Variational Deep Unrolling for High-Fidelity Facial Depth Estimation on Mobile Architectures

This paper presents MPID-Net, a physics-informed framework for monocular facial depth estimation designed for mobile deployment. We address the ill-posed nature of single-image depth recovery by integrating Total Variation (TV) and Alternating Direction Method of Multipliers (ADMM) principles directly into a lightweight neural architecture via differentiable optimization layers. We derive the mathematical foundations, including discretized Euler-Lagrange equations and ADMM unrolling, to ensure convergence and physical plausibility. Additionally, we analyze post-training quantization for NPU deployment. With only 2.3 million parameters, MPID-Net achieves state-of-the-art performance on C3I-SynFace and AFLW2000-3D. Our quantized INT8 model operates at 142 FPS on mobile hardware, improving RMSE by 18.7% and SSIM by 23.4% over baselines while maintaining sharp facial boundaries.