Vegetation plays a vital role in preserving the environment and mitigating the effects of climate change. Therefore, it is essential to identify areas of stress and non-vegetation factors to develop a plan to establish vegetation and combat desertification, which positively affects climate change and ensures a sustainable future. Remote sensing and satellite images have been used to identify vegetation areas and their density, which is a challenging problem. According to the literature, the Normalized Difference Vegetation Index (NDVI) is used in most studies to identify vegetation areas, while few utilize fractal dimensions and Land Surface Temperature (LST). Fractals are known for their effectiveness in identifying complex distribution patterns, such as vegetation areas in satellite images. This study will tackle the issue of categorizing the vegetation area into healthy, stressful, and non-vegetation regions based on satellite images. Two clustering methods are applied, namely K-means and threshold-based labelling, to categorize the vegetation area in the three aforementioned areas. The K-means and threshold-based labelling will be evaluated and compared based on the Silhouette score, Davies-Bouldin index (DBI), and Entropy metrics. The effect of selecting the proper features on clustering performance is also studied. The experimental results show that the threshold-based clustering method suits datasets with well-defined threshold boundaries between clusters. Conversely, the K-means clustering method provides flexibility for adaptive clustering with no pre-defined thresholds. Finally, it is worth noting that Fractal dimensions (FD) with threshold-based labelling achieve the best clustering results, making it crucial for detecting vegetation health and analyzing land surfaces.