This paper presents a mathematical modeling approach for fall detection using a 3D vision-based contrastive learning framework. Traditional models struggle with high false positives and poor generalization across environments. To address this, we propose a self-supervised contrastive learning model that maps 3D skeletal motion sequences into a low-dimensional embedding space, optimizing feature separation between falls and non-falls. Our method employs spatial-temporal modeling and a contrastive loss function based on cosine similarity to enhance discrimination. By leveraging graph-based feature representation, the model ensures robust performance even with missing or noisy data. Experimental results on benchmark fall detection datasets demonstrate a significant reduction in false positives while maintaining high accuracy, making the framework well-suited for real-world healthcare applications.
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