## 3 Methodology
### Dynamic Region Depth Estimation  
Depth estimation in dynamic regions presents a unique set of challenges due to the inherent motion of objects within the scene. Monocular depth estimation frameworks, usually optimized for static scenes, face challenges in dynamic environments. Moving objects like cars, pedestrians, or other entities disrupt the assumptions of rigid scene geometry and photometric consistency between frames. To address this issue, our proposed DI-MDE framework decouples the depth estimation for static and dynamic regions, providing a separate estimation process for each.  
Static regions, where the scene remains unchanged between frames, are handled by a separate static depth estimation network. This network adopts a traditional self-supervised monocular depth estimation approach, leveraging geometric constraints between consecutive frames. The architecture is a U-Net-based encoder-decoder, pre-trained on large-scale datasets to ensure robust feature extraction. The photometric reconstruction and smoothness loss are employed for static regions to optimize the depth predictions. The static depth estimation network is integrated with the overall DI-MDE framework, providing reliable depth predictions for areas unaffected by motion. References to existing works, such as Monodepth2 [13], have been included to contextualize the design choices for this network.  
The DI-MDE framework is designed to operate in a self-supervised manner, meaning it does not rely on expensive ground truth depth labels for training. Instead, the network is trained using monocular video sequences, and supervision is derived from the relationships between consecutive frames in the video. This self-supervised paradigm is highly advantageous because it allows the network to learn from large amounts of unlabeled data, making it scalable and suitable for real-world applications where labeled depth data are scarce. The self-supervised training framework leverages a combination of photometric consistency losses, depth smoothness losses, and scale-alignment losses to optimize the depth predictions across both static and dynamic regions. In this section, we describe the core components of the self-supervised training framework and explain how these components are integrated into the overall DI-MDE architecture. At the heart of the self-supervised depth estimation framework is the photometric consistency loss, which ensures that the predicted depth map and estimated camera pose between consecutive frames are geometrically consistent. The idea is that if we predict the depth for a reference frame \(I_{r}\) and the relative camera motion between this frame and a source frame \(I_{s}\), we can use this information to synthesize the source frame from the reference frame. The difference between the real and synthesized images forms the basis of the photometric consistency loss.  
In this section, we introduce our method for estimating depth in dynamic regions by first identifying and segmenting moving objects and then predicting their depth through a dedicated process. To ensure depth consistency between static and dynamic regions, we further introduce a scale-alignment mechanism.