Efficient waste management is crucial for urban environments to maintain cleanliness, reduce environmental impact, and optimize resource allocation. Traditional waste collection systems often rely on scheduled pickups or manual inspections, leading to inefficient resource utilization and potential overflow issues. This paper presents a novel approach to automate the detection of garbage container fullness from images using machine learning techniques. More specifically, we explore three transformer-based architectures, namely, vision transformer, Swin transformer, and pyramid vision transformer to classify input images of garbage bins as clean or dirty. Our experimental results on the publicly available Clean dirty containers in Montevideo dataset suggest that transformer-based architectures are effective in garbage fullness detection. Moreover, a comparison with existing methods reveals that the proposed approach using the vision transformer surpasses the state-of-the-art, achieving a 96.74% accuracy in detecting garbage container fullness. In addition, the generalizability of the proposed approach is evaluated by testing the transformer-based classification frameworks on a synthetic image dataset generated using various generative AI models. The proposed approach achieved a highest test accuracy of 80% on this synthetic dataset, thereby highlighting its ability to generalize across different datasets. Synthetic dataset used in this work can be found at: https://www.kaggle.com/datasets/6df0652d2c4eb3b9f00043c40fba0afa0778b46d7c0685e212807c2f6967fe6f.