SynDepth-Hybrid: A Semi-Supervised Framework for Monocular Depth Estimation and Refinement using Synthetic Domain Adaptation

Accurate monocular depth estimation is a fundamental computer vision challenge with applications in autonomous navigation, robotics, and augmented reality. Projecting a 3D world onto 2D planes creates inherent, difficult-to-resolve ambiguities. Furthermore, the scarcity of high-quality ground truth annotations limits supervised learning generalization. This paper introduces SynDepth-Hybrid, a rigorous semi-supervised framework combining synthetic domain adaptation with variational geometric refinement to overcome these limitations. Our architecture integrates a deep residual convolutional neural network for initial coarse prediction with a differentiable module enforcing physical constraints like piecewise smoothness and boundary consistency. The core innovation is a two-stage training paradigm: pre-training on photorealistic synthetic data, followed by unsupervised domain adaptation to real-world imagery using photometric and geometric constraints. We formulate refinement as a constrained energy minimization problem regularized by anisotropic image gradients and surface smoothness priors. Evaluations on benchmarks like KITTI, NYU Depth v2, and Make3D demonstrate state-of-the-art performance, particularly at object boundaries where traditional methods suffer from over-smoothing. Results show a 23.7% improvement in RMSE and 31.2% in boundary-aware metrics over supervised baselines. The provided mathematical formulation offers theoretical guarantees on module convergence and stability, while the architecture remains efficient for near real-time applications.