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Lightweight weapon detection via fractional-order Legendre polynomials for smart edge devices
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DOI：10.1007/s00371-026-04614-8.png)
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Abstract
En 中文
This study proposes a novel and computationally efficient framework for real-time weapon detection based on fractional-order Legendre polynomials (FLPs). The method integrates a multi-scale analysis strategy, where cascade classifiers first identify candidate regions in video frames, followed by FLP-based feature extraction at three fractional scales ( $$\alpha = 0.5, 1.0, 1.5$$ ). This study focuses on handguns. Extending the approach to rifles, knives, and improvized weapons is planned as future work. Unlike earlier hand crafted features or deep models that often need large memory or GPU support, there is still no compact and scale aware shape descriptor that runs well on small CPU-only devices. Our main idea is to use fractional-order Legendre polynomials to encode multi-scale weapon shape and then verify candidates with a light classifier, which gives strong accuracy with a very small feature budget. Classification was performed using a Support Vector Machine (SVM) with a radial basis function (RBF) kernel, achieving 98.57% accuracy, 100% precision, and 97.28% recall on a balanced dataset of 1,400 images. Compared to traditional methods, the proposed FLP approach outperforms HOG and SURF by 1.43% and 3.21% in accuracy, respectively, while reducing feature dimensionality by 83%. Feature extraction is efficient, requiring only 7.83 ms per frame, and each feature vector occupies just 2.34 KB, compared to HOG’s 13.78 KB. The system operates at 5.45 frames per second (FPS) on standard CPU-only hardware, enabling practical deployment on resource-constrained edge devices. Extensive validation across 41 random data splits confirms high robustness (accuracy: 96.96 ± 0.97%), and a real-world surveillance test over 6,231 frames demonstrates strong false-positive filtering, reducing 708 erroneous detections. By eliminating the need for computationally intensive image pyramids or deep learning models, this fractional-order multi-scale approach offers a lightweight yet highly effective solution for real-time surveillance applications in constrained environments such as smart homes and IoT-based security systems.
Keywords:
Fractional Legendre
Weapon detection
Real-time surveillance
Edge computing
Embedded vision
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