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Deep learning models have achieved significant success in various image-related tasks. However, they often encounter challenges related to computational complexity and overfitting. In this paper, we propose an approach that leverages efficient polygonal representations of input images by utilizing either dominant points or coordinates of contours. Our method transforms input images into polygonal forms using one of these techniques, which are then employed to train deep neural networks. This representation offers a concise and flexible depiction of images. By converting images into either dominant points or contour coordinates, we substantially reduce the computational burden associated with processing large image datasets. This reduction not only accelerates the training process but also conserves computational resources, rendering our approach suitable for real-time applications and resource-constrained environments. Additionally, these representations facilitate improved generalization of the trained models. Both dominant points and contour coordinates inherently capture essential features of the input images while filtering out noise and irrelevant details, providing an inherent regularization effect that mitigates overfitting. Our approach results in lightweight models that can be efficiently deployed on edge devices, making it highly applicable for scenarios with limited computational resources. Despite the reduced complexity, our method achieve performance comparable to state-of-the-art methods that use full images as input. We validate our approach through extensive experiments on benchmark datasets, demonstrating its effectiveness in reducing computation, preventing overfitting, and enabling deployment on edge computing platforms. Overall, this work presents a methodology in image processing that leverages polygonal representations through either dominant points or contour coordinates to streamline computations, mitigate overfitting, and produce lightweight models suitable for edge computing. These findings indicate that this approach holds significant potential for advancing the field of deep learning by enabling efficient, accurate, and scalable solutions in real-world applications. The code for the experiments of the paper are provided at \url{https://anonymous.4open.science/r/PolygoNet-7374}