLICM further improved the impact of noise, but it ignored the influence of spatial constraints on the relationship between the central pixel and adjacent pixels. Then, [PERSON] et al. [26] further proposed the kernel-weighted FLICM (KWFLICM). The KWFLICM proposed a trade-off weighted fuzzy factor and used kernel metric to define the dissimilarity. KWFLICM achieved good results, but it limited the dimensionality of the input image to only one dimension. Thus, [PERSON] and [PERSON] [27] proposed the generalization of KWFLICM (GKWFICM).