## 1 Introduction  
Accurate ground surface reconstruction and soil volume estimation are essential for modern construction site management, underpinning precise planning, efficient resource allocation, and the effective monitoring of excavation activities. These processes are increasingly critical in the context of autonomous excavation in construction sites, where systems depend on sensory data to perceive and interact with their environments. Despite substantial advancements in sensor technology, significant challenges remain in harnessing raw sensor data effectively for high-fidelity surface modeling and precise soil volume estimation in digging areas. Sensors such as depth cameras, commonly employed to capture site data, often produce noisy, incomplete, or inconsistent measurements, limiting their utility in creating accurate surface models and volume calculations. Noise, invalid pixels, and outliers in raw sensor data can significantly distort ground surface representations, introducing inaccuracies in subsequent computations. Traditional surface reconstruction and volume estimation methods often struggle with these data quality issues. Many rely on computationally intensive algorithms unsuitable for real-time applications, particularly in dynamic environments like construction sites. Additionally, these methods frequently lack the robustness to handle the inherent uncertainties in sensory data, leading to unreliable outputs that undermine their suitability for automation and decision-making tasks. A major limitation in existing approaches lies in their inability to effectively bridge the gap between raw sensor data and actionable metrics [1; 2; 3; 4; 5; 6]. Raw data, while providing a snapshot of the environment, often yield suboptimal results when directly applied to algorithms for tasks such as volume and mass estimation. Without robust preprocessing and advanced modeling techniques, this data remains insufficient for generating the precise and reliable information required for autonomous operations and effective site management. This study addresses these challenges by proposing a novel methodology that integrates curve approximation techniques with the marching cubes algorithm to achieve accurate ground surface reconstruction and soil volume estimation. The approach transforms pixelated depth data into smooth, continuous surface representations, effectively mitigating the challenges resulting from imprecise sensor data and unexpected deviations. By approximating raw sensor data using analytical equations, the method ensures accuracy and continuity in surface modeling, making it suitable for the dynamic and complex conditions of construction sites. In addition, the marching cubes algorithm is a cornerstone of the proposed framework, enabling the conversion of reconstructed surfaces into volumetric representations. This facilitates the efficient calculation of critical soil metrics such as volume and mass, supporting excavation monitoring and operational planning. Computational efficiency is a key focus, with the method leveraging parallelization to deliver low-latency performance while maintaining robustness against uncertainties in sensory data. The primary objective of this study is to provide a scalable, accurate, and efficient solution for surface reconstruction and volume estimation tailored to the demands of autonomous excavation and construction site management. By addressing the challenges posed by noisy and inconsistent sensory data, the proposed methodology represents a significant improvement over traditional approaches. Specifically, it not only enhances the accuracy and reliability of extracted metrics but also reduces computational cost, making it practical for deployment in automated systems. Experimental validation demonstrates the effectiveness of the proposed methodology during the excavation process. The results illustrate its capability to transform raw depth data collected by depth cameras into actionable insights.