## 1 Introduction  
MDE is a fundamental problem in computer vision, crucial for applications such as autonomous driving, robotics, and augmented reality [1]. The task involves predicting a dense depth map from a single RGB image, an inherently ill-posed problem due to the absence of 3D information in 2D images [2]. Traditionally, supervised learning approaches have leveraged datasets with ground truth depth maps, but acquiring such labeled data, particularly for large-scale dynamic scenes, is both expensive and time-consuming. As a result, self-supervised learning approaches have emerged, utilizing video sequences to bypass the need for a depth ground truth [3]. There has been significant progress, but challenges remain. Depth predictions struggle with scale issues and inaccuracies, especially in scenes with moving objects. A key issue in monocular depth estimation is scale ambiguity. Depth predictions are not absolute and are often only correct up to an unknown scale. This is particularly problematic in dynamic scenes where moving objects cause disruptions in depth predictions [4]. Methods that predict depth based on image reconstruction loss without explicitly modeling object motion often fail to handle these dynamic regions, resulting in significant errors. Many approaches rely on single-stage predictions and are unable to refine depth estimates once an initial guess has been made, leading to poor performance in challenging environments [5]. Recent advances in self-supervised depth estimation have attempted to tackle the challenges of dynamic scenes and scale ambiguity. For instance, the authors of [6] propose a method that decouples the depth estimation of static and dynamic regions, allowing for more accurate predictions in dynamic regions by leveraging pseudo-depth labels. Similarly, the authors of [7] introduce the concept of iterative elastic bins (IEBins), an innovative framework that progressively refines depth predictions by adjusting depth bin widths dynamically based on uncertainty estimates. This strategy significantly improves depth accuracy by focusing on regions where depth uncertainty is higher. However, these methods remain limited in their ability to handle the combined challenges of dynamic regions and scale ambiguity in a fully integrated and iterative framework. Existing approaches either address dynamic regions or refine depth estimates iteratively, but not both. Furthermore, the scale consistency between static and dynamic regions often remains unresolved, leading to depth inconsistencies in scenes with both static backgrounds and moving objects. In this work, we introduce DI-MDE, a novel framework designed to address these challenges. The key idea behind DI-MDE is to combine the strengths of iterative depth refinement and scale alignment for dynamic regions. Our method uses an iterative refinement process with elastic depth bins. It also includes a scale-alignment module to ensure depth consistency between static and dynamic regions. By iteratively refining depth predictions for both static and dynamic regions while aligning their scales, we significantly reduce depth prediction errors in complex scenes. Our proposed framework builds on the following key innovations:  
* We introduce a scale-alignment module that resolves scale ambiguities between dynamic and static regions. This ensures that moving objects, whose depth predictions typically suffer from inconsistencies due to motion, are aligned with the depth scale of the static background. * Inspired by the IEBins framework [7], we propose an iterative refinement process where depth bin widths are adjusted dynamically based on uncertainty estimates. This allows for finer granularity in depth predictions, especially in regions where the depth is uncertain or where large depth discontinuities exist. * Our method leverages self-supervised learning, using monocular video sequences to train the depth estimation network without requiring expensive ground truth depth labels.