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3D modelling from range images captured using laser scanning systems finds a wide range of applications in computer vision and industrial robotics. However due to the presence of scanning noise, accumulative registration errors, and improper data fusion, the reconstructed surfaces from multiple registered range images captured from different viewpoints are often distorted with thick patches, false connections and blurred features. Moreover, the existing integration methods are often expensive in the sense of computational time and data storage. These shortcomings will hinder the wide applications of 3D modelling using the latest laser scanning systems. In this paper, the k-means clustering approach from the pattern recognition and machine learning literatures is employed to optimally fuse the overlapping areas between two range images captured from two neighbouring viewpoints and to iteratively minimize the integration error. The final fused point set is then triangulated using an improved Delaunay method, guaranteeing a watertight surface. The new method is theoretically guaranteed to converge. A comparative study based on real images shows that the proposed algorithm is computationally efficient and significantly reduces the integration error, while desirably retaining geometric details of object surface.