Doubly Smoothed Density Estimation with Application on Miners' Unsafe Act Detection

TL;DR

This paper introduces a doubly smoothed density estimator for anomaly detection in fixed-camera images, improving accuracy and efficiency, and demonstrates its effectiveness in mine safety monitoring with high detection accuracy.

Contribution

The paper proposes a novel doubly smoothed density estimator that leverages spatial structure, along with a grid point approximation for efficient computation, enhancing anomaly detection in images.

Findings

GPA-DS achieves the lowest MSE in simulations.

GPA-DS operates at near real-time speed.

In case study, the method detects unsafe acts with approximately 99% accuracy.

Abstract

We study anomaly detection in images under a fixed-camera environment and propose a \emph{doubly smoothed} (DS) density estimator that exploits spatial structure to improve estimation accuracy. The DS estimator applies kernel smoothing twice: first over the value domain to obtain location-wise classical nonparametric density (CD) estimates, and then over the spatial domain to borrow information from neighboring locations. Under appropriate regularity conditions, we show that the DS estimator achieves smaller asymptotic bias, variance, and mean squared error than the CD estimator. To address the increased computational cost of the DS estimator, we introduce a grid point approximation (GPA) technique that reduces the computation cost of inference without sacrificing the estimation accuracy. A rule-of-thumb bandwidth is derived for practical use. Extensive simulations show that GPA-DS achieves the lowest MSE with near real-time speed. In a large-scale case study on underground mine surveillance, GPA-DS enables remarkable sub-image extraction of anomalous regions after which a lightweight MobileNet classifier achieves $\approx$99\% out-of-sample accuracy for unsafe act detection.