Introduction

In the real world, visual motion helps us understand how objects move and interact, which is important for making decisions. Motion cues provide more reliable information than static images, making the task of estimating motion from image sequences known as optical flow estimation essential in computer vision. Optical flow estimation supports a wide range of applications, from autonomous vehicle navigation and robotics to augmented reality and sports analysis. By capturing continuous movement across frames, optical flow enhances real-time decision-making in these applications, enabling systems to track and interpret motion in diverse environments. Optical flow uses color-coded fields to represent the direction and speed of motion, improving our ability to perceive movement. These visualizations are useful not only for machine interpretation but also for human analysis, providing a clear, intuitive view of motion patterns. This process is important for tasks like motion segmentation, tracking, and understanding object structure, where accurate movement detection is essential for separating foreground objects from the background and reconstructing scene dynamics. However, significant challenges remain in accurately estimating motion under difficult outdoor conditions, such as haze, fog, rain, and low light. The aim is to estimate the motion of each pixel between consecutive images and to separate the scene into moving objects (foreground) and the static background. Addressing these challenges has become a focus of recent research, with approaches that include adaptive models capable of adjusting to environmental conditions. Techniques such as non-local total variation and support-weight functions help mitigate noise and enhance boundary clarity, making optical flow estimation more reliable even when visibility is reduced.