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Image classification under foggy conditions remains a critical challenge for computer vision systems in autonomous vehicles, surveillance, and remote sensing. While deep learning approaches have shown promise, they often require large datasets and extensive computational resources, while traditional methods struggle with feature extraction in varying fog densities. This paper presents a novel hybrid approach that combines the feature extraction power of ResNet-50 with the classification robustness of Support Vector Machines (SVM) to distinguish between clear, low fog, and dense fog scenes efficiently. Our method leverages transfer learning from ImageNet to extract discriminative features using ResNet-50, followed by SVM classification, which enhances generalization on limited training data. Experiments on benchmark foggy image datasets demonstrate that our approach achieves 83.39% accuracy (improving upon pure ResNet-50 by 0.53% and SVM on handcrafted features by 8.51%. Additionally, the SVM's decision boundaries provide interpretability, identifying key fog-affected features—a crucial advantage for safety-critical applications. This work bridges the gap between deep learning performance and traditional machine learning efficiency, offering a practical solution for real-time foggy image classification in edge devices.