With the rapid growth of the construction industry, architectural design has become more diverse and refined. In recent years, an increasing number of buildings featuring unique shapes and intricate curves have emerged, far surpassing those of the past. For such buildings, accurately and efficiently performing the necessary dimensional measurements for calibration, as well as ensuring comprehensive life-cycle management, presents significant challenges. This study presents a method for extracting the medial axis using unbalanced optimal transport theory, which allows for the automatic reverse modeling of engineering structures. This method optimizes the use of point cloud data by inputting, preprocessing, obtaining the initial medial axis point set, extracting the rough medial axis, refining the medial axis, and performing BIM reconstruction. These processes enable the extraction of medial axis features from the target point cloud and the automated BIM modeling based on the extracted medial axis. Test results show that this method successfully finds the central part of a real engineering structure. It is very accurate and strong, leading to a great model reconstruction. The numerical calculation yielded a maximum error of 1.309 mm in the model.