Abstract
Facial landmark tracking plays a vital role in applications such as facial recognition, expression analysis, and medical diagnostics. In this paper, we consider the performance of the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) in tracking 3D facial motion in both deterministic and stochastic settings. We first analyze a noise-free environment where the state transition is purely deterministic, demonstrating that UKF outperforms EKF by achieving lower mean squared error (MSE) due to its ability to capture higher-order nonlinearities. However, when stochastic noise is introduced, EKF exhibits superior robustness, maintaining lower mean square error (MSE) compared to UKF, which becomes more sensitive to measurement noise and occlusions. Our results highlight that UKF is preferable for high-precision applications in controlled environments, whereas EKF is better suited for real-world scenarios with unpredictable noise. These findings provide practical insights for selecting the appropriate filtering technique in 3D facial tracking applications, such as motion capture and facial recognition.
Abstract (translated)
面部特征点追踪在诸如面部识别、表情分析和医学诊断等应用中扮演着至关重要的角色。本文研究了扩展卡尔曼滤波器（EKF）与无迹卡尔曼滤波器（UKF）在跟踪三维面部运动时，在确定性和随机环境下的性能表现。 首先，我们在没有噪声的环境中进行分析，此时状态转移是完全确定性的。结果显示，由于UKF能够捕捉到更高的非线性特性，因此其均方误差（MSE）低于EKF，从而表现出更好的性能。然而，当引入随机噪声时，EKF展现出更强的鲁棒性，在测量噪声和遮挡的影响下仍能保持更低的均方误差（MSE），而UKF则变得更易受到这些因素的影响。 我们的研究结果表明，对于控制环境中的高精度应用（例如实验室测试条件下的面部追踪），优选使用UKF；而对于存在不可预测噪声的真实世界场景（如视频会议或户外监控中的人脸识别和跟踪），EKF是更合适的选择。这一发现为在三维面部追踪应用（包括动作捕捉和人脸识别）中选择合适的滤波技术提供了实用的见解。
URL
https://arxiv.org/abs/2502.15179
