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.

翻译：面部关键点追踪在面部识别、表情分析和医学诊断等应用中发挥着至关重要的作用。本文研究了扩展卡尔曼滤波器（EKF）和无迹卡尔曼滤波器（UKF）在确定性与随机性场景下追踪三维面部运动的性能。我们首先分析了状态转移完全确定的无噪声环境，结果表明UKF由于能够捕捉更高阶的非线性特性，其均方误差（MSE）更低，性能优于EKF。然而，当引入随机噪声时，EKF表现出更强的鲁棒性，与对测量噪声和遮挡更为敏感的UKF相比，能保持更低的均方误差（MSE）。我们的研究结果强调，UKF更适用于受控环境下的高精度应用，而EKF则更适合存在不可预测噪声的真实场景。这些发现为在三维面部追踪应用（如动作捕捉和面部识别）中选择合适的滤波技术提供了实践指导。