Cluster analysis is a crucial issue in multivariate statistics and data science due to its application in various fields. This study proposes a cutting-edge clustering algorithm for image data with important improvements. First, we extract the texture features from each image and represent them as two-dimensional intervals, which serve as effective input data for recognizing similarities between images. Subsequently, we introduce a measure called overlap distance for evaluating the similarity between intervals in multi-dimensional cases. Furthermore, the study develops an automatic fuzzy clustering algorithm specifically designed for images. This algorithm addresses multiple challenges simultaneously, including determining the appropriate number of clusters, identifying specific elements within clusters, and estimating the probability of each element belonging to clusters. In addition, the study implements a Matlab program to test the effectiveness and practical applications of the proposed algorithm. The results obtained from the proposed algorithm outperform those of current methods when applied to datasets with variations in the number of elements, fields, and characteristics of images.