Visual Context-Aware Person Fall Detection
Aleksander Nagaj, Zenjie Li, Dim P. Papadopoulos, Kamal Nasrollahi
TL;DR
This work analyzes the existence of $T$-periodic solutions in convex Hamiltonian systems under subquadratic and sublinear growth conditions. It employs a variational dual-action framework, defining a dual functional $\psi$ and exploiting spectral data of the associated linearized operator to derive concrete nontriviality conditions, such as $\lambda+\gamma<0$ and $\gamma< -\lambda < \delta$, that guarantee a $T$-periodic orbit. The results establish when solutions are nonzero for all $t$ and when minimizers have minimal period $T$, and they extend to subharmonics and forcing scenarios via subquadratic at infinity frameworks. Historical context highlights how duality and convexity techniques yield existence and multiplicity results, connecting to prior work by Rabinowitz, Clarke & Ekeland, and Michalek & Tarantello, with practical criteria depending on $A_{\infty},B_{\infty}$ and eigenvalue spectra. The paper thus advances the theory of periodic orbits in Hamiltonian dynamics with precise, verifiable conditions rooted in convex analysis and spectral theory.
Abstract
As the global population ages, the number of fall-related incidents is on the rise. Effective fall detection systems, specifically in healthcare sector, are crucial to mitigate the risks associated with such events. This study evaluates the role of visual context, including background objects, on the accuracy of fall detection classifiers. We present a segmentation pipeline to semi-automatically separate individuals and objects in images. Well-established models like ResNet-18, EfficientNetV2-S, and Swin-Small are trained and evaluated. During training, pixel-based transformations are applied to segmented objects, and the models are then evaluated on raw images without segmentation. Our findings highlight the significant influence of visual context on fall detection. The application of Gaussian blur to the image background notably improves the performance and generalization capabilities of all models. Background objects such as beds, chairs, or wheelchairs can challenge fall detection systems, leading to false positive alarms. However, we demonstrate that object-specific contextual transformations during training effectively mitigate this challenge. Further analysis using saliency maps supports our observation that visual context is crucial in classification tasks. We create both dataset processing API and segmentation pipeline, available at https://github.com/A-NGJ/image-segmentation-cli.