Fast and accurate three-dimensional (3D) particle reconstruction from X-ray micro-computed tomography (μCT) images is crucial for understanding granular micromechanics and developing digital twins. In this study, we propose a novel method that employs a large vision model (LVM) for efficient and precise 3D particle reconstruction. First, the point-prompted LVM extracts two-dimensional (2D) particles from μCT images along two arbitrary orthogonal axes. Then, these 2D segmentations are optimized through a discrete relabeling scheme, which operates on the principle that segmentations along one axis can inform and improve segmentations along the other axis. Following this optimization process, 2D segmentations are transformed into one 3D segmentation, where each particle is assigned a unique label value. The effectiveness of this method is validated on a reported dataset comprising 2,123 carbonate sand particles. Compared to the benchmark, our method achieves a 10% improvement in accuracy while reducing computational time by 43%. These results demonstrate the superiority of our method in 3D particle reconstruction.